Distance (PlnMthd) - 4 Cutting Pln Mthd - 2 Development (Cone) - 2 Cut/Fill - 1 Distance Between Lines (line Me wavaudio\proj2-1.wav wavaudio\proj2-2.wav wavaudio\proj2-3.wav wavaudio\proj3-1.wav wavaudio\proj3-2.wav wavaudio\ptproj-2.wav wavaudio\ptproj-3.wav wavaudio\ptproj-4.wav wavaudio\ptproj-5.wav wavaudio\ptproj-6.wav wavaudio\ptproj-7.wav wavaudio\ptproj-8.wav wavaudio\10bgeo-1.wav wavaudio\10bgeo-2.wav wavaudio\10bgeo-3.wav wavaudio\10bgeo-4.wav wavaudio\10bgeo-5.wav wavaudio\10bgeo-6.wav wavaudio\10bgeo-7.wav wavaudio\10bgeo-9.wav wavaudio\bps-3-2.wav wavaudio\bps-3-3.wav wavaudio\bps-3-4.wav wavaudio\bps-3-5.wav wavaudio\bps-3-6.wav wavaudio\bps-3-7.wav wavaudio\bps-3-8.wav wavaudio\bps-3-9.wav wavaudio\bps-3-10.wav wavaudio\bps-3-11.wav wavaudio\bps-3-12.wav wavaudio\bps-3-13.wav wavaudio\bps-3-14.wav wavaudio\bps-3-15.wav wavaudio\bps-1-2.wav wavaudio\bps-1-3.wav wavaudio\bps-1-4.wav wavaudio\bps-2-2.wav wavaudio\bps-2-3.wav wavaudio\bps-2-4.wav wavaudio\bps-2-5.wav wavaudio\bps-2-6.wav wavaudio\bps-2-7.wav wavaudio\iss-2-2.wav wavaudio\iss-2-3.wav wavaudio\iss-2-4.wav wavaudio\iss-2-5.wav wavaudio\iss-2-6.wav wavaudio\iss-2-7.wav wavaudio\iss-2-8.wav wavaudio\dcy-2-2.wav wavaudio\dcy-1-2.wav wavaudio\dcy-2-3.wav wavaudio\dcy-2-4.wav wavaudio\dcy-2-5.wav wavaudio\dcy-2-6.wav wavaudio\dcy-2-7.wav wavaudio\c&f-1-2.wav wavaudio\c&f-1-3.wav wavaudio\c&f-1-4.wav wavaudio\c&f-2-2.wav wavaudio\c&f-2-3.wav wavaudio\c&f-2-4.wav wavaudio\c&f-2-5.wav c:\paul\dkl3.bmp wavaudio\lvis-1-1.wav wavaudio\lvis-1-2.wav wavaudio\lvis-3-2.wav wavaudio\lvis-3-3.wav wavaudio\lvis-3-4.wav wavaudio\lvis-3-5.wav wavaudio\lvis-3-6.wav wavaudio\lvis-4-2.wav wavaudio\lvis-4-3.wav wavaudio\lvis-4-4.wav wavaudio\lvis-4-5.wav wavaudio\lvis-4-6.wav wavaudio\ptview-2.wav wavaudio\ptview-3.wav wavaudio\ptview-4.wav wavaudio\ptview-5.wav wavaudio\ptview-6.wav wavaudio\ptview-7.wav wavaudio\ptview-8.wav wavaudio\ptview-9.wav wavaudio\ptview10.wav wavaudio\dlm-1-2.wav wavaudio\dlm-1-3.wav wavaudio\dlm-1-4.wav wavaudio\dlm-1-5.wav wavaudio\dlm-1-6.wav wavaudio\dlm-1-7.wav wavaudio\dlm-1-8.wav wavaudio\dlm-1-9.wav wavaudio\dlm-1-10.wav wavaudio\dlm-1-11.wav wavaudio\dlm-2-2.wav wavaudio\dlm-2-3.wav wavaudio\dlm-2-4.wav wavaudio\dlm-2-5.wav wavaudio\dlm-2-6.wav wavaudio\dlm-2-7.wav wavaudio\dlm-2-8.wav wavaudio\dlm-2-9.wav wavaudio\dlm-2-10.wav wavaudio\dlm-2-11.wav wavaudio\dlm-2-12.wav wavaudio\dlm-2-13.wav wavaudio\dlm-2-14.wav wavaudio\dlm-2-15.wav wavaudio\evt-1-2.wav wavaudio\evt-1-3.wav wavaudio\evt-1-4.wav wavaudio\evt-1-5.wav wavaudio\evt-1-6.wav wavaudio\evt-1-7.wav wavaudio\evt-1-8.wav wavaudio\evt-1-9.wav wavaudio\evt-1-10.wav wavaudio\evt-1-11.wav wavaudio\evt-1-12.wav wavaudio\evt-1-13.wav wavaudio\evt-1-14.wav wavaudio\evt-2-2.wav wavaudio\evt-2-3.wav wavaudio\evt-2-4.wav wavaudio\evt-2-5.wav wavaudio\evt-2-6.wav wavaudio\evt-2-7.wav wavaudio\evt-2-8.wav wavaudio\evt-2-9.wav wavaudio\evt-2-10.wav wavaudio\evt-2-11.wav wavaudio\evt-2-12.wav wavaudio\evt-3-2.wav wavaudio\evt-3-3.wav wavaudio\evt-3-4.wav wavaudio\evt-3-5.wav wavaudio\evt-3-6.wav wavaudio\evt-3-7.wav wavaudio\evt-3-8.wav wavaudio\evt-3-9.wav wavaudio\evt-3-10.wav wavaudio\evt-3-11.wav wavaudio\diang-2.wav wavaudio\diang-3.wav wavaudio\diang-4.wav wavaudio\diang-5.wav wavaudio\diang-6.wav wavaudio\diang-7.wav wavaudio\diang-8.wav wavaudio\diang-9.wav wavaudio\diang-10.wav wavaudio\diang-11.wav wavaudio\dpm-1-2.wav wavaudio\dpm-1-3.wav wavaudio\dpm-1-4.wav wavaudio\dpm-1-5.wav wavaudio\dpm-1-6.wav wavaudio\dpm-1-7.wav wavaudio\dpm-1-8.wav wavaudio\dpm-1-9.wav wavaudio\dpm-1-10.wav wavaudio\dpm-1-11.wav wavaudio\dpm-2-2.wav wavaudio\dpm-2-3.wav wavaudio\dpm-2-4.wav wavaudio\dpm-2-5.wav wavaudio\dpm-2-6.wav wavaudio\dpm-2-7.wav wavaudio\dpm-2-8.wav wavaudio\dpm-2-9.wav wavaudio\dpm-2-10.wav wavaudio\dpm-2-11.wav wavaudio\dpm-2-12.wav wavaudio\dpm-2-13.wav wavaudio\dpm-2-14.wav wavaudio\dpm-2-15.wav wavaudio\dpm-2-16.wav wavaudio\dpm-3-2.wav wavaudio\dpm-3-3.wav wavaudio\dpm-3-4.wav wavaudio\dpm-3-5.wav wavaudio\dpm-3-6.wav wavaudio\dpm-3-7.wav wavaudio\dpm-3-8.wav wavaudio\dpm-3-9.wav wavaudio\dpm-3-10.wav wavaudio\dpm-3-11.wav wavaudio\dpm-3-12.wav wavaudio\dpm-3-13.wav wavaudio\dpm-3-14.wav wavaudio\dpm-3-15.wav wavaudio\dpm-3-16.wav wavaudio\dpm-3-17.wav wavaudio\dpm-4-2.wav wavaudio\dpm-4-3.wav wavaudio\dpm-4-4.wav wavaudio\dpm-4-5.wav wavaudio\dpm-4-6.wav wavaudio\dpm-4-7.wav wavaudio\dpm-4-8.wav wavaudio\dpm-4-9.wav wavaudio\dpm-4-10.wav wavaudio\dpm-4-11.wav wavaudio\dpm-4-12.wav wavaudio\dpm-4-13.wav wavaudio\dpm-4-14.wav wavaudio\dpm-4-15.wav wavaudio\dpm-4-16.wav wavaudio\dpm-4-17.wav wavaudio\ilp-1-2.wav wavaudio\ilp-2-2.wav wavaudio\ilp-2-3.wav wavaudio\ilp-2-4.wav wavaudio\ilp-2-5.wav wavaudio\ilp-2-6.wav wavaudio\ilp-2-7.wav wavaudio\ilp-2-8.wav wavaudio\ilp-2-9.wav wavaudio\ilp-2-10.wav wavaudio\ilp-2-11.wav wavaudio\ilp-2-12.wav wavaudio\ilp-2-13.wav wavaudio\cpm-1-2.wav wavaudio\cpm-1-3.wav wavaudio\cpm-1-4.wav wavaudio\cpm-1-5.wav wavaudio\cpm-1-6.wav wavaudio\cpm-1-7.wav wavaudio\cpm-2-2.wav wavaudio\cpm-2-3.wav wavaudio\cpm-2-4.wav wavaudio\cpm-2-5.wav wavaudio\cpm-2-6.wav wavaudio\cpm-2-7.wav wavaudio\ipp-1-2.wav wavaudio\ipp-1-3.wav wavaudio\ipp-1-4.wav wavaudio\ipp-1-5.wav wavaudio\ipp-1-6.wav wavaudio\ipp-1-7.wav wavaudio\ipp-1-8.wav wavaudio\ipp-2-2.wav wavaudio\ipp-2-3.wav wavaudio\ipp-2-4.wav wavaudio\ipp-2-5.wav wavaudio\ipp-2-6.wav wavaudio\ipp-2-7.wav wavaudio\ipp-2-8.wav wavaudio\ipp-2-9.wav wavaudio\ipp-2-10.wav wavaudio\inp-1-2.wav wavaudio\inp-1-3.wav wavaudio\inp-1-4.wav wavaudio\inp-1-5.wav wavaudio\inp-1-6.wav wavaudio\inp-1-7.wav wavaudio\inp-1-8.wav wavaudio\inp-1-9.wav wavaudio\inp-1-10.wav wavaudio\inp-1-11.wav wavaudio\inp-2-2.wav wavaudio\inp-2-3.wav wavaudio\inp-2-4.wav wavaudio\inp-2-5.wav wavaudio\inp-2-6.wav wavaudio\inp-2-7.wav wavaudio\inp-2-8.wav wavaudio\inp-2-9.wav wavaudio\inp-2-10.wav wavaudio\inp-2-11.wav wavaudio\inp-2-12.wav wavaudio\ips-1-2.wav wavaudio\ips-1-3.wav wavaudio\ips-1-4.wav wavaudio\ips-1-5.wav wavaudio\ips-1-6.wav wavaudio\ips-1-7.wav wavaudio\ips-1-8.wav wavaudio\ips-1-9.wav wavaudio\ips-1-10.wav wavaudio\ips-1-11.wav wavaudio\ips-1-12.wav wavaudio\ips-1-13.wav wavaudio\ips-1-14.wav wavaudio\ips-1-15.wav wavaudio\ips-2-2.wav wavaudio\ips-2-3.wav wavaudio\ips-2-4.wav wavaudio\ips-2-5.wav wavaudio\ips-2-6.wav wavaudio\ips-2-7.wav wavaudio\ips-2-8.wav wavaudio\ips-2-9.wav wavaudio\ips-2-10.wav wavaudio\ips-2-11.wav wavaudio\ips-2-12.wav wavaudio\ips-2-13.wav wavaudio\ips-2-14.wav wavaudio\ips-2-15.wav wavaudio\iss-1-2.wav wavaudio\iss-1-3.wav wavaudio\iss-1-4.wav wavaudio\iss-1-5.wav wavaudio\iss-1-6.wav wavaudio\iss-1-7.wav wavaudio\iss-1-8.wav wavaudio\iss-1-9.wav wavaudio\iss-1-10.wav wavaudio\iss-3-2.wav wavaudio\iss-3-3.wav wavaudio\iss-3-4.wav wavaudio\iss-3-5.wav wavaudio\iss-4-2.wav wavaudio\iss-4-3.wav wavaudio\iss-4-4.wav wavaudio\iss-4-5.wav wavaudio\iss-4-6.wav wavaudio\dvp-1-2.wav wavaudio\dvp-1-3.wav wavaudio\dvp-1-4.wav wavaudio\dvp-1-5.wav wavaudio\dvp-1-6.wav wavaudio\dvp-1-7.wav wavaudio\dvp-1-8.wav wavaudio\dvp-1-9.wav wavaudio\dvp-1-10.wav wavaudio\dvp-1-11.wav wavaudio\dvp-1-12.wav wavaudio\dvp-1-13.wav wavaudio\dvp-2-2.wav wavaudio\dvp-2-3.wav wavaudio\dvp-2-4.wav wavaudio\dco-1-2.wav wavaudio\dco-1-3.wav wavaudio\dco-1-4.wav wavaudio\dco-1-5.wav wavaudio\dco-1-6.wav wavaudio\dco-1-7.wav wavaudio\dco-2-2.wav wavaudio\dco-2-3.wav wavaudio\dco-2-4.wav wavaudio\dco-2-5.wav wavaudio\dco-2-6.wav wavaudio\dco-3-2.wav wavaudio\dco-3-3.wav wavaudio\dco-3-4.wav wavaudio\dco-3-5.wav wavaudio\dco-3-6.wav wavaudio\pro-1-2.wav wavaudio\pro-1-3.wav wavaudio\pro-1-4.wav wavaudio\pro-1-5.wav wavaudio\c&f-1-2.wav wavaudio\c&f-1-3.wav wavaudio\c&f-1-4.wav wavaudio\c&f-2-2.wav wavaudio\c&f-2-3.wav wavaudio\c&f-2-4.wav wavaudio\c&f-2-5.wav wavaudio\sha-1-2.wav wavaudio\sha-1-3.wav wavaudio\sha-1-4.wav wavaudio\sha-2-2.wav wavaudio\sha-2-3.wav wavaudio\sha-3-2.wav wavaudio\sha-3-3.wav wavaudio\sha-3-4.wav wavaudio\sha-3-5.wav wavaudio\sha-3-6.wav wavaudio\sha-3-7.wav wavaudio\lvis-2.wav audio\chapter9.wav anim\cutplan2.flc anim\rint.flc anim\vint.flc anim\2planes.flc anim\2ndprinc.flc anim\1stprinc.flc wavaudio\dg2.wav .wavo wavaudio\dg3.wav wavaudio\dg4.wav wavaudio\dg6.wav \ptpk wavaudio\dg7.wav wavaudio\dg8.wav wavaudio\dg9.wav .wavg wavaudio\dg10.wav wavaudio\dg11.wav wavaudio\dg12.wav wavaudio\dg13.wav wavaudio\dg14.wav wavaudio\dg15.wav wavaudio\dg28.wav wavaudio\dg32.wav wavaudio\dg37.wav wavaudio\dg45.wav wavaudio\dg48.wav wavaudio\dg57.wav wavaudio\dg60.wav wavaudio\dg64.wav wavaudio\dg70.wav wavaudio\dg74.wav wavaudio\dg79.wav wavaudio\dg84.wav wavaudio\dg87.wav wavaudio\dg93.wav wavaudio\dg94.wav wavaudio\dg96.wav wavaudio\dg97.wav wavaudio\dg98.wav wavaudio\dg101.wav wavaudio\dg57.wav wavaudio\dg57.wav wavaudio\dg57.wav anim\linp.flc linp.fl anim\dihed.flc anim\pinp.flc anim\2solids.flc anim\cutfill.flc anim\grade.flc syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "There are no steps. Press the arrow Bbelow." ("ptproj-"&( playing fwd)) picture ( 8 - 1) m - 1) allow students click through )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("BPS-1-"&( playing -fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("BPS-3-"&( playing -fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait D"ptView-10" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd)) +1)) -- E+1)) i+1)) -- +1)) yieldApp() audioerror update default p = 10 normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("ptView-"&( playing .fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait D"DistLM-1-11" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update B"Forward" default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("DistLM-1-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update B"Forward" default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"DistLM-2-15" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update B"Forward" default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("DistLM-2-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("EV&TS-3-"&( playing ("EV&TS-3-"&( ("EV&TS-3-"&(fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace ("EV&TS-3-"&( ("EV&TS-3-"&( ("EV&TS-3-"&( ("EV&TS-3-"&(fwd-1)) -- volume cVolume -- control mmplay ("EV&TS-3-"&( ("EV&TS-3-"&( ("EV&TS-3-"&( yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("DiAng-"&( playing -fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("DistPM-1-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update B"Forward" default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("DistPM-2-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update B"Forward" default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("DistPM-4-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"IntL&P-2-13" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntL&P-2-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"CutPlnM-1-7" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("CutPlnM-1-"&( playing 1fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait Y"CutPlnM-2-9" playing picture "2" allow students click through the steps )their -- own pace "&(4)) volume cVolume -- control mmplay "&(4)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("CutPlnM-2-"&( playing 1fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"IntP&P(r)-2-10" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntP&P(r)-2-"&( playing 3fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntP&P(v)-1-"&( playing 3fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntP&P(v)-2-"&( playing 3fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update B"Forward" default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntP&S-1-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntP&S-2-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntS&S-2-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() % - 1) > -1) audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntS&S-4-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"Dvpmt(Pr)-1-13" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Dvpmt(Pr)-1-"&( playing 3fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Dvpmt(Pr)-2-4" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) +1)) -- "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Dvpmt(Pr)-2-"&( playing 3fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Dvpmt(Cyl)-1-"&( playing 4fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Profile-1-"&( playing 1fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Cut&Fill-1-"&( playing 2fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"IntP&S-2-15" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("EV&TS-1-"&( playing ("EV&TS-1-"&( ("EV&TS-1-"&(fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace ("EV&TS-1-"&( ("EV&TS-1-"&( ("EV&TS-1-"&( ("EV&TS-1-"&(fwd-1)) -- volume cVolume -- control mmplay ("EV&TS-1-"&( ("EV&TS-1-"&( ("EV&TS-1-"&( yieldApp() audioerror update default picture "2" ("LinVis-3-"&( : - 1) default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" picture "2" ("LinVis-4-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" picture "2" ("IntS&S-2-"&( Gfwd)) default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" 4wavPlayable syserrornumber = 0 mmIsOpen clip "Profile-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "Dvpmt(Pr)-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntS&S-3-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntP&S-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntP&S-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntP&P(v)-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntP&P(v)-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "DiAng-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "LinVis-4-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "ptproj-2" mmclose audioerror syslockscren = picture "2" showVolume clearVolume mmopen mmstatus clip paused mmstop mmrewind ? wait C"BPS-1-4" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) +1)) -- "&(fwd+1)) -- yieldApp() update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Dvpmt(Cyl)-2-7" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" picture "2" U"l6" U"l7" yieldApp() U"l6" U"l7" U"l6" update B"forward_silent" default normalgraphic = icon "repeat_silent" fwd_slnt" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Dvpmt(Cyl)-1-2" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) +1)) -- "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" J"Page Title" clearVolume 4wavPlayable, nam audioenable "p15-105" syserrornumber = 0 mmplay clip -<> 0 audioerror TO HANDLE THE ANIMATIONS 4thisanim, ref = "2planes" ) <> mmopen stage "animationstage" hold animerror , nam mmstatus % = "playing" < = "paused" mmstop V wait mmclose showVolume B"repeat" audiodisable J"Page Title" clearVolume 4wavPlayable, nam audioenable "p2-105" syserrornumber = 0 wavplayable mmplay clip "p2-105" J<> 0 audioerror TO HANDLE THE ANIMATIONS 4thisanim, ref = "2planes" ) <> mmopen stage "animationstage" hold animerror mmstatus = "playing" = "paused" mmstop mmclose showVolume B"repeat" audiodisable B"Show example" 4wavPlayable audioenable "stage" J"Page Title" 4fwd, nam syserrornumber = 0 "p3-105" mmIsOpen clip "projection2-1" mmopen wavplayable mmplay audioerror TO HANDLE THE ANIMATIONS 4thisanim, ref = "1stprinc" + <> "animationstage" hold animerror queue 0 mmstatus 3-105" "playing" 3-105" "paused" mmstop 3-105" wait mmclose showVolume B"repeat" -- example_silent" tstep_silent" B"reset_silent" clearVolume -- audiodisable -- -- 4x, y, thiswav, vol, audioon, ref / = 0 x = 1 y = 1 seek1 = noanim = h = 1 x = 1 y = 30 x = 30 y = 40 x = 40 y = 50 -- Always - either frame1 a segment mmseek mmshow "Animationstage" syserrornumber = 0 mmstatus clip paused "playing" mmstop mmrewind wait O"10BasGeom-1" volume cVolume --control mmplay audioerror yieldApp() picture "5" "perp" default 4wavPlayable, nam syserrornumber = 0 mmIsOpen clip "10BasGeom-1" mmclose mmstatus 8p6-105" "playing" Rp6-105" "paused" mmstop op6-105" audioerror picture "5" "perp" 4fwd, nam audioenable mmopen \ = "p6-105" wavplayable mmplay showVolume -- B"repeat" B"Geometric1" B"Geometric1_silent" clearVolume -- audiodisable -- -- syserrornumber = 0 mmstatus clip "p7-105" "paused" = "playing" mmstop 1wait A10BasGeom-2" mmrewind picture "2" cVolume mmplay audioerror yieldApp() default syserrornumber = 0 mmstatus clip "p8-105" "paused" "playing" mmstop 0wait @10BasGeom-3" mmrewind picture "2" cVolume mmplay audioerror yieldApp() default 4wavPlayable syserrornumber = 0 mmIsOpen clip "10BasGeom-4" mmclose mmstatus 3p9-105" "paused" Lp9-105" "playing" mmstop kp9-105" wait audioerror picture "2" 4fwd, nam audioenable mmopen W = "p9-105" wavplayable mmplay showVolume -- B"repeat" B"Geometric4" B"Geometric4_silent" clearVolume -- audiodisable -- -- syserrornumber = 0 mmstatus clip "p9-105" "playing" "paused" mmstop 0wait @10BasGeom-4" mmrewind picture "2" cVolume mmplay audioerror yieldApp() default syserrornumber = 0 mmstatus clip "p10-105" "paused" = "playing" mmstop 2wait B10BasGeom-5" mmrewind picture "2" cVolume mmplay audioerror yieldApp() default 4wavPlayable 4fwd, nam audioenable syserrornumber = 0 mmIsOpen clip "10BasGeom-6" mmopen z = "p11-105" wavplayable = mmplay audioerror mmclose mmstatus "paused" = "playing" mmstop wait showVolume -- B"repeat" B"Geometric6" B"Geometric6_silent" clearVolume -- audiodisable -- -- syserrornumber = 0 mmstatus clip "p11-105" "paused" = "playing" mmstop 2wait C10BasGeom-6" mmrewind cVolume mmplay audioerror --animation commands yieldApp() picture ( E"36" default syserrornumber = 0 mmstatus clip "p12-105" "paused" = "playing" mmstop 2wait B10BasGeom-7" mmrewind picture "2" cVolume mmplay audioerror yieldApp() default syserrornumber = 0 mmstatus clip "p14-105" "paused" = "playing" mmstop 2wait B10BasGeom-9" mmrewind picture "2" cVolume mmplay audioerror yieldApp() default .&, " .&, " .&, " pageScrolled .&+ +E interuptBack default dghelp.vwr Table .&+ +E .&, " interuptBack dghelp.vwr default Previous .&+ +E .&, " interuptBack dghelp.vwr default .&+ +E e28revad.exe false interuptBack default "modBack DG Help dghelp.vwr HelpBack interuptBack DG Help e28revad.exe HelpSearch .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> ptproj- }gyieldApp forward ptproj-8 paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> There are no previous steps. Press the forward arrow button below. }gyieldApp forward ptproj- paused audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused BPS-1- Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused default Press the forward arrow button below. audioerror playing FcVolume BPS-3- update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward ptView-10 paused ptView- update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused ptView- Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp Forward paused DistLM-1- Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused Press the forward arrow button below. audioerror playing FcVolume EV&TS-3- default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> DiAng- }gyieldApp forward paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> IntL&P-2-13 }gyieldApp forward paused FcVolume update audioerror playing IntL&P-2- default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward CutPlnM-1- paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> .&, " .&, " CutPlnM-2- }gyieldApp forward paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused Press the forward arrow button below. audioerror IntS&S-4- playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused Dvpmt(Pr)-2- Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused default Press the forward arrow button below. audioerror playing FcVolume Dvpmt(Con)-3- update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> Profile-1- forward paused Press the forward arrow button below. audioerror }gyieldApp playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused Press the forward arrow button below. audioerror Shad-2- playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward Shad-3- paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " .&, " .&, " .&, " }gyieldApp forward IntP&S-2- IntP&S-2-15 paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused Press the forward arrow button below. EV&TS-1- audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " .&, " forward_silent update LinVis-3- default buttonUp repeat_silent fwd_slnt update .&+ +E .&, " .&, " .&, " LinVis-4- forward_silent update default buttonUp repeat_silent fwd_slnt update .&+ +E .&, " .&, " .&, " forward_silent update IntS&S-2- default buttonUp repeat_silent fwd_slnt update false Dvpmt(Pr)-2-2 Dvpmt(Pr)-2-4 audioerror Dvpmt(Pr)-2-3 enterPage Dvpmt(Pr)-2-2 Dvpmt(Pr)-2-4 audioerror Dvpmt(Pr)-2-3 leavePage IntS&S-4-3 false IntS&S-4-2 IntS&S-4-4 audioerror IntS&S-4-5 IntS&S-4-6 enterPage IntS&S-4-2 IntS&S-4-4 IntS&S-4-3 audioerror IntS&S-4-5 IntS&S-4-6 leavePage IntS&S-3-4 false IntS&S-3-5 IntS&S-3-3 audioerror IntS&S-3-2 enterPage IntS&S-3-5 IntS&S-3-3 IntS&S-3-4 audioerror IntS&S-3-2 leavePage IntP&S-2-14 IntP&S-2-9 IntP&S-2-2 IntP&S-2-4 false IntP&S-2-11 IntP&S-2-10 IntP&S-2-15 IntP&S-2-8 IntP&S-2-5 IntP&S-2-7 IntP&S-2-6 IntP&S-2-13 IntP&S-2-3 audioerror IntP&S-2-12 enterPage IntP&S-2-14 IntP&S-2-9 IntP&S-2-2 IntP&S-2-4 IntP&S-2-11 IntP&S-2-10 IntP&S-2-15 IntP&S-2-8 IntP&S-2-5 IntP&S-2-7 IntP&S-2-6 IntP&S-2-13 IntP&S-2-3 audioerror IntP&S-2-12 leavePage IntP&P(v)-2-7 IntP&P(v)-2-6 IntP&P(v)-2-3 false IntP&P(v)-2-12 IntP&P(v)-2-9 IntP&P(v)-2-2 IntP&P(v)-2-4 IntP&P(v)-2-11 audioerror IntP&P(v)-2-10 IntP&P(v)-2-8 IntP&P(v)-2-5 enterPage IntP&P(v)-2-6 IntP&P(v)-2-3 IntP&P(v)-2-12 IntP&P(v)-2-9 IntP&P(v)-2-2 IntP&P(v)-2-4 IntP&P(v)-2-11 audioerror IntP&P(v)-2-10 IntP&P(v)-2-8 IntP&P(v)-2-5 IntP&P(v)-2-7 leavePage IntP&P(v)-1-10 IntP&P(v)-1-8 IntP&P(v)-1-5 false IntP&P(v)-1-7 IntP&P(v)-1-6 IntP&P(v)-1-3 audioerror IntP&P(v)-1-9 IntP&P(v)-1-2 IntP&P(v)-1-4 IntP&P(v)-1-11 enterPage IntP&P(v)-1-10 IntP&P(v)-1-8 IntP&P(v)-1-5 IntP&P(v)-1-7 IntP&P(v)-1-6 IntP&P(v)-1-3 audioerror IntP&P(v)-1-9 IntP&P(v)-1-2 IntP&P(v)-1-4 IntP&P(v)-1-11 leavePage DiAng-8 DiAng-5 DiAng-7 DiAng-6 false DiAng-3 DiAng-9 DiAng-2 audioerror DiAng-4 DiAng-11 DiAng-10 enterPage DiAng-8 DiAng-5 DiAng-7 DiAng-6 DiAng-3 DiAng-9 DiAng-2 audioerror DiAng-4 DiAng-11 DiAng-10 leavePage false ptView-9 ptView-2 ptView-4 ptView-10 ptView-8 ptView-5 audioerror ptView-7 ptView-6 ptView-3 enterPage ptView-9 ptView-2 ptView-4 ptView-10 ptView-8 ptView-5 audioerror ptView-7 ptView-6 ptView-3 leavePage LinVis-2 audioerror leavePage false LinVis-2 audioenable audioerror enterPage showVolume false pause clearVolume repeat wavplayable audioenable showVolume false pause clearVolume repeat wavplayable audiodisable .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp BPS-1-4 forward paused BPS-1- update playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> Dvpmt(Cyl)-2- }gyieldApp Dvpmt(Cyl)-2-7 forward paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> .&, " .&, " .&, " .&, " }gyieldApp forward paused Press the forward arrow button below. IntP&P(r)-1- audioerror playing FcVolume update default buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " .&, " .&, " .&, " }gyieldApp forward IntP&P(r)-1- paused update IntP&P(r)-1-8 audioerror playing FcVolume default buttonUp forward repeat update .&+ +E }gyieldApp 10BasGeom-1 paused audioerror playing FcVolume default buttonUp 10BasGeom-1 p6-105 paused audioerror playing leavePage false audioenable 10BasGeom-1 p6-105 audioerror wavPlayable enterPage showVolume false pause clearVolume repeat Geometric1 Geometric1_silent wavplayable audioenable showVolume false pause clearVolume repeat Geometric1 Geometric1_silent wavplayable audiodisable .&+ +E }gyieldApp p8-105 paused audioerror 10BasGeom-3 playing FcVolume default buttonUp .&+ +E }gyieldApp 10BasGeom-4 paused audioerror playing FcVolume default p9-105 buttonUp .&+ +E p10-105 }gyieldApp paused 10BasGeom-5 audioerror playing FcVolume default buttonUp .&+ +E .&, " .&, " p11-105 }gyieldApp paused 10BasGeom-6 audioerror playing FcVolume default buttonUp .&+ +E }gyieldApp paused default 10BasGeom-7 audioerror playing FcVolume p12-105 buttonUp .&+ +E 10BasGeom-9 }gyieldApp paused audioerror playing FcVolume default p14-105 buttonUp clearVolume audioerror audioenable wavPlayable p28-105 enterPage paused audioerror playing p28-105 leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable program repeat forward fwd_slnt bwd_slnt repeat_silent smpause smpausedis wwwwwwwwwwp DDDDD DDDD@""+ DDD@""+ DD@""+ D@""+ DDDDH DDDDH **""""""**" ********** ********* ******** "" *""""" ****" pageScrolled currentPage focusWindow scrollPosition > 4320 0,4320 ` > 4320 0,4320 -- These scripts accept commands the navigation bar, which a separate opened 8"e28revad.exe" Table 4interuptBack 8"dghelp.vwr" -- default Contents -- allows user Previous (pg-1) -- Allows users (pg+1) HelpBack 4modifiedBack modBack -- To repeated use HelpSearch mmstatus clip paused mmstop mmrewind ? wait "Press the arrow Bbelow." ("IntS&S-3-"&( playing picture (fwd) - 1) = - 1) allow students click through steps )their own pace -1)) -- volume cVolume -- control mmplay fwd-1)) yieldApp() update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind b wait C"ptproj-8" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("LinVis-4-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"LinVis-4-6" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"BPS-2-7" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("BPS-2-"&( playing -fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait D"BPS-3-15" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"EV&TS-1-14" playing `"EV&TS-1-14" t"EV&TS-1-14" picture "2" allow students click through the steps )their -- own pace ("EV&TS-1-"&(2)) volume cVolume -- control mmplay ("EV&TS-1-"&(2)) ("EV&TS-1-"&( ("EV&TS-1-"&( ("EV&TS-1-"&(fwd)) ("EV&TS-1-"&( +1)) -- ("EV&TS-1-"&( O+1)) ("EV&TS-1-"&( y+1)) -- ("EV&TS-1-"&( yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("EV&TS-2-"&( playing ("EV&TS-2-"&( ("EV&TS-2-"&(fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace ("EV&TS-2-"&( ("EV&TS-2-"&( ("EV&TS-2-"&( ("EV&TS-2-"&(fwd-1)) -- volume cVolume -- control mmplay ("EV&TS-2-"&( ("EV&TS-2-"&( ("EV&TS-2-"&( yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("DistPM-3-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"IntL&P-1-2" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) +1)) -- "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntL&P-1-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"IntP&P(v)-1-11" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"IntP&P(v)-2-12" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"IntS&S-2-8" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"IntS&S-3-5" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) +1)) -- "&(fwd+1)) -- yieldApp() audioerror update B"Forward" default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"IntS&S-4-6" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update B"Forward" default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Dvpmt(Cyl)-2-"&( playing 4fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Dvpmt(Con)-1-7" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Dvpmt(Con)-1-"&( playing 4fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Dvpmt(Con)-2-6" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Dvpmt(Con)-2-"&( playing 4fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Dvpmt(Con)-3-6" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Dvpmt(Con)-3-"&( playing 4fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Profile-1-5" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Cut&Fill-1-4" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Cut&Fill-2-5" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Cut&Fill-2-"&( playing 2fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update B"Forward" default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Shad-1-4" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Shad-1-"&( playing .fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"Shad-2-3" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) +1)) -- "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Shad-2-"&( playing .fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait A"Shad-3-7" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("Shad-3-"&( playing .fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind i wait "Press the arrow Bbelow." ("LinVis-3-"&( playing (fwd) picture ( - 1) P - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind i wait C"LinVis-3-6" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) +1)) -- +1)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" picture "2" ("CutPlnM-2-"&( ^- 1) default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" picture "2" ("IntP&P(v)-1-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" picture "2" ("IntP&P(v)-2-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" picture "2" ("IntP&S-1-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" picture "2" ("IntP&S-2-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" picture "2" ("IntS&S-1-"&( - 1) default update B"forward_silent" = 10 normalgraphic = icon "repeat_silent" fwd_slnt" picture "2" ("Dvpmt(Pr)-1-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" 4wavPlayable syserrornumber = 0 mmIsOpen clip "Cut&Fill-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntS&S-4-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntP&P(r)-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntP&P(r)-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "CutPlnM-2-4" mmopen audioerror mmclose picture "1" 4wavPlayable syserrornumber = 0 mmIsOpen clip "CutPlnM-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntL&P-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "DistPM-4-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "EV&TS-3-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "DistLM-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "ptView-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "BPS-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "LinVis-3-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "LinVis-2" mmclose ^<> 0 audioerror "one" "two" audioenable -- doesn't matter /disable; the fn checks mmopen 4wavplayable showVolume -- B"repeat" clearVolume -- audiodisable -- -- syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntP&P(r)-1-"&( playing 3fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay yieldApp() U"l6" U"l7" U"l6" audioerror update default syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait B"IntP&P(r)-1-8" playing picture "2" U"l6" U"l7" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() U"l6" U"l7" U"l6" audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait "Press the arrow Bbelow." ("IntS&S-1-"&( playing 0fwd)) picture ( * - 1) _ - 1) allow students click through steps )their own pace fwd-1)) -- volume cVolume -- control mmplay YieldApp() yieldApp() audioerror update default 4wavPlayable syserrornumber = 0 mmIsOpen clip "10BasGeom-3" mmclose mmstatus 3p8-105" "paused" Lp8-105" "playing" mmstop kp8-105" wait audioerror picture "2" 4fwd, nam audioenable mmopen W = "p8-105" wavplayable mmplay showVolume -- B"repeat" B"Geometric3" B"Geometric3_silent" clearVolume -- audiodisable -- -- 4wavPlayable syserrornumber = 0 mmIsOpen clip "10BasGeom-5" mmclose mmstatus 3p10-105" "paused" = "playing" mmstop 1wait audioerror picture "2" 4fwd, nam audioenable mmopen W = " wavplayable mmplay showVolume -- B"repeat" B"Geometric5" B"Geometric5_silent" clearVolume -- audiodisable -- -- 4wavPlayable syserrornumber = 0 mmIsOpen clip "10BasGeom-7" mmclose mmstatus 3p12-105" "paused" = "playing" mmstop 1wait audioerror picture "2" 4fwd, nam audioenable mmopen W = " wavplayable mmplay showVolume -- B"repeat" B"Geometric7" B"Geometric7_silent" clearVolume -- audiodisable -- -- 4wavPlayable syserrornumber = 0 mmIsOpen clip "10BasGeom-9" mmclose mmstatus 3p14-105" "paused" = "playing" mmstop 1wait audioerror picture "2" 4fwd, nam audioenable mmopen W = " wavplayable mmplay showVolume -- B"repeat" B"Geometric9" B"Geometric9_silent" clearVolume -- audiodisable -- -- J"Page Title" clearVolume 4wavPlayable, nam audioenable "p28-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref mmstatus = "playing" = "paused" mmstop wait showVolume B"repeat" audiodisable J"Page Title" clearVolume 4wavPlayable, nam audioenable "p32-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref mmstatus = "playing" = "paused" mmstop wait showVolume B"repeat" audiodisable .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " }gyieldApp forward BPS-2- BPS-2-7 paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> .&, " }gyieldApp forward BPS-2- paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward paused default update audioerror playing FcVolume BPS-3-15 BPS-3- buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp Forward DistLM-1-11 paused DistLM-1- update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp Forward paused DistLM-2- update DistLM-2-15 audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward DistLM-2- paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp EV&TS-2- forward paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp Forward paused Press the forward arrow button below. audioerror DistPM-1- playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused FcVolume Press the forward arrow button below. audioerror playing IntL&P-2- default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward CutPlnM-1- CutPlnM-1-7 paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " .&, " CutPlnM-2- }gyieldApp forward paused CutPlnM-2-9 playing FcVolume audioerror default update buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " .&, " }gyieldApp forward IntP&P(r)-2-10 IntP&P(r)-2- paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> .&, " .&, " .&, " .&, " }gyieldApp forward IntP&S-2- paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused Dvpmt(Con)-1- Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward Dvpmt(Con)-2- paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> Profile-1- Profile-1-5 forward paused update audioerror playing FcVolume }gyieldApp default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward Cut&Fill-1-4 paused update Cut&Fill-1- audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused Press the forward arrow button below. Cut&Fill-1- audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward Cut&Fill-2- Cut&Fill-2-5 paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp Forward Cut&Fill-2- paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward paused update audioerror Shad-1-4 playing FcVolume default Shad-1- buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused Press the forward arrow button below. audioerror playing FcVolume default update Shad-1- buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> .&, " .&, " }gyieldApp forward paused Press the forward arrow button below. LinVis-3- audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " .&, " }gyieldApp forward paused update LinVis-3- audioerror LinVis-3-6 playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " .&, " CutPlnM-2- forward_silent default update buttonUp repeat_silent fwd_slnt update .&+ +E .&, " .&, " .&, " .&, " IntP&P(v)-1- forward_silent update default buttonUp repeat_silent fwd_slnt update false IntS&S-2-2 IntS&S-2-4 IntS&S-2-8 audioerror IntS&S-2-5 IntS&S-2-7 IntS&S-2-6 IntS&S-2-3 enterPage IntS&S-2-2 IntS&S-2-4 IntS&S-2-8 audioerror IntS&S-2-5 IntS&S-2-7 IntS&S-2-6 IntS&S-2-3 leavePage IntP&S-1-14 false IntP&S-1-12 IntP&S-1-9 IntP&S-1-2 IntP&S-1-4 IntP&S-1-11 IntP&S-1-10 IntP&S-1-15 IntP&S-1-8 IntP&S-1-5 audioerror IntP&S-1-7 IntP&S-1-6 IntP&S-1-13 IntP&S-1-3 enterPage IntP&S-1-14 IntP&S-1-12 IntP&S-1-9 IntP&S-1-2 IntP&S-1-4 IntP&S-1-11 IntP&S-1-10 IntP&S-1-15 IntP&S-1-8 IntP&S-1-5 audioerror IntP&S-1-7 IntP&S-1-6 IntP&S-1-13 IntP&S-1-3 leavePage IntP&P(r)-2-9 IntP&P(r)-2-2 IntP&P(r)-2-4 false IntP&P(r)-2-10 IntP&P(r)-2-8 IntP&P(r)-2-5 IntP&P(r)-2-7 IntP&P(r)-2-6 IntP&P(r)-2-3 audioerror enterPage IntP&P(r)-2-2 IntP&P(r)-2-4 IntP&P(r)-2-10 IntP&P(r)-2-8 IntP&P(r)-2-5 IntP&P(r)-2-7 IntP&P(r)-2-6 IntP&P(r)-2-3 audioerror IntP&P(r)-2-9 leavePage false IntP&P(r)-1-2 IntP&P(r)-1-4 IntP&P(r)-1-8 IntP&P(r)-1-5 audioerror IntP&P(r)-1-7 IntP&P(r)-1-6 IntP&P(r)-1-3 enterPage IntP&P(r)-1-2 IntP&P(r)-1-4 IntP&P(r)-1-8 IntP&P(r)-1-5 audioerror IntP&P(r)-1-7 IntP&P(r)-1-6 IntP&P(r)-1-3 leavePage CutPlnM-2-8 CutPlnM-2-5 false CutPlnM-2-6 CutPlnM-2-9 CutPlnM-2-7 CutPlnM-2-4 audioerror enterPage CutPlnM-2-5 CutPlnM-2-7 CutPlnM-2-6 CutPlnM-2-9 audioerror CutPlnM-2-4 CutPlnM-2-8 leavePage CutPlnM-1-4 false CutPlnM-1-5 CutPlnM-1-7 CutPlnM-1-6 CutPlnM-1-3 audioerror CutPlnM-1-2 enterPage CutPlnM-1-4 CutPlnM-1-5 CutPlnM-1-7 CutPlnM-1-6 CutPlnM-1-3 audioerror CutPlnM-1-2 leavePage false DistLM-1-2 DistLM-1-4 DistLM-1-11 DistLM-1-10 DistLM-1-9 DistLM-1-8 DistLM-1-5 DistLM-1-7 DistLM-1-6 audioerror DistLM-1-3 enterPage DistLM-1-9 DistLM-1-2 DistLM-1-4 DistLM-1-11 DistLM-1-10 DistLM-1-8 DistLM-1-5 DistLM-1-7 DistLM-1-6 audioerror DistLM-1-3 leavePage BPS-2-4 false BPS-2-5 BPS-2-7 BPS-2-6 BPS-2-3 audioerror BPS-2-2 enterPage BPS-2-4 BPS-2-5 BPS-2-7 BPS-2-6 BPS-2-3 audioerror BPS-2-2 leavePage LinVis-4-5 false LinVis-4-6 LinVis-4-3 audioerror LinVis-4-2 LinVis-4-4 enterPage LinVis-4-5 LinVis-4-6 LinVis-4-3 audioerror LinVis-4-2 LinVis-4-4 leavePage .&+ +E .&, " .&, " .&, " .&, " .&, " forward_silent }gyieldApp update default buttonUp repeat_silent fwd_slnt update animationstage clearVolume thisanim audioerror 2planes audioenable animerror wavPlayable p2-105 enterPage thisanim paused audioerror playing animerror p2-105 leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable 10BasGeom-2 p7-105 paused audioerror playing leavePage 10BasGeom-2 false audioenable p7-105 audioerror wavPlayable enterPage showVolume false pause clearVolume repeat Geometric2 Geometric2_silent wavplayable audioenable showVolume false pause clearVolume repeat Geometric2 Geometric2_silent wavplayable audiodisable .&+ +E 10BasGeom-2 }gyieldApp p7-105 paused audioerror playing FcVolume default buttonUp 10BasGeom-4 paused audioerror playing p9-105 leavePage false 10BasGeom-4 audioenable audioerror wavPlayable p9-105 enterPage showVolume false pause clearVolume repeat Geometric4 Geometric4_silent wavplayable audioenable showVolume false pause clearVolume repeat Geometric4 Geometric4_silent wavplayable audiodisable p11-105 false audioenable 10BasGeom-6 audioerror wavPlayable enterPage p11-105 paused 10BasGeom-6 audioerror playing leavePage Geometric6 Geometric6_silent showVolume false pause clearVolume repeat wavplayable audioenable Geometric6 Geometric6_silent showVolume false pause clearVolume repeat wavplayable audiodisable paused 10BasGeom-7 audioerror playing p12-105 leavePage false audioenable 10BasGeom-7 audioerror p12-105 wavPlayable enterPage showVolume false Geometric7_silent pause clearVolume repeat wavplayable Geometric7 audioenable showVolume false Geometric7_silent pause clearVolume repeat wavplayable Geometric7 audiodisable clearVolume cutplane p60-105 thisanim audioerror audioenable animerror wavPlayable enterPage thisanim p60-105 paused audioerror playing animerror example leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> .&, " .&, " LinVis-4- }gyieldApp forward paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " .&, " LinVis-4- }gyieldApp LinVis-4-6 forward paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> EV&TS-1-14 }gyieldApp forward paused update EV&TS-1- audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp EV&TS-2- forward paused update audioerror playing FcVolume EV&TS-2-12 default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward paused update EV&TS-3-11 playing FcVolume EV&TS-3- default audioerror buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> DiAng- }gyieldApp forward paused update audioerror playing FcVolume DiAng-11 default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> DistPM-1-11 }gyieldApp forward paused update audioerror DistPM-1- playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> DistPM-2-16 }gyieldApp forward paused DistPM-2- update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> DistPM-3- }gyieldApp forward paused update audioerror playing FcVolume DistPM-3-2 default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> DistPM-4-17 }gyieldApp forward DistPM-4- paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> IntL&P-1- }gyieldApp forward paused update audioerror IntL&P-1-2 playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> IntL&P-1- }gyieldApp forward paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " .&, " .&, " }gyieldApp forward paused FcVolume update audioerror playing IntS&S-1-10 default IntS&S-1- buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " .&, " }gyieldApp forward paused update IntS&S-2-8 audioerror IntS&S-2- playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward Shad-3- paused Shad-3-7 update audioerror playing FcVolume default buttonUp forward repeat update Shad-3-2 Shad-3-4 false Shad-3-5 Shad-3-7 Shad-3-6 Shad-3-3 audioerror enterPage Shad-3-2 Shad-3-4 Shad-3-5 Shad-3-7 Shad-3-6 Shad-3-3 audioerror leavePage Cut&Fill-2-2 Cut&Fill-2-4 false Cut&Fill-2-5 Cut&Fill-2-3 audioerror enterPage Cut&Fill-2-2 Cut&Fill-2-4 Cut&Fill-2-5 Cut&Fill-2-3 audioerror leavePage Dvpmt(Con)-3-6 Dvpmt(Con)-3-3 false Dvpmt(Con)-3-2 Dvpmt(Con)-3-4 audioerror Dvpmt(Con)-3-5 enterPage Dvpmt(Con)-3-6 Dvpmt(Con)-3-3 Dvpmt(Con)-3-2 Dvpmt(Con)-3-4 audioerror Dvpmt(Con)-3-5 leavePage Dvpmt(Con)-2-4 false Dvpmt(Con)-2-5 Dvpmt(Con)-2-6 Dvpmt(Con)-2-3 audioerror Dvpmt(Con)-2-2 enterPage Dvpmt(Con)-2-4 Dvpmt(Con)-2-5 Dvpmt(Con)-2-6 Dvpmt(Con)-2-3 audioerror Dvpmt(Con)-2-2 leavePage Dvpmt(Con)-1-2 false Dvpmt(Con)-1-4 Dvpmt(Con)-1-5 Dvpmt(Con)-1-7 Dvpmt(Con)-1-6 audioerror Dvpmt(Con)-1-3 enterPage Dvpmt(Con)-1-2 Dvpmt(Con)-1-4 Dvpmt(Con)-1-5 Dvpmt(Con)-1-7 Dvpmt(Con)-1-6 audioerror Dvpmt(Con)-1-3 leavePage Dvpmt(Cyl)-2-5 false Dvpmt(Cyl)-2-7 Dvpmt(Cyl)-2-6 Dvpmt(Cyl)-2-3 audioerror Dvpmt(Cyl)-2-2 Dvpmt(Cyl)-2-4 enterPage Dvpmt(Cyl)-2-5 Dvpmt(Cyl)-2-7 Dvpmt(Cyl)-2-6 Dvpmt(Cyl)-2-3 audioerror Dvpmt(Cyl)-2-2 Dvpmt(Cyl)-2-4 leavePage DistPM-4-15 DistPM-4-17 DistPM-4-16 false DistPM-4-13 DistPM-4-9 DistPM-4-2 DistPM-4-4 DistPM-4-8 DistPM-4-12 DistPM-4-5 DistPM-4-14 audioerror DistPM-4-7 DistPM-4-6 DistPM-4-11 DistPM-4-3 DistPM-4-10 enterPage DistPM-4-15 DistPM-4-17 DistPM-4-16 DistPM-4-13 DistPM-4-9 DistPM-4-2 DistPM-4-4 DistPM-4-8 DistPM-4-12 DistPM-4-5 DistPM-4-14 audioerror DistPM-4-7 DistPM-4-6 DistPM-4-11 DistPM-4-3 DistPM-4-10 leavePage DistPM-2-16 DistPM-2-13 false DistPM-2-9 DistPM-2-2 DistPM-2-4 DistPM-2-8 DistPM-2-12 DistPM-2-5 DistPM-2-14 audioerror DistPM-2-7 DistPM-2-6 DistPM-2-11 DistPM-2-3 DistPM-2-10 DistPM-2-15 enterPage DistPM-2-16 DistPM-2-13 DistPM-2-9 DistPM-2-2 DistPM-2-4 DistPM-2-8 DistPM-2-12 DistPM-2-5 DistPM-2-14 audioerror DistPM-2-7 DistPM-2-6 DistPM-2-11 DistPM-2-3 DistPM-2-10 DistPM-2-15 leavePage EV&TS-3-7 EV&TS-3-6 EV&TS-3-3 false EV&TS-3-9 EV&TS-3-2 EV&TS-3-4 EV&TS-3-11 audioerror EV&TS-3-10 EV&TS-3-8 EV&TS-3-5 enterPage EV&TS-3-6 EV&TS-3-3 EV&TS-3-11 EV&TS-3-9 EV&TS-3-2 EV&TS-3-4 EV&TS-3-7 audioerror EV&TS-3-10 EV&TS-3-8 EV&TS-3-5 leavePage EV&TS-2-4 EV&TS-2-11 EV&TS-2-10 false EV&TS-2-8 EV&TS-2-5 EV&TS-2-7 EV&TS-2-6 EV&TS-2-3 audioerror EV&TS-2-12 EV&TS-2-9 EV&TS-2-2 enterPage EV&TS-2-4 EV&TS-2-11 EV&TS-2-10 EV&TS-2-8 EV&TS-2-5 EV&TS-2-7 EV&TS-2-6 EV&TS-2-3 audioerror EV&TS-2-12 EV&TS-2-9 EV&TS-2-2 leavePage EV&TS-1-12 EV&TS-1-9 EV&TS-1-2 false EV&TS-1-4 EV&TS-1-11 EV&TS-1-10 EV&TS-1-14 EV&TS-1-8 EV&TS-1-5 EV&TS-1-7 EV&TS-1-6 EV&TS-1-13 audioerror EV&TS-1-3 enterPage EV&TS-1-12 EV&TS-1-9 EV&TS-1-2 EV&TS-1-4 EV&TS-1-11 EV&TS-1-10 EV&TS-1-14 EV&TS-1-8 EV&TS-1-5 EV&TS-1-7 EV&TS-1-6 EV&TS-1-13 audioerror EV&TS-1-3 leavePage DistLM-2-4 DistLM-2-11 false DistLM-2-10 DistLM-2-8 DistLM-2-5 DistLM-2-14 DistLM-2-7 DistLM-2-6 DistLM-2-3 DistLM-2-15 audioerror DistLM-2-12 DistLM-2-13 DistLM-2-9 DistLM-2-2 enterPage DistLM-2-4 DistLM-2-11 DistLM-2-10 DistLM-2-8 DistLM-2-5 DistLM-2-14 DistLM-2-7 DistLM-2-6 DistLM-2-3 DistLM-2-15 audioerror DistLM-2-12 DistLM-2-13 DistLM-2-9 DistLM-2-2 leavePage BPS-3-14 BPS-3-7 BPS-3-6 BPS-3-13 BPS-3-3 false BPS-3-12 BPS-3-9 BPS-3-2 BPS-3-4 audioerror BPS-3-11 BPS-3-10 BPS-3-15 BPS-3-8 BPS-3-5 enterPage BPS-3-7 BPS-3-6 BPS-3-13 BPS-3-3 BPS-3-12 BPS-3-14 BPS-3-9 BPS-3-2 BPS-3-4 audioerror BPS-3-11 BPS-3-10 BPS-3-15 BPS-3-8 BPS-3-5 leavePage projection2-1 false audioenable Show example projection2-3 p3-105 stage audioerror thisanim 1stprinc projection2-2 queue animerror wavPlayable enterPage projection2-1 projection2-3 paused thisanim p3-105 audioerror projection2-2 playing animerror leavePage next step_silent showVolume false last step_silent reset_silent pause clearVolume repeat show example show example_silent wavPlayable audioenable next step_silent showVolume false last step_silent reset_silent pause clearVolume repeat show example show example_silent wavPlayable audiodisable animationstage seek1 thisanim noanim animerror Animationstage queue p4-105 false animerror audioenable projection3-2 projection3-1 Stage audioerror thisanim queue 2ndprinc wavPlayable enterPage p4-105 FALSE projection3-2 paused thisanim p3-105 projection3-1 audioerror PageId6 playing animerror leavePage next step_silent showVolume false reset_silent pause clearVolume Show example repeat show example_silent wavPlayable audioenable next step_silent showVolume false reset_silent pause clearVolume Show example repeat show example_silent wavPlayable audiodisable animationstage seek1 thisanim noanim animerror Animationstage queue p48-105 clearVolume audioerror audioenable wavPlayable enterPage p48-105 paused audioerror playing leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable p64-105 clearVolume thisanim audioerror audioenable animerror wavPlayable enterPage p64-105 thisanim paused audioerror playing animerror example leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable clearVolume p70-105 thisanim audioerror audioenable animerror wavPlayable enterPage thisanim p70-105 paused audioerror playing animerror example leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable animationstage clearVolume p57-105 thisanim audioerror queue audioenable animerror wavPlayable enterPage n;dequeue thisanim p57-105 Show example audioerror playing animerror update paused leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable p57b-105 p57c-105 p57-105 audioerror FcVolume p57a-105 queue paused audioerror playing FcVolume dequeue show example queue update reset p45-105 dihed clearVolume thisanim audioerror audioenable animerror wavPlayable enterPage p45-105 thisanim paused audioerror playing animerror example leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable p74-105 clearVolume thisanim audioerror audioenable animerror wavPlayable enterPage p74-105 thisanim paused audioerror playing animerror example leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable p79-105 2solids clearVolume thisanim audioerror audioenable animerror wavPlayable enterPage p79-105 thisanim paused audioerror playing animerror example leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable = vol U <> 0 "step3txt" "highlight3" play3on play4off Cut-and-Fills Descriptive Geometry Problems -- Contours Cut-and-Fills When performing landscape work, it is important to know how the land will look after the work is done. This usually means that the areas that have been dug out and the areas that have been filled in need to be shown. A cut and fill drawing shows where the tops of the cuts and the toes of the fills exist, with the cut portions and the filled portions cross-hatched to emphasize those areas. These areas are then assumed to be planar with their respective cut or fill ratios. Cut or fill ratios are the vertical:horizontal (i.e., vertical to horizontal) displacements for land that has been cut out or filled in to create new surfaces not at the original land height. 1:1 Cut 1:2 Fill[ pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Cut-and-Fills pointProjection EV & TS of Plane - 1 Development (Cone) - 3 Intersections of Planes and Sol $!&!&! Cut-and-Fill Descriptive Geometry Problems -- Contours Cut-and-Fills, cont'd To create a level road across variable height land, first consider the profile view of the land. Any land above the road (120 m) will need to be cut, and any land below needs to be filled. Filling the land below the road (elevation 115 m) creates new elevation contour lines. If the fill ratio was 1:2, these new lines would appear as parallel to the road, but 10 m away from it. The reason is that for every 5 m drop in elevation due to fill, the toe of the fill moves out by 10 m. The filling stops when the elevation of the land matches the fill elevation below the land. The same procedure is then used for each successive 5 m fill under the road.oad...................................................... Land+ Road 120 mi 2 $ / 115 m 110 m 115 m 110 m 110 m Road 120 m 115 m Front View Top View= 10 mU pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat animationstage thisanim animerror example buttonclick buttonclick 4thisanim, ref "example" syserrornumber = 0 mmplay clip stage "animationstage" hold Q<> 0 animerror Animation example thisanim example buttonclick buttonclick 4thisanim mmstatus clip "playing" mmstop "example" animationstage animationstage thisanim animerror buttonclick buttonclick 4thisanim, ref syserrornumber = 0 ) <> mmplay clip stage "animationstage" hold a<> 0 animerror Repeat Animation Click on the background to return to Real Intersections. Cut-and-Fill Descriptive Geometry Problems -- Contours Cut-and-Fills, cont'd To create a road at a grade, say a 10% grade, we need to know the length of the run on the road. For a 10% grade for every 50 m of run, the road rises 5 m, and the toe of the fill line extends outward an additional 10 m. Thus the constant elevation contours appear as lines which extend from the road at an angle of arctan(outward extension/run), or in this case, arctan(10/50) for the fill. We are using the same cut and fill ratios as for a level road..................................... L : I Road 120 m] 120 m 115 m 130 m 125 m 125 m Roadc 130 m Front View Top Viewg 110 m 130 m 125 m pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat animationstage thisanim animerror example buttonclick buttonclick 4thisanim, ref "example" syserrornumber = 0 mmplay clip stage "animationstage" hold Q<> 0 animerror Animation example thisanim example buttonclick buttonclick 4thisanim mmstatus clip "playing" mmstop "example" animationstage animationstage thisanim animerror buttonclick buttonclick 4thisanim, ref syserrornumber = 0 ) <> mmplay clip stage "animationstage" hold a<> 0 animerror Repeat Animation Click on the background to return to Real Intersections. Cut & Fill - 1 false Cut&Fill-1-2 Cut&Fill-1-4 audioerror Cut&Fill-1-3 enterPage Cut&Fill-1-2 audioerror leavePage 4wavPlayable syserrornumber = 0 mmIsOpen clip "Cut&Fill-1-2" mmopen audioerror mmclose picture "2" Descriptive Geometry Problems -- Contours Cut-and-Fills Example 1. Show the cut-and-fill for a level road, going from A to B, at an elevation of 120 m on the land profile shown below.rom A to B.......from A to B........................to B............ backward forward To see the step-by-step solution, click the forward arrow below................. First, the road is drawn from A to B. Because the level of the road is 120 m, the cuts and fills begin there. The ratio of the cut is 1:1, so the cut lines are drawn 5 m out from the road for every 5 m increase in elevation. The ratio of the fill is 1:2, so the fill lines are drawn 10 m out for every 5 m decrease in elevation. Then intersections of the cut and fill lines and the elevation lines are found for each elevation. Connecting these points gives the outlines of the cuts and fills. Note that the connections were splined to give a smooth transition between elevations. Finally, the cuts and fills are cross-hatched. The fill area is much larger than the cut area because the fill ratio was lower than the cut ratio. Click the forward arrow to see this example again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. Cut&Fill-1- default update buttonUp "Press the arrow Bbelow." picture ( ("Cut&Fill-1-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent update Cut&Fill-1- default buttonUp repeat_silent fwd_slnt update picture "2" ("Cut&Fill-1-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" Cut & Fill - 2 Descriptive Geometry Problems -- Contours Cut-and-Fills Example 2. Show the cut-and-fill for a road which has a 10% grade from left to right, and an elevation of 120 m at the location indicated.cated..................................... ENTPOSITIONN SETMETAFILEBITS backward forward To see the step-by-step solution, click the forward arrow below................. The first step is to mark the point at which the road is level with the ground (120 m) and points 50 m to the left and right. We chose 50 m because a 10% grade will give a 5 m offset for the cut and 10 m offset for the fill at that distance. The constant elevation lines appear as lines which extend from the road at an angle of arctan(5/50) for the cut and arctan(10/50) for the fill. The intersections of the constant elevation contours are found to give the outlines of the cut and fill. This is only done for one side of the road in this example. Finally, the cut and fill are cross-hatched. The solution (for one side of the road) is now complete. To see the example again, click the forward arrow below.M pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Cut&Fill-2- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("Cut&Fill-2-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent Cut&Fill-2- update default buttonUp repeat_silent fwd_slnt update picture "2" ("Cut&Fill-2-"&( Ifwd)) default update B"forward_silent" H = 5 normalgraphic = icon "repeat_silent" fwd_slnt" Shadows Descriptive Geometry Problems -- Shadows Shadows Architects, and engineers who work with solar heating and cooling and HVAC (Heating, Ventilation, and Air Conditioning) worry a lot about shadows. Builders are concerned with the shadows cast upon their structure by other structures, at different hours of the day and different times of the year, since this can greatly affect the comfort within their structure and its appearance. Also, builders need to be concerned with how shadows from their structure affect the function and appearance of other structures. Finding shadows is usually a direct application of the problem of the intersection of a line and a plane. Solutions for four different cases are outlined below: 1. The shadow cast by a single point from a light source travels a straight line from the source, through the point, until it strikes the surface. 2. For a planar object, the procedure is extended to finding the striking points of several points, then connecting the intersection points to form the total shadow of the object. 3. If the object is solid, the simplest approach is to solve for the front plane shadow, then add the back plane shadow, then connect the corresponding edges of the solid to account for its depth. 4. For a curved object, a series of points may be taken along the curved surface. pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Shadows LinVis - 3 Int (Pln & Pln) Virt - 1 Cut/Fill - 2 Cut & Fill - 1 Shadow - 1 false Shad-1-3 Shad-1-2 audioerror Shad-1-4 enterPage Shad-1-3 Shad-1-2 audioerror Shad-1-4 leavePage 4wavPlayable syserrornumber = 0 mmIsOpen clip "Shad-1-2" mmopen audioerror mmclose picture "2" Descriptive Geometry Problems -- Shadows Shadows Example 1. Find the shadow formed by the point from the light source shown. source shown. backward forward To see the step-by-step solution, click the forward arrow below................. A ray from the light source travels through the point to the ground. Here, the intersection between the ray and the ground give the shadow of the point. A projection line is created that travels from the shadow in the frontal view into the horizontal view. The shadow is found in the horizontal view as the intersection of the projection line and the ray from the light source passing through the point. The solution is now complete. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. default update Shad-1- buttonUp "Press the arrow Bbelow." picture ( ("Shad-1-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent update default Shad-1- buttonUp repeat_silent fwd_slnt update picture "2" ("Shad-1-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" Shadow - 2 Shad-2-3 false Shad-2-2 audioerror enterPage Shad-2-3 Shad-2-2 audioerror leavePage 4wavPlayable syserrornumber = 0 mmIsOpen clip "Shad-2-2" mmopen z<> 0 audioerror mmclose picture "2" Descriptive Geometry Problems -- Shadows Shadows Example 2. Find the shadow cast by the rectangular plane from the sun. colors cgmimw picture "1 show f backward forward To see the step-by-step solution, click the forward arrow below................. Create lines parallel to the ray in the frontal view and project the shadow points into the horizontal view. Similarly, create lines parallel to the ray in the horizontal view. The intersections of these rays with the corresponding projections from the frontal view gives the vertices of the shadow of the triangle. Connecting these points gives the shadow of the triangle in the horizontal view. The final solution of a shadow problem should always be cross-hatched. The solution is now complete. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. Shad-2- default update buttonUp "Press the arrow Bbelow." picture ( ("Shad-2-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent update Shad-2- default buttonUp repeat_silent fwd_slnt update picture "2" ("Shad-2-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" Shadow - 3 Descriptive Geometry Problems -- Shadows Shadows Example 3. Find the shadow cast upon the ground by Etcheverry Hall. Etcheverry Hall. SETMETA FILEBITSBE TRBLT REALIZ SERBITMAP OFFSETVI OWORGEX STRETCHBLT# GETDEVI C,] v+f&v+ GETGLYPHOUTLINE5 CREATEPi ATEPENINDI RECT> WINDOWORGE GETBIT MAPDIMENSI YMETAFILE{ backward forward row below. The first step is to create projection lines parallel to the rays and use the intersection points to (separately) find the shadows of the front and back planes. The projection points are connected to find the shadow of the first plane, which gives the shadow of the front of the building. The second plane is parallel to the first, but gives the shadow of the back of the buliding. The upper and lower planes are connected.3 The portion of the shadow on the ground is cross hatched. The shadow also falls on a portion of the building itself, so that part must also be cross-hatched. The solution is now complete. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Shad-3- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("Shad-3-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent Shad-3- update default buttonUp repeat_silent fwd_slnt update picture "2" ("Shad-3-"&( default update B"forward_silent" { = 7 normalgraphic = icon "repeat_silent" fwd_slnt" To see the step-by-step solution, click the forward arrow below................. Etcheverry clearVolume enterPage audioenable audiodisable clearVolume audioenable audiodisable The End You have reached the conclusion of Graphics Interactive. Please direct comments/suggestions to: Prof. Dennis K. Lieu 5128 Etcheverry Hall University of California at Berkeley Berkeley, CA 94720 dlieu@euler.berkeley.edu BPS - 2 EV & TS of Plane - 2 Int (Pln & Pln) Real - 1 The edge view and true shape o The Edge View and True Shape of BPS - 3 EV & TS of Plane - 3 Dihedral Ang - 1 Distance (PlnMthd) - 1 Int (Sld & Sld) - 2 Shadow - 2 Distance (PlnMthd) - 3 Int (Pln & Sld) - 1 Development (Prsm) - 2 AX4K9>F?+DZ Int (Sld & Sld) - 1 Descriptive Geometry Problems -- Intersections Intersection of Two Solids Example 1. Find the intersection of the triangular prism and the rectangular prism DEFG. PostScript Courier ourie backward forward To see the step-by-step solution, click the forward arrow below................. First, the intersection of the prism between lines A and B is found. Lines from line DG in view H are projected into view F.. The intersection points in view F are connected. The visibility is determined, and the construction lines are removed. Next, the intersection between lines B and C are found. The virtual intersection point of DG with line C is found.c Using the virtual intersection point, the intersection is bounded by the edge of the rectangular prism.9 The visibility is determined and the construction lines are removed. Now the intersection between lines A and C is determined. The virtual intersections of these lines are found in view F. These construction lines bound the intersection within the area of the rectangular prism. This part of the intersection is behind the rectangular prism, so the lines are dashed. Note that the portion of the rectangular prism that is visible is shown, but the parts within the intersection are not shown. The solution is now complete. Click the forward arrow below to see the solution again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " .&, " .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. default IntS&S-1- update buttonUp "Press the arrow Bbelow." picture "5" ("IntS&S-1-"&(fwd-1)) keep y" lock-out working "repeat" force nam take values that are valid -- clip references default update B"forward_silent" forward_silent Int (Sld & Sld) - 2 Descriptive Geometry Problems -- Intersections Intersection of Two Solids Example 2. Find the intersection of the cylinder and the rectangular prism DEFG........................................ PostScript Times &lines Defaul t &Colorq backward forward To see the step-by-step solution, click the forward arrow below................. First we must draw the end view of the cylinder. Because this is a circular object and we cannot simply connect the ends of lines to find the intersection, we must find a way of representing the circle with lines. In order to imagine the circular end of the cylinder as a series of straight lines, points are created around the circle. Imagine that the short lines between these points are straight. Be careful that you draw the points in the correct positions in adjacent views. Project each point into views H and F from the end views of the cylinder. The point of intersection will be where the projection line from view H to view F meets with the projection line from the end view next to view F. This is done with each point (1 through 7) on the cylinder. For now, we only consider these points because they are in front in view F. These points are connected to show the intersection, and the construction lines are removed. The points are originally connected with straight lines, which are then splined to give a curved appearance. Notice that the larger number of points you use, the more accurate the solution.M Now projections from the back side of the cylinder are done. These points will be hidden in view F. The hidden points are connected, then splined to give a smooth curve. The solution is now complete. In order to see this solution again, click the forward arrow below. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. IntS&S-2- default update buttonUp "Press the arrow Bbelow." picture "5" ("IntS&S-2-"&( keep y" lock-out working "repeat" force nam take values that are valid -- clip references default update B"forward_silent" forward_silent Int (Sld & Sld) - 3 Descriptive Geometry Problems -- Intersections Intersection of Two Solids Example 3. Find the intersection of the two cylinders shown below..................................... L%=![1=! [1=![1 L%=!L%n$ L%"-L% #L%n$~% 'S,[&)-~%?-L%"- backward forward The first step is to draw the end view of the angled cylinder for views H and F. Create points around the end of the cylinder. We will only solve for the visible points, that is, points 1 through 7. Be careful that the points are oriented and labelled correctly in the end views.5 The projection lines are drawn from view H and view F. The intersections of these projection lines show the intersection points of the angled cylinder with the upright cylinder.] The intersection points are connected and shown solid (since we only solved for the visible part of the intersection). The solution is now complete. Click the forward arrow below to see the solution again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> IntS&S-3- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("IntS&S-3-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent IntS&S-3- update default buttonUp repeat_silent fwd_slnt update picture "2" ("IntS&S-3-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" To see the step-by-step solution, click the forward arrow below.ard arrow below. Int (Sld & Sld) - 4 Descriptive Geometry Problems -- Intersections Intersection of Two Solids Example 4. Find the intersection of the cone and the cylinder shown below...... cylinder shown below. l2H/(" J*M-J* ("H/J* z-[.X%9& pictur e "2" the edge of the rectangular prK backward forward To see the step-by-step solution, click the forward arrow below.ard arrow below. First draw view 1 to get the cylinder in end view. Create evenly spaced points 1 through 5 in view H, then project them into views F and 1. We are only using these points because we will only find the visible part of the intersection. Rays are drawn from the tip of the cone to each of the points we just created. The intersection of the rays on the surface of the cone and the end view of the cylinder in view 1 give the intersection points. The intersection points are then projected into view F. The intersection points are connected to find the intersection line. The solution is now complete. .lick the forward arrow below to see it again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. IntS&S-4- default update buttonUp "Press the arrow Bbelow." picture ( ("IntS&S-4-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent update IntS&S-4- default buttonUp repeat_silent fwd_slnt update picture "2" ("IntS&S-4-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" Development of Prismatic Surface Descriptive Geometry Problems -- Developments Development of Prismatic Surfaces A development is the unfolding of a three dimensional object to create a single flat surface. It is a "map" of the surface of the object. Folded correctly, the flat surface will reform the original 3-D object. Developments represent a departure from the strict discipline of descriptive geometry. In a development, all lines are shown in true length, and all planes in true shape, in a single view. Note, however, that the development is NOT unique. Many other possibilities exist. Limitations: Only surfaces that can be generated by straight lines can be developed, i.e. prismatic solids, cylinders, and cones. Warped surfaces, such as spheres, cannot be developed. Process: Obtain true lengths and true shapes, and put them in a single view for assembly. Take advantage of views which contain them already. Use your aptitude with descriptive geometry......... pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Development (Prsm) - 1 !@"^#h$f%2& Descriptive Geometry Problems -- Developments Development of Prismatic Surfaces Example 1. Develope the surface of the triangular prism shown below. below.... DATAICON COMMI t!'"Q! !t!C!t!'" btuser.i sServe rDirectoryS +!" 9) 31\BKTOOLS\DATA\BT )5$A)n$ ckerTools Disk Info )5$A)n$ C:\WIN backward forward To see the step-by-step solution, click the forward arrow below................. First, the distances bordering the triangular prism are labelled 1, 2, and 3. Also note that the vertical lines lengthwise down the prism in view F are in true length because they are in point view in view H.)))) The development is begun by drawing line BC in true length. We will create the development view next to view F because it is a convenient place to project the true length lines.9 Next, line CR is drawn in the development view. From view H, we know that the distance between the parallel lines BQ and CR is the same as distance 2 in view H. Lines BC and QR are connected to somplete this face of the prism. We will now use this face as the center of the development and draw the other faces around it. o &%[ The next face to be developed is ABPQ. Line AP is drawn in true length and offset from line BQ by a distance equal to line 1 in view H. AB and PQ are connected and this face is completed.=" Next, face ACPR is developed. Line AP is drawn again, but this time to the right of the face BCPQ and at a distance equal to line 3 in view H.H. Lines AC and PR are drawn in. Now all the side faces of the prism have been developed. Only the ends of the prism remain. Since the triangular end ABC of the prism has simply the lengths AB, BC, and CA, point A can be located by swinging arcs from points B and C.c% Lines AB and AC are drawn in, and the construction arcs are removed. The same is done for end PQR. Arcs are swung from points Q and R to locate point P in the development. Lines PQ and PR are drawn in. The solution is now complete. In order to see it again, click the forward arrow below. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, " .&, " .&, #> update forward_silent Press the forward arrow button below. Dvpmt(Pr)-1- default buttonUp "Press the arrow Bbelow." picture ( ("Dvpmt(Pr)-1-"&( a"10" ~"12" keep y" lock-out working "repeat" force nam take values that are valid -- clip references default update B"forward_silent" forward_silent Development (Prsm) - 2 Descriptive Geometry Problems -- Developments Development of Prismatic Surfaces Example 2. Develop the surface of the four sided symmetrical hopper shown below................................... P"E P"y 0" P"K! .e)O& .e)O& * 3f*S3 %d$!%/$!%)# %9(i%m( %3'i%3' ")+d#)+ #/,d#c, backward forward To see the step-by-step solution, click the forward arrow below................. The first step is to get one side of the hopper in true shape. Using simple descriptive geometry, we draw view 1 parallel to line BD in view F, and we get the lengths of the projection lines from view H. The side of the hopper BDSR is in true shape in view 1. It is in true shape because view 1 was drawn parallel to BD and SR in view F and lines BS and DR were in point view in view F. Since the problem states that the hopper is symmetrical, we can simply copy and flip the same side four times in order to get the complete development. The solution is now complete. In order to see it again, click the forward arrow below.y pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Dvpmt(Pr)-2- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("Dvpmt(Pr)-2-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent Dvpmt(Pr)-2- update default buttonUp repeat_silent fwd_slnt update picture "2" ("Dvpmt(Pr)-2-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" Development of Cones and Cylinde Descriptive Geometry Problems -- Developments Development of Cones and Cylinders In the development of cones and cylindrical surfaces, we use the same basic principles as with the prismatic surface. Again, we will use some mathematics to solve problems more easily. We will also use the method of creating points around circles in order to approximate them as groups of straight lines, as we did with intersections. pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Devlopment (Cylin) - 1 Dvpmt(Cyl)-1-2 false audioerror enterPage Dvpmt(Cyl)-1-2 audioerror leavePage 4wavPlayable syserrornumber = 0 mmIsOpen clip "Dvpmt(Cyl)-1-2" mmopen f<> 0 audioerror mmclose picture "2" Descriptive Geometry Problems -- Developments Development of Cones and Cylinders Example 1. Develop the surface of the cylinder below. 1]2\) 1H($2 1991. Al l rights r eserved. backward forward To see the solution, click the forward arrow below.............................. This problem is very simple to solve. Using geometry, we can easily calculate the circumference of the cylinder. This is will be the length of the developed cylinder, and h will be the height. The solution is now complete.now complete. complete.. complete. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent Dvpmt(Cyl)-1- update default buttonUp repeat_silent fwd_slnt update picture "2" ("Dvpmt(Cyl)-1-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" Development (Cylin) - 2 Descriptive Geometry Problems -- Developments Development of Cones and Cylinders Example 2. Develop the surface of the truncated cylinder below.] z*H.z*4% q,H.q, h.H.h. ^0H.^0#) U2H.U2 backward forward To see the step-by-step solution, click the forward arrow below................. First, points are created around the cylinder end in view H. Remember that the larger number of points, the more accurate the solution. These points are projected into vertical lines around the circumference of cylinder in view F. Only lines 1 through 7 are visible; the rest of the lines are hidden behind the cylinder. The development view is begun. The length of the line, which represents the base of the cylinder, is the circumference. The points are spaced evenly on this line. The first 3 lines are projected onto the development view as shown. We also could simply copy the lines from view F, since the vertical lines are shown in true length.; The rest of the lines are projected. Noting that the truncated cylinder is symmetrical will save time. The tops of the lines are connected, then the connection is splined to give a smooth curve. The solution is now complete. To so it again, click the forward arrow below.A pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> Dvpmt(Cyl)-2- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("Dvpmt(Cyl)-2-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " Dvpmt(Cyl)-2- forward_silent update default buttonUp repeat_silent fwd_slnt update picture "2" ("Dvpmt(Cyl)-2-"&( default update B"forward_silent" { = 7 normalgraphic = icon "repeat_silent" fwd_slnt" Development (Cone) - 1 Descriptive Geometry Problems -- Developments Development of Cones and Cylinders Example 3. Develop the surface of the right circular cone below. PostScript ZapfChanc S 4/S &Help 'u.3* ,2,N* %9#z- FASTWINDOWFRAME CREATEP backward forward To see the step-by-step solution, click the forward arrow below................. Create points around the end view in view H. Project the points in to view F. Draw in the lines in view F. These are the lines you will see in the final development. Find the true length of a line on the side of the cone as shown. S is the distance between two points on the circle. Remember that the distance S is an approximation. It should actually be the length of an arc rather than a linear distance. Lines 1 through 12 are drawn in the development view. Remember that they are in true length and the distance between them at the outside is S. Spline the curve connecting these points. The solution is now complete. Click the forward arrow below to see in again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Dvpmt(Con)-1- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("Dvpmt(Con)-1-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent Dvpmt(Con)-1- update default buttonUp repeat_silent fwd_slnt update picture "2" ("Dvpmt(Con)-1-"&( default update B"forward_silent" { = 7 normalgraphic = icon "repeat_silent" fwd_slnt" GZ!\!\!V Development (Cone) - 2 Descriptive Geometry Problems -- Developments Development of Cones and Cylinders Example 4. Develop the surface of the truncated right circular cone below. below. All Righ %Q$A&*# backward forward To see the step-by-step solution, click the forward arrow below................. Create points around the base of the cone, and project the lines into view H. Find the true length of a line on the untruncated cone and show the development. (This was done in the previous problem.) Find the true length of each of the lines over the truncated region. Measure the rise in view F and the run in view H and find the true length either graphically or using the pythagorean theorem. Using the lengths just measured, draw points on the untruncated development at the appropriate distances from the center point. Connect all the points and spline the curve to get the final development. The solution is now complete. Click the forward arrow below to see it again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> Dvpmt(Con)-2- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("Dvpmt(Con)-2-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent Dvpmt(Con)-2- update default buttonUp repeat_silent fwd_slnt update picture "2" ("Dvpmt(Con)-2-"&( default update B"forward_silent" b = 6 normalgraphic = icon "repeat_silent" fwd_slnt" Development (Cone) - 3 Descriptive Geometry Problems -- Developments Development of Cones and Cylinders Example 5. Develop the surface of the oblique cone below.A N!j%d. +N!j% N!j%@2J( N!j%f1 N!j%,- &x/N!j% +( N!j% /N!j% $# 1Q# 1 :# 1:#&0$#L0 5&80L& &^05& (F0k(F0 backward forward To see the step-by-step solution, click the forward arrow below................. First, create points evenly spaced around the base of the cone. Project the points into view F. Draw in lines from the tip of the cone to the points on the base in both views.y Find the true length of each line, using the rise from view F and the run from view H. Also, use a circle to mark the distance along the base between points in view H. Draw the true length lines in the development view. Make sure that they are appropriately spaced, using the same circle you created in view H. Draw in the outline, splining the curved edge. The solution is now complete. Click the forward arrow below to see it again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent default Press the forward arrow button below. Dvpmt(Con)-3- update buttonUp "Press the arrow Bbelow." picture ( ("Dvpmt(Con)-3-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent default update Dvpmt(Con)-3- buttonUp repeat_silent fwd_slnt update picture "2" ("Dvpmt(Con)-3-"&( default update B"forward_silent" b = 6 normalgraphic = icon "repeat_silent" fwd_slnt" Contours Descriptive Geometry Problems -- Contours Contours A contour map is a map of some constant quality in an area. The mapping may be of constant temperature, pressure, height, etc. Most familiar are contour maps of elevation of land. A example is shown below. In this aerial view of a piece of land, the contours of constant elevation are shown. Thus the land goes from an elevation of 100 m on the right, to a peak elevation of 145 on the left. Note that this map is an approximation, and is only as accurate as the surveyor could be on the site when it was made. The areas between the contour lines are not flat, but must be interpolated to give a smooth transition.transition. pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Profiles Descriptive Geometry Problems -- Contours Profiles A profile of the land is a section view of the land made by a vertical cutting plane. A true shape of the section can be contructed by a viewing plane parallel to the vertical cutting plane. Note that the construction is an approximation, due to the very nature of a contour map. Also note that the vertical and horizontal scale may not be the same. Different horizontal and vertical scales are used to emphasize the vertical displacement of the land.................... pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Profiles - 1 Descriptive Geometry Problems -- Contours Profiles Example. Generate a profile of the hillside on a line from point A to point B.................nt B............... backward forward First, draw in the vertical cutting plane between lines A and B. Mark the points where the contour lines intersect it. Set up the profile view. In this solution, we will make 1 m = 5 mm in the profile view.u Project the intersection points into the profile view. Make sure that each projection line ends at the appropriate elevation.i Connect the points at the ends of the projection lines to find the final profile and spline the resulting line to get a smooth curve. The solution is now complete. Click the forward arrow below to see it again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> Profile-1- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("Profile-1-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent Profile-1- update default buttonUp repeat_silent fwd_slnt update picture "2" ("Profile-1-"&( Hfwd)) default update B"forward_silent" H = 5 normalgraphic = icon "repeat_silent" fwd_slnt" To see the step-by-step solution, click the forward arrow below................. ypxytvsu udoyw_ppu uvvv{xg{ wrzkmjsiqpo{ ~okqombe Int (Pln & Pln) Real - 2 Descriptive Geometry Problems -- Intersections Intersection of Two Planes -- Real Intersection Example 2. Find the intersection of planes ABC and QRS. Show correct visibility................................. PostScript Courier ourie backward forward First, determine which lines (plane edges) are involved in the intersection. From view F, it is obvious that AB and QS are not in the intersection. Their visbilities are determined and shown in view H and F. Four lines remain to be determined: AC, BC, QR, and RS. Using the visibility test, it is determined that lines BC and RS are not involved in the intersection and their visibility is shown accordingly. The cutting plane method will now be used to determine the point of intersection of edge QR. Projection lines from the apparent intersection of QR and plane ABC in view H are drawn into view F. The cutting plane is drawn across plane ABC in view F, and the intersection between the cutting plane and line QR shows the intersection point. This point is projected into view H and is labelled I. The visibility is determined in views H and F and line QR is drawn in. The projection and construction lines have been erased. The cutting plane method is now done for line AC. First, projection lines from the cutting plane in view H are drawn into view F.A The cutting plane is drawn in view F and the intersection of line AC and the cutting plane in view F gives the intersection point. The intersection point is labelled J and is projected into view H.} The visibility of line AC is determined on both sides of the intersection point J in views H and F. The last step is to draw in the intersection line, which is a straight line between the points I and J. Try to picture these planes in three dimensions. The solution is now complete. Click the forward arrow below to see this solution again. To see the step-by-step solution, click the forward arrow below................. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " .&, " V, #> .&, " .&, #> forward_silent IntP&P(r)-2- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture "5" ("IntP&P(r)-2-"&( keep y" lock-out working "repeat" force nam take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " .&, " .&, " forward_silent IntP&P(r)-2- update default buttonUp repeat_silent fwd_slnt update picture "2" ("IntP&P(r)-2-"&( default update B"forward_silent" = 10 normalgraphic = icon "repeat_silent" fwd_slnt" Intersection of Two Planes (Rea wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Intersection of Two Planes (Real Intersection) Quiz - 1/3 Quiz 9.20 Given two intersecting planes, if one edge of a plane is in front of the other plane in the horizontal view, then that edge is completely visible in the front view.....................false. Go to the next page after you have tried answering the question. Quiz 8.20. Given two intersecting planes, if one edge of a plane is in front of the other plane in the horizontal view, then that edge is completely visible in the front view.......... Button answer True. If the edge is in front in the horizontal view, then it cannot be hidden by the other plane in the front view....S misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Intersection of Two Planes (Real Intersection) Quiz - 2/3 Quiz 9.21 Given two intersecting planes, if one edge of a plane is in back of the other plane in the horizontal view, then that edge is completely hidden in the front view.....................r false. Go to the next page after you have tried answering the question. Quiz 8.21. Given two intersecting planes, if one edge of a plane is in back of the other plane in the horizontal view, then that edge is completely hidden in the front view. Button answer Inconclusive. Only the portion of the edge inside the intersection area is hidden; the remaining part is visible. misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Intersection of Two Planes (Real Intersection) Quiz - 3/3 Quiz 9.22 The intersection of two bounded planes is a line.nt is false, or "Inconclusive" (if applicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.22. The intersection of two bounded planes is a line.......... Button answer Inconclusive. The intersection of two bounded planes can be a line, a point, or an overlapping area. misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" Inconclusive reference Intersection of Two Planes -- Vi Descriptive Geometry Problems -- Intersections1 Intersection of Two Planes -- Virtual Intersection In the previous method, we considered the lines of both planes, intersecting the respective "other planes" to establish the intersection. In this alternate method, we consider only the intersections of the lines of one plane on the other. To do this, we imagine that one plane is infinitely large. The intersection of the other plane must then be a line between two sides. The procedure is to find the unbounded intersection, then bound it. animationstage thisanim animerror example buttonclick buttonclick 4thisanim, ref "example" syserrornumber = 0 mmplay clip stage "animationstage" hold Q<> 0 animerror Animation example thisanim example buttonclick buttonclick 4thisanim mmstop clip "example" animationstage animationstage thisanim animerror buttonclick buttonclick 4thisanim, ref syserrornumber = 0 ) <> mmplay clip stage "animationstage" hold a<> 0 animerror Repeat Animation Click on the background to return to Virtual Intersections. pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Int (Pln & Pln) Virt - 1 : f!2"h# Descriptive Geometry Problems -- Intersections Intersection of Two Planes -- Virtual Intersection Example 1. Determine the intersection of planes ABC and XYZ. Show correct visibility............................... U =% U =%U <%T!<%h!d% &T!*& backward forward To see the step-by-step solution, click the forward arrow below................. Lines AB, AC, XZ, and ZY can be seen in their entirety outside the instersection area, therefore they do not intersect other planes. Their visbility is easily esablished using the visbility test.Q In the solution for a real intersection, we considered the lines of both planes. In this solution, however, we will only consider the lines of plane XYZ and imagine that plane ABC is infinite. For line XY, the cutting plane method is still used and projection lines are drawn into view F. The cutting plane is projected into view F and the intersection point of line XY with plane ABC, called 2, is found. Visibility is established for line XY. The procedure has been, up to this point, identical to the real intersection method. Now we will consider line YZ. Even though we have already established its visibility, it can be used to find the other real intersection point.... Projection lines from ZY's apparent interesection with plane ABC in view H are drawn into view F. The line representing the cutting plane in view F is extended to intersect with YZ. This point, labelled point 3, is projected back into view H. This is a virtual intersection point (where line YZ would have intersected plane ABC if plane ABC were unbounded). The intersection of XYZ on the unbounded plane ABC would have been a straight line between points 2 and 3. In reality, plane ABC is bounded at edge BC, thus the intersection line actually stops there, at point 1. Point 1 is found at the intersection between the line between 2 and 3 and the edge BC. This is also the intersection point of BC with plane XYZ. Point 1 is projected into view F. The visibility of line BC is found using the visibility test. The intersection of planes ABC and XYZ is shown as a straight line between points 1 and 2. The solution is now complete. Click the forward arrow below to see this solution again.e# pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " .&, " .&, " V, #> .&, " .&, #> IntP&P(v)-1- Press the forward arrow button below. forward_silent default update buttonUp "Press the arrow Bbelow." picture "3" ("IntP&P(v)-1-"&(fwd-1)) keep y" lock-out working "repeat" force nam take values that are valid -- clip references default update B"forward_silent" forward_silent Int (Pln & Pln) Virt - 2 Descriptive Geometry Problems -- Intersections Intersection of Two Planes -- Virtual Intersection Example 2. Determine the intersection of planes ABC and QRS. Show correct visibility.......................................................................... asic G7 asic Geome tric - 10 ources: rocset Win 35Dict 3 1 font %s %d %d % d %d B %d %d %d EndData ave %d %d translate %d %d scal definefont } if cleartomark ont %s rentfile e backward forward As in the previous problems, first we determine which lines (plane edges) are involved in the intersection. From view F, it is obvious that AB and QS are not in the intersection. Their visibilities are determined and shown in views H and F. Four lines remain to be determined: AC, BC, QR, and RS. Using the visibility test, it is determined that lines BC and RS are not involved in the intersection and their visibility is shown accordingly. To see the step-by-step solution, click the forward arrow below................. The cutting plane method is now used on line AC. Projection lines for the cutting plane are drawn from view H into view F. The intersection of line AC and plane QRS is found at point J in view F, which is then projected into view H. The visibility is determined and the construction lines have been removed for clarity. Now we will find a virtual intersection point. We will consider plane QRS to be the unbounded plane. Draw projection lines from line BC in view H down to view F. Point K is the virtual intersection point. The virtual intersection point K is projected into view H. The line between points J and K is what the intersection line would look like if plane QRS was unbounded. Notice that this virtual intersection line crosses the actual boundary of plane QRS. The intersection between line JK and QR finds point I, which is the actual intersection point of line QR with the plane ABC. Visibility is determined for line QR. Line IJ is the actual intersection between the two planes ABC and QRS. The solution is now complete. To see this solution again, click the forward arrow below. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " .&, " .&, " V, #> .&, " .&, #> update forward_silent Press the forward arrow button below. IntP&P(v)-2- default buttonUp "Press the arrow Bbelow." picture "4" ("IntP&P(v)-2-"&(fwd-1)) keep y" lock-out working "repeat" force nam take values that are valid -- clip references default update B"forward_silent" forward_silent Intersection of two planes (vir wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Intersection of Two Planes (Virtual Intersection) Quiz - 1/1Q Quiz 9.23 A virtual intersection is located on a bounded plane.s false, or "Inconclusive" (if applicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.23. A virtual intersection is located on a bounded plane.......... Button answer False. A virtual intersection is located off a bounded plane. Part of the definition of a virtual intersection is that the bounded plane is extended to infinity........ misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference Intersection of two planes (virt Distance (LinMthd) - 1 Development (Cylin) - 2 Distance between lines (plane m Intersection of a Plane and a So Animation example Descriptive Geometry Problems -- Intersections Intersection of a Plane and a Solid The basic approach to finding the intersection of a plane and a solid is similar to that of two planes. However, to simplify the problem, you must use some principles of virtual intersection, spatial reasoning abilities, and common sense. The procedure is as follows: 1. Identify all lines. It helps to write down a list so that you don't forget to consider any of the lines. 2. Identify the intersection area. 3. Find the intersections, or virtual intersections, of the solid edges on the plane. You will treat the solid surface as a group of planes. 4. Establish intersection lines, bounded by the physical limits of the objects. 5. Establish visibility. pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat animationstage thisanim animerror example buttonclick buttonclick 4thisanim, ref "example" syserrornumber = 0 mmplay clip stage "animationstage" hold Q<> 0 animerror thisanim example buttonclick buttonclick 4thisanim mmstatus clip "playing" mmstop "example" animationstage animationstage thisanim animerror buttonclick buttonclick 4thisanim, ref syserrornumber = 0 ) <> mmplay clip stage "animationstage" hold a<> 0 animerror Repeat Animation Click on the background to return to Real Intersections. Intersection of a Plane and a So Development of Cones and Cylinde Intersection of two planes (vir 10 Basic Geometric-5 Fp>j>j> Int (Pln & Sld) - 1 Descriptive Geometry Problems -- Intersections Intersection of a Plane and a Solid Example 1. Find the intersection between the rectangular plane and the triangular prism. Do not show lines within the prism............................... Dashed construction lines are drawn in both views to complete plane ABCD. These are not the final lines, but they are needed to find the intersections between the prism and the plane in the following steps. backward forward To see the step-by-step solution, click the forward arrow below.ard arrow below. First, lines 1 and 2 of the prism are dashed in black. Their presence will be needed to show the visibility of lines AB and CD. Note that AB and CD are not involved in the intersection, as both are shown in their entirety in view H.. The visibility of lines AB and CD is determined using the visibility test and shown in view F. Notice that point A is behind the prism in view F, while edge CD is in front of the prism. The cutting plane method is used with line 1, beginning in view H. Projection lines are drawn into view F, stopping at the appropriate plane edges.a Point X is found from the intersection of the cutting plane and line 1 in view F. Then it is projected into view H. X is the intersection point between line 1 and the plane ABCD. The visibility of line 1 is determined on both sides of the intersection point. The construction lines have been removed for clarity. Now the cutting plane method is begun with line 2. However, line 2 does not intersect plane ABCD in view F, so we must find the virtual intersection point. Point Y is the point where line 2 would have intersected plane ABCD if the plane was unbounded. This virtual intersection point was first found in view F, and then projected into view H. Since line 2 does not intersect plane ABCD, visibility is trivial to determine. In view H, line 2 is behind the prism. In view F, it is only hidden where it is covered by the edge of plane ABCD. Point Y is marked for later use in finding the intersection lines. Now the cutting plane method is used with line 3. Projection lines are drawn from view H into view F, stopping at the edges of plane ABCD. The real intersection point Z is found in view F, and then projected into view H.+ The visibility around point Z is determined, and the construction lines are removed. We now have three points of intersection, X, Y, and Z. (Don't forget that Y is a virtual intersection point.) The intersection of the bounded plane ABCD with the prism is found, and the visibilities can be found intuitively or using the visibility test. To see how this intersection was found, you may want to go back and look at the previous step again. The solution is now complete. A triangular plane is formed by points X, Y, and Z. This triangular plane would be the intersection of the prism with plane ABCD if the plane was unbounded. However, since the plane is bounded, one more step is needed to show the final intersection and correct visibility. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " .&, " .&, " .&, " V, #> .&, " .&, #> forward_silent IntP&S-1- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture "2" (fwd) ("IntP&S-1-"&( 1-1)) keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent Copyright 1986 Micro soft C?( N#,)2) Z)f)6 level the prism 6%5)6% L!.(l' 'L!.( Shelllt 64;2;2; Int (Pln & Sld) - 2 $P&N' Descriptive Geometry Problems -- Intersections Intersection of a Plane and a Solid Example 2. Find the intersection of the plane ABC and the tetrahedron QSRT..... tonUp mousY s - 1 ATEPEN= ETRELABS CLOSEMETA STRETCHB GETDE WRITESPO OFFSE TRGNe ALGDIINIT GETD; DEATH SELECTO BJECT- backward forward To see the step-by-step solution, click the forward arrow below.ard arrow below. There are 9 different lines to consider in this problem. Two of the edges of plane ABC, AB and BC, are not involved in the intersection. Their visibility is found and shown. D!< A! Three of the lines on the tetrahedron, RS, ST, and RT can also be seen in their entirety outside the intersection area, so they do not intersect the plane. Their visibility is found by a visibility test on the tetrahedron. Temporary construction lines are drawn to complete plane ABC. These lines will be needed when we use the cutting plane method to determine the intersections of the lines of the tetrahedron with the plane. The cutting plane method is first done with line QS. The cutting plane is created in view F, and projection lines are draw into view H. Line QS in view H is drawn temporarily as a dashed black line. The intersection of the cutting plane and line QS in view H finds the intersection point, 1, of QS with plane ABC. Point 1 is then projected back into view F. &&>%#& The visibility of line 1 is found in both views and the construction lines are removed for clarity. The position of point 1 remains marked so that it can be used later in finding the complete intersection.. Now the cutting plane method is begun with line QT. The cutting plane is created in view F and projection lines are drawn into view H. The cutting plane is projected into view H and intersection point 2 is found. The visibility of line QT is found in both views. The cutting plane method is begun for line QR. However, line QR does not intersect the plane, so a virtual intersection point must be found. Point 3 is found in view H and projected back into view F. As a virtual intersection point, point 3 is the point where line QR would have intersected the plane ABC if the plane was unbounded. Line QR is completely visible in both views, but point 3 remains marked for use in finding the complete intersection. The intersection would appear as a triangular plane between points 1, 2, and 3 if plane ABC was unbounded. In order to get the final solution, this triangle is bounded by plane ABC. v.N-s. This is how the final solution appears. All the lines within the intersection are removed, and the correct visibility of all the lines is shown. Try to picture this intersection in three dimensions. Click the forward arrow to see the tutorial again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " .&, " .&, " .&, " V, #> .&, " .&, #> forward_silent IntP&S-2- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture "5" (fwd) ("IntP&S-2-"&( 1-1)) keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent Intersections of Planes and Sol wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Intersection of a Plane and a Solid Quiz - 1/2C Quiz 9.24 The intersection region of a plane and a tetrahedron can be a triangle................." (if applicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.24. The intersection region of a plane and a tetrahedron can be a triangle.......... Button answer True. The previous example problem showed that this is possible. If the plane ABC had been larger, the intersection would have been a triangle.... misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Intersection of a Plane and a Solid Quiz - 2/2C Quiz 9.25 The intersection region of a plane and a tetrahedron can be a quadrilateral....................plicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.25. The intersection region of a plane and a tetrahedron can be a quadrilateral.eral. Button answer True. At certain angles, a plane can intersect with all four faces of a tetrahedron.on.{ misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference Intersection of Two Solids Descriptive Geometry Problems -- Intersections Intersection of Two Solids This type of problem is usually very complicated. It involves multiple solutions of the plane-solid intersection problem. Tactics: 1. Get the easy ones first. 2. Use methods of real and virtual intersections 3. Work with one plane at a time. 4. It may be useful to turn extruded prisms on edge view, to use cutting planes. Animation example pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat animationstage animationstage thisanim animerror example buttonclick buttonclick 4thisanim, ref "example" syserrornumber = 0 mmplay clip stage "animationstage" hold Q<> 0 animerror thisanim example buttonclick buttonclick 4thisanim mmstatus clip "playing" mmstop "example" animationstage thisanim animerror buttonclick buttonclick 4thisanim, ref syserrornumber = 0 ) <> mmplay clip stage "animationstage" hold a<> 0 animerror Repeat Animation Click on the background to return to Real Intersections. A6L=F9I2?;BGKV >h "?z =R!N>d! HN"WI`" 8#9 J# on#Rp Y6$zYJ$ Y^$JZr$ [:%e\N% ]D&}]X& ]l&M^ R)r d) v)N! **6!<* -/a*- g>-'hR- hf-%hz- i\/hij/ ix/4j m<0TnJ0 mf0Xnt0 projection2-1 projection2-2 projection2-3 projection3-1 projection3-2 ptproj-2 ptproj-3 ptproj-4 ptproj-5 ptproj-6 ptproj-7 ptproj-8 10BasGeom-1 10BasGeom-2 10BasGeom-3 10BasGeom-4 10BasGeom-5 10BasGeom-6 10BasGeom-7 10BasGeom-9 BPS-3-2 BPS-3-3 BPS-3-4 BPS-3-5 BPS-3-6 BPS-3-7 BPS-3-8 BPS-3-9 BPS-3-10 BPS-3-11 BPS-3-12 BPS-3-13 BPS-3-14 BPS-3-15 BPS-1-2 BPS-1-3 BPS-1-4 BPS-2-2 BPS-2-3 BPS-2-4 BPS-2-5 BPS-2-6 BPS-2-7 IntS&S-2-2 IntS&S-2-3 IntS&S-2-4 IntS&S-2-5 IntS&S-2-6 IntS&S-2-7 IntS&S-2-8 Dvpmt(Cyl)-2-2 Dvpmt(Cyl)-1-2 Dvpmt(Cyl)-2-3 Dvpmt(Cyl)-2-4 Dvpmt(Cyl)-2-5 Dvpmt(Cyl)-2-6 Dvpmt(Cyl)-2-7 Cut&Fill-1-2 Cut&Fill-1-3 Cut&Fill-1-4 Cut&Fill-2-2 Cut&Fill-2-3 Cut&Fill-2-4 Cut&Fill-2-5 LinVis-1-1 LinVis-1-2 LinVis-3-2 LinVis-3-3 LinVis-3-4 LinVis-3-5 LinVis-3-6 LinVis-4-2 LinVis-4-3 LinVis-4-4 LinVis-4-5 LinVis-4-6 ptView-2 ptView-3 ptView-4 ptView-5 ptView-6 ptView-7 ptView-8 ptView-9 ptView-10 DistLM-1-2 DistLM-1-3 DistLM-1-4 DistLM-1-5 DistLM-1-6 DistLM-1-7 DistLM-1-8 DistLM-1-9 DistLM-1-10 DistLM-1-11 DistLM-2-2 DistLM-2-3 DistLM-2-4 DistLM-2-5 DistLM-2-6 DistLM-2-7 DistLM-2-8 DistLM-2-9 DistLM-2-10 DistLM-2-11 DistLM-2-12 DistLM-2-13 DistLM-2-14 DistLM-2-15 EV&TS-1-2 EV&TS-1-3 EV&TS-1-4 EV&TS-1-5 EV&TS-1-6 EV&TS-1-7 EV&TS-1-8 EV&TS-1-9 EV&TS-1-10 EV&TS-1-11 EV&TS-1-12 EV&TS-1-13 EV&TS-1-14 EV&TS-2-2 EV&TS-2-3 EV&TS-2-4 EV&TS-2-5 EV&TS-2-6 EV&TS-2-7 EV&TS-2-8 EV&TS-2-9 EV&TS-2-10 EV&TS-2-11 EV&TS-2-12 EV&TS-3-2 EV&TS-3-3 EV&TS-3-4 EV&TS-3-5 EV&TS-3-6 EV&TS-3-7 EV&TS-3-8 EV&TS-3-9 EV&TS-3-10 EV&TS-3-11 DiAng-2 DiAng-3 DiAng-4 DiAng-5 DiAng-6 DiAng-7 DiAng-8 DiAng-9 DiAng-10 DiAng-11 DistPM-1-2 DistPM-1-3 DistPM-1-4 DistPM-1-5 DistPM-1-6 DistPM-1-7 DistPM-1-8 DistPM-1-9 DistPM-1-10 DistPM-1-11 DistPM-2-2 DistPM-2-3 DistPM-2-4 DistPM-2-5 DistPM-2-6 DistPM-2-7 DistPM-2-8 DistPM-2-9 DistPM-2-10 DistPM-2-11 DistPM-2-12 DistPM-2-13 DistPM-2-14 DistPM-2-15 DistPM-2-16 DistPM-3-2 DistPM-3-3 DistPM-3-4 DistPM-3-5 DistPM-3-6 DistPM-3-7 DistPM-3-8 DistPM-3-9 DistPM-3-10 DistPM-3-11 DistPM-3-12 DistPM-3-13 DistPM-3-14 DistPM-3-15 DistPM-3-16 DistPM-3-17 DistPM-4-2 DistPM-4-3 DistPM-4-4 DistPM-4-5 DistPM-4-6 DistPM-4-7 DistPM-4-8 DistPM-4-9 DistPM-4-10 DistPM-4-11 DistPM-4-12 DistPM-4-13 DistPM-4-14 DistPM-4-15 DistPM-4-16 DistPM-4-17 IntL&P-1-2 IntL&P-2-2 IntL&P-2-3 IntL&P-2-4 IntL&P-2-5 IntL&P-2-6 IntL&P-2-7 IntL&P-2-8 IntL&P-2-9 IntL&P-2-10 IntL&P-2-11 IntL&P-2-12 IntL&P-2-13 CutPlnM-1-2 CutPlnM-1-3 CutPlnM-1-4 CutPlnM-1-5 CutPlnM-1-6 CutPlnM-1-7 CutPlnM-2-4 CutPlnM-2-5 CutPlnM-2-6 CutPlnM-2-7 CutPlnM-2-8 CutPlnM-2-9 IntP&P(r)-1-2 IntP&P(r)-1-3 IntP&P(r)-1-4 IntP&P(r)-1-5 IntP&P(r)-1-6 IntP&P(r)-1-7 IntP&P(r)-1-8 IntP&P(r)-2-2 IntP&P(r)-2-3 IntP&P(r)-2-4 IntP&P(r)-2-5 IntP&P(r)-2-6 IntP&P(r)-2-7 IntP&P(r)-2-8 IntP&P(r)-2-9 IntP&P(r)-2-10 IntP&P(v)-1-2 IntP&P(v)-1-3 IntP&P(v)-1-4 IntP&P(v)-1-5 IntP&P(v)-1-6 IntP&P(v)-1-7 IntP&P(v)-1-8 IntP&P(v)-1-9 IntP&P(v)-1-10 IntP&P(v)-1-11 IntP&P(v)-2-2 IntP&P(v)-2-3 IntP&P(v)-2-4 IntP&P(v)-2-5 IntP&P(v)-2-6 IntP&P(v)-2-7 IntP&P(v)-2-8 IntP&P(v)-2-9 IntP&P(v)-2-10 IntP&P(v)-2-11 IntP&P(v)-2-12 IntP&S-1-2 IntP&S-1-3 IntP&S-1-4 IntP&S-1-5 IntP&S-1-6 IntP&S-1-7 IntP&S-1-8 IntP&S-1-9 IntP&S-1-10 IntP&S-1-11 IntP&S-1-12 IntP&S-1-13 IntP&S-1-14 IntP&S-1-15 IntP&S-2-2 IntP&S-2-3 IntP&S-2-4 IntP&S-2-5 IntP&S-2-6 IntP&S-2-7 IntP&S-2-8 IntP&S-2-9 IntP&S-2-10 IntP&S-2-11 IntP&S-2-12 IntP&S-2-13 IntP&S-2-14 IntP&S-2-15 IntS&S-1-2 IntS&S-1-3 IntS&S-1-4 IntS&S-1-5 IntS&S-1-6 IntS&S-1-7 IntS&S-1-8 IntS&S-1-9 IntS&S-1-10 IntS&S-3-2 IntS&S-3-3 IntS&S-3-4 IntS&S-3-5 IntS&S-4-2 IntS&S-4-3 IntS&S-4-4 IntS&S-4-5 IntS&S-4-6 Dvpmt(Pr)-1-2 Dvpmt(Pr)-1-3 Dvpmt(Pr)-1-4 Dvpmt(Pr)-1-5 Dvpmt(Pr)-1-6 Dvpmt(Pr)-1-7 Dvpmt(Pr)-1-8 Dvpmt(Pr)-1-9 Dvpmt(Pr)-1-10 Dvpmt(Pr)-1-11 Dvpmt(Pr)-1-12 Dvpmt(Pr)-1-13 Dvpmt(Pr)-2-2 Dvpmt(Pr)-2-3 Dvpmt(Pr)-2-4 Dvpmt(Con)-1-2 Dvpmt(Con)-1-3 Dvpmt(Con)-1-4 Dvpmt(Con)-1-5 Dvpmt(Con)-1-6 Dvpmt(Con)-1-7 Dvpmt(Con)-2-2 Dvpmt(Con)-2-3 Dvpmt(Con)-2-4 Dvpmt(Con)-2-5 Dvpmt(Con)-2-6 Dvpmt(Con)-3-2 Dvpmt(Con)-3-3 Dvpmt(Con)-3-4 Dvpmt(Con)-3-5 Dvpmt(Con)-3-6 Profile-1-2 Profile-1-3 Profile-1-4 Profile-1-5 Cut&Fill-1-2 Cut&Fill-1-3 Cut&Fill-1-4 Cut&Fill-2-2 Cut&Fill-2-3 Cut&Fill-2-4 Cut&Fill-2-5 Shad-1-2 Shad-1-3 Shad-1-4 Shad-2-2 Shad-2-3 Shad-3-2 Shad-3-3 Shad-3-4 Shad-3-5 Shad-3-6 Shad-3-7 LinVis-2 objectives cutplane 2planes 2ndprinc 1stprinc p2-105 p3-105 p4-105 p6-105 p7-105 p8-105 p9-105 p10-105 p11-105 p12-105 p13-105 p14-105 p15-105 p28-105 p32-105 p37-105 p45-105 p48-105 p57-105 p60-105 p64-105 p70-105 p74-105 p79-105 p84-105 p87-105 p93-105 p94-105 p96-105 p97-105 p98-105 p101-105 p57a-105 p57b-105 p57c-105 dihed 2solids cutfill1 cutfill2 wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Distance Between Lines (Plane Method) Quiz - 2/4E Quiz 9.16 The location of the shortest connector between two skew lines is found in a view where both lines are in true length......................... determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.16. The location of the shortest connector between two skew lines is found in a view where both lines are in true length.......... Button answer True. This was shown in examples 1 and 2 of this section.... misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Distance Between Lines (Plane Method) Quiz - 3/4S Quiz 9.17 The true length of the shortest connector between skew lines is found when one of the skew lines is in true length..................... determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.17. The true length of the shortest connector between skew lines is found when one of the skew lines is in true length.. Button answer False. The true length of the shortest connector can only be found if one of the lines is in point view or if both skew lines appear to be parallel... misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Distance Between Lines (Plane Method) Quiz - 4/4E Quiz 9.18 The location of the shortest horizontal connector is found in a view 90 degrees from the horizontal view.....information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.18. The location of the shortest horizontal connector is found in a view 90 degrees from the horizontal view........... Button answer The location of the shortest horizontal connector is found in a view that is orthogonal to both the horizontal view and a vertical view where both skew lines appear to be parallel................ misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" Inconclusive reference Intersection of a Line and a Pla Descriptive Geometry Problems -- Intersectionsssss Intersection of a Line and a Plane This is the simplest kind of intersection. We will also be looking at intersections involving plane with plane, plane with solid, and solid with solid. All these more complicated intersections are based on the line-plane intersection, so you must be absolutely clear on this type of intersection before you continue. Procedure: 1) First you must determine if that line and plane actually intersect. By using the visbility test at the apparent interesections between the line and the plane's edges, you can determine this. If the line is visible or invisible at both edges, it did not intersect the plane. 2) Find the a view with the plane in true shape, then create an adjacent view parallel to line which intersects the plane. This will give you the true length of the line and the edge view of the plane. Not only will this allow you to find the intersection point, but also the angle between the line and the plane. 3) Note that, using Descriptive Geometry, this is a long process involving the creation of at least three new views. Later you will learn a "shortcut method" called the cutting plane method that is the only practical way to solve more complicated intersections. Show example n;dequeue }gyieldApp queue update buttonUp Next Step Show Steps Repeat update yieldApp() ; <> 0 dequeue ( update = "Show Steps" = "Repeat" = "Next step0 pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat Audio step1 1) First you must determine if the line and plane actually intersect. By using the visibility test at the apparent intersections between the line and the plane's edges, you can determine this. If the line is visible or invisible at both edges, it does not intersect the plane............................... step2 2) Find a view with the plane in true shape, then create an adjacent view parallel to the line which intersects the plane. This will give you the true length of the line and the edge view of the plane. Not only will this allow you to find the intersection point, but also the angle between the line and the plane............................... step3 3) Note that, using Descriptive Geometry, this is a long process involving the creation of at least three new views. Later you will learn a "shortcut method" called the cutting plane method that is the only practical way to solve more complicated intersections. Click on the button "Show Steps" to see the steps of the solution for these problems. Show Steps animationstage Int (Ln & Pln) - 1 false audioerror IntL&P-1-2 enterPage audioerror IntL&P-1-2 leavePage 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntL&P-1-2" mmopen _<> 0 audioerror mmclose picture "2" Descriptive Geometry Problems -- Intersections Intersection of a Line and a Plane Example 1. Determine if the bounded plane ABC and the line DE intersect? To see the solution, click the forward arrow below..............ow. backward forward Create projection lines 1 and 2 from the apparent intersections in view H. Using visibility, we find that the plane edge AB is on top of DE, but the plane edge BC is below DE. This means that line DE must pass through the bounded plane. Therefore, they must intersect. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( default update B"forward_silent" forward_silent .&+ +E .&, " IntL&P-1- forward_silent update default buttonUp repeat_silent fwd_slnt update picture "2" ("IntL&P-1-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" Int (Ln & Pln) - 2 ' (4)2* Descriptive Geometry Problems -- Intersections Intersection of a Line and a Plane Example 2. A line DE intersects plane ABC. Determine the point of intersection and the true angle between the line and the plane................................................................................................................................................................................ To see the step-by-step solution, click the forward arrow below.ard arrow below. backward forward First create a line on plane ABC in view H parallel to the view line. Draw in the projection lines... Draw the new line in view F. Note that it is now in true length. The only reason we have created this line is to allow us to get the edge view of the plane quickly. Create view 1 perpendicular to the line in true length in view F.[% Draw in the projection lines... Construct the edge view of plane ABC and line DE in view 1. Point P is the point of intersection between the line and the plane. ~'2'{' Create view 2 parallel to the edge view of plane ABC in view 1. Draw in the projection lines... Construct the true shape of plane ABC and line DE in view 2. Plane ABC is now in true shape because view 2 is parallel to view 1, where the plane is in edge view.1) Create view 3 parallel to line DE in view 2. Remember that any view adjacent to a plane in true shape will give the edge view of the plane. Draw in the projection lines... The final construction in view 3 gives the edge view of plane ABC and the true length of line DE. The point of intersection is labelled P, and the true angle can be measured in this view. The solution is now complete. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. IntL&P-2- default update buttonUp "Press the arrow Bbelow." picture ( ("IntL&P-2-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent update IntL&P-2- default buttonUp repeat_silent fwd_slnt update picture "2" ("IntL&P-2-"&(fwd)) default update B"forward_silent" D = 13 normalgraphic = icon "repeat_silent" fwd_slnt" The Cutting Plane Method Descriptive Geometry Problems -- Intersections1 The Cutting Plane Method This is a shortcut method for finding the intersection point between a line and a plane without creating any additional views as done in the previous example. Technique: Given a plane and a line intersecting it, consider a "cutting plane" perpendicular to one of the original views (so it appears in edge view) and also containing the intersecting line. That is, the cutting plane is drawn in edge view directly over the line in one of the original views. The intersection point between the original line and plane is also contained in the intersection between the original plane and the cutting plane. Project the intersection of the cutting plane and the original plane (called the "cut line") into the other view. The solution is the intersection of the cut line and the original line, since both contain the intersection between the original line and plane. This is point P. Project P into the adjacent view and establish visibility. animationstage thisanim animerror example buttonclick buttonclick 4thisanim, ref "example" syserrornumber = 0 mmplay clip stage "animationstage" hold Q<> 0 animerror Animation example thisanim example buttonclick buttonclick 4thisanim mmstop clip "example" animationstage animationstage thisanim animerror buttonclick buttonclick 4thisanim, ref syserrornumber = 0 ) <> mmplay clip stage "animationstage" hold a<> 0 animerror Repeat Animation Click on the background to return to Cutting Plane Method. pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat The Cutting Plane Method Point View Ex. Cutting Pln Mthd - 1 Descriptive Geometry Problems -- Intersections The Cutting Plane Method Example 1. Find the intersection point P between line m and plane ABC................................ Default &Color leaveB To see the step-by-step solution, click the forward arrow below.ow. backward forward Draw the cutting plane (1,2) in edge view in view F. Draw its projection lines into view H, intersecting with the correct edges of plane ABC. Draw the cutting plane in view H. Point P is the intersection of the plane ABC and line m.c Project point P into view F...... Show the visibility in view H. The red dashed line indicates where line m is under the plane ABC. This is the invisible portion of the line becuase a projection line from the apparent intersection of line m and the edge AC would hit AC first in view F. Show the visibility in view F. The red dashed line indicates where line m is under the plane ABC. The solution is now complete. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> CutPlnM-1- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("CutPlnM-1-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent CutPlnM-1- update default buttonUp repeat_silent fwd_slnt update picture "2" - 1) ("CutPlnM-1-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" Cutting Pln Mthd - 2 L!*'O Descriptive Geometry Problems -- Intersections The Cutting Plane Method Example 2. Find the intersection point P between line m and plane ABC. This is identical to the previous problem, but shows an alternate solution method........................ u,`!q&n &l#!' "!'h" Default &Color M)P( To see the step-by-step solution, click the forward arrow below................. backward forward First, create the cutting plane. In this example, we will make it in view H. Draw in the projection lines for the cutting plane, terminating them at the correct edges of plane ABC. Construct the cutting plane in view F. The intersection of the cutting plane, line m, and plane ABC is at point P. Project point P into view H. Determine the visibility of view H. A projection line drawn from the apparent intersection of edge AC and line m in view H will hit AC first in view F, thus the part of line m to the left of P in view H is invisible. Determine the visibility of view F. A projection line drawn from the apparent intersection of edge AB and line m in view F will hit line m first in view F, thus the part of line m to the right of P in view F is invisible. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " V, #> .&, " V, #> V, #> .&, " .&, #> CutPlnM-2- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture "8" ("CutPlnM-2-"&( (fwd) '-1)) keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent Cutting PLane Method (1) wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Cutting Plane Method Quiz - 1/1 Quiz 9.19 Consider the case of a line intersecting a plane. In one view, the edge view of a cutting plane is coincident with the line. In an adjacent view, the intersection of the two planes forms a line that contains the intersection of the original line and plane...utting plane intersects another plane with a line in one view and contains it in an adjacent view.........n an adjacent view.......... Button answer True. This is the definition of a cutting plane.... misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference Cutting PLane Method (1) Cutting PLane Method (1) Intersection of Two Planes -- Re Descriptive Geometry Problems -- Intersections1 Intersection of Two Planes -- Real Intersection There are two methods for solving problems involving the intersection of two planes. This, the first, solves the problem by real intersection. Virtual intersection is covered in the next section. In these problems, you are usually given the outlines of two planes. You are asked to find the shape of the intersection (which should be a line), and to establish the visibility of all the lines. Procedure: 1. Identify all the lines (edges of the planes). 2. Identify the "intersection" area. 3. Determine if the lines intersect the other plane (i.e. if on the same side of the plane in the intersection area). a. If it doesn't intersect - establish its visibility b. If it does intersect - find the intersection point - establish visibility of the lines - establish the intersection line on the plane animationstage thisanim animerror example buttonclick buttonclick 4thisanim, ref "example" syserrornumber = 0 mmplay clip stage "animationstage" hold Q<> 0 animerror Animation example thisanim example buttonclick buttonclick 4thisanim mmstatus clip "playing" mmstop "example" "example" animationstage animationstage thisanim animerror buttonclick buttonclick 4thisanim, ref syserrornumber = 0 ) <> mmplay clip stage "animationstage" hold a<> 0 animerror Repeat Animation Click on the background to return to Real Intersections. pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Int (Pln & Pln) Real - 1 Descriptive Geometry Problems -- Intersections Intersection of Two Planes -- Real Intersection Example 1. Determine the intersection of planes ABC and XYZ. Show correct visibility. To see the step-by-step solution, click the forward arrow below................. backward forward There are six lines to consider in this problem: AB, BC, AC, XY, YZ, and XZ. From view H, it is obvious that AB and XZ are not involved in the intersection. From view F, one can see that AC, XZ, and YZ are also not involved. The visibilities of these four lines are determined. Two lines remain: XY and BC. For now, these lines are dashed in gray. The following steps will determine the points of intersection of these lines, and their visibility will be shown..A The cutting plane method is begun on line XY. Projection lines are drawn from the apparent intersection of XY with ABC in view H.9 The intersection of line XY and plane ABC has been found. The visibility was determined, and line XY was dashed at the invisible portions.. The cutting plane method is also used with line BC. The point of intersection of line BC with plane XYZ is shown and visibility is determined. The last step is to draw in the intersection line. Simply draw a line between the intersection points we have just found. This intersection is shown in red, and the unnecessary construction lines have been erased. The solution is now complete. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " .&, " .&, " .&, " .&, " }gyieldApp forward_silent Press the forward arrow button below. update default buttonUp "Press the arrow Bbelow." picture ( - 1) yieldApp() U"l6" U"l7" U"l6" update B"forward_silent" default forward_silent ez~_swfz~i{ cxzavzWryKw \l0n{FpzQmuVqx^w|ax}bw|ex~gx~gv|hw}jv}kw~lx wEB=.55hvyat|bu Edge View and True Shape of a Pl Descriptive Geometry Problems -- Basic Examples The Edge View and True Shape of a Plane Finding the edge view and true shape of a plane is very simple when you have mastered the principles behind finding the true length and point view of a line. While solving these types of problems, keep in mind: 1) The point view of a line is also the edge view of any plane parallel to that line. 2) Note that the edge view is not unique. There are an infinite number of edge views for a given plane. 3) Thus, to get the edge view of a plane, find the point view of any edge of the plane. To do this, create a view showing the edge in true length, then create the point view. Creating a plane parallel to the edge view will give the true shape. There is a shortcut, which is shown on a few of the example problems. Note that the method above requires the construction of two additional views to get the edge view. There is a way to get the edge view with the construction of only one additonal viewing plane. In one of the two views of the original plane, construct any line that is parallel to the other viewing plane on the original plane. Project this line to the other view, where it is now in true length. Now create the point view of this line, which also gives the edge view of the original plane... plane. pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat EV & TS of Plane - 1 x!t" Descriptive Geometry Problems -- Basic Examples The Edge View and True Shape of a Plane Example 1. Find the edge view and true shape of plane ABC. )"<*c" D!<*}!<* _)g!_) YSTEMPALET TEENTRIESw SCANLR ABORTDOC~ RKINGDIR# G/Courie ',P ms you can expect to encounter %d 10 div 3 -1 roll setscreen Olivetti LPk PostScript Courier ourie Arial backward forward To see the step-by-step solution, click the forward arrow below.ard arrow below. Draw in the projection lines from view F and view H. Construct view 1 parallel to line AC of the plane in view H. Draw the projection lines... Draw the projection lines in view 1. The lengths of these projection lines are the same as those in view F. From the projection lines just drawn, create plane ABC in view 1. Note that the edge AC of the plane is now in true length. Draw view 2 perpendicular to line AC. Since the view is perpendicular to a line on plane ABC, it is also perpendicular to the plane itself. Draw in the projection lines... Draw the projection lines in view 2. Note that points A and C appear on top of each other. Construct the edge view of the plane in view 2.i$ Make view 3 parallel to the edge view of plane ABC. Draw in the projection lines... Draw the projection lines in view 3. Note that points A and C lie along the same line, but at different distances from the view line. Connect the ends of the projection lines to show plane ABC in True Shape (TS) in view 3. The solution is now complete. Click the forward arrow below to see the solution again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent EV&TS-1- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("EV&TS-1-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references ("EV&TS-1-"&(2)) default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent EV&TS-1- update default buttonUp repeat_silent fwd_slnt update picture "2" ("EV&TS-1-"&( default update B"forward_silent" \ = 14 normalgraphic = icon "repeat_silent" fwd_slnt" r3$#Q3 EV & TS of Plane - 2 Descriptive Geometry Problems -- Basic Examples The Edge View and True Shape of a Plane Example 2. Find the edge view and true shape of plane XYZ. backward forward This solution uses a simple trick to find the solution without creating as many views as in the previous problem. To see the step-by-step solution, click the forward arrow below. below. WRITESPO OFFSE TRGNe ALGDIINIT GETD Courier urier && Microso ft Corp. All Righ Construct a line WZ in the plane parallel to the view line in view F.y Draw in the projection lines. Line WZ is now in true length because it was parallel to the view line in the previous view. View 1 is drawn perpendicular to WZ in view H. Draw in the projection lines... The projection lines are drawn in view 1. (The lengths were obtained from the projection lines in view F.) ~ 6$i The edge view is constructed in view 1. The plane is in edge view because line WZ, which lies on plane XYZ and was in true length in the previous view, is now in point view. View 2 is constructed parallel to the edge view of plane XYZ. The projection lines are drawn in... The projection lines are drawn in view 2. These lengths are obtained from view H. T3N"%# Finally, the true shape of plane XYZ is constructed. It is not necessary to show line WZ, since it was only created to assist in the solution. lick the forward arrow to see the solution again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> EV&TS-2- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("EV&TS-2-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references ("EV&TS-2-"&(2)) default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent EV&TS-2- update default buttonUp repeat_silent fwd_slnt update picture "2" ("EV&TS-2-"&(fwd)) default update B"forward_silent" D = 12 normalgraphic = icon "repeat_silent" fwd_slnt" EV & TS of Plane - 3 $0(Z,{ Descriptive Geometry Problems -- Basic Examples The Edge View and True Shape of a Plane Example 3. Find the perpendicular connector between point P and plane ABC. Show the connector in all views.r in all views............................... && Microso ft Corp. All Righ served <0t!8! backward forward To see the step-by-step solution, click the forward arrow below.ard arrow below. First, construct line AD in view H parallel to the view line.i Draw in the projection lines... Draw line AD in view F. Notice that it is now in true length. Draw view 1 perpendicular to line AD in view F.C Draw in the projection lines... Draw the projection lines in view 1.e Construct the edge view of plane ABC and point P in view 1. Construct the perpendicular connector in view 1. Its end points are P and Q and it is in true length in this view.. Find line PQ in view F. It is parallel to the view line between F and 1 because it was in true length in view 1. Finally, find line PQ in view H. The solution is now complete. .Click the forward arrow below to repeat the solution. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. EV&TS-3- default update buttonUp "Press the arrow Bbelow." picture ( ("EV&TS-3-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references ("EV&TS-3-"&(2)) default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent update EV&TS-3- default buttonUp repeat_silent fwd_slnt update picture "2" ("EV&TS-3-"&( default update B"forward_silent" = 11 normalgraphic = icon "repeat_silent" fwd_slnt" The Edge View and True Shape of wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable The Edge View and True Shape of a Plane Quiz - 1/4E Quiz 9.10 A plane is in true shape when two lines in that plane are in true length...............h.(if applicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.10. A plane is in true shape when two lines in that plane are in true length.......... Button answer Inconclusive. Two parallel lines may be in true length, but the plane containing them may not be in true shape. (Think 3-D!) misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable The Edge View and True Shape of a Plane Quiz - 2/4E Quiz 9.11 Any view orthogonal to a viewing plane showing a plane in edge view will show that plane in true shape. edge view of a plane will show that plane in true shape..t is true or false. Go to the next page after you have tried answering the question. Quiz 8.11. Any view orthogonal to the edge view of a plane will show that plane in true shape.......... Button answer Inconclusive. The view orthogonal to the edge view of the plane must be parallel to the edge view in order to show the true shape. misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable The Edge View and True Shape of a Plane Quiz - 3/4E Quiz 9.12 There is only one true shape view of a plane.tement is false, or "Inconclusive" (if applicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.12. There is only one true shape view of a planeeeeeeeeee Button answer False. There are two views of the two sides of a plane, plus an infinite number of views created by rotating a true shape view...} misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable The Edge View and True Shape of a Plane Quiz - 4/4E Quiz 9.13 There are three edge views for a triangular bounded plane. false, or "Inconclusive" (if applicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.13. There are three edge views for a triangular bounded plane.......... Button answer False. There are an infinite number of edge views for a plane... misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference Dihedral Angle Descriptive Geometry Problems -- Basic Examples Dihedral Angle Finding the Dihedral angle of two intersecting planes is an extension of the edge view procedure. In this kind of problem, you need to find the edge view of both the intersecting planes. Procedure: 1) Find the line which is the intersection of the two planes, that is, the line which belongs to both planes. 2) Create a view which gives the true length of this line. 3) Create a view perpendicular to the true length line, which will give the edge views of both planes. 4) Measure the dihedral angle between the two edge views. Animation example pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat animationstage animationstage thisanim animerror example buttonclick buttonclick 4thisanim, ref "example" syserrornumber = 0 mmplay clip stage "animationstage" hold Q<> 0 animerror thisanim example buttonclick buttonclick 4thisanim mmstatus clip "playing" mmstop "example" animationstage thisanim animerror buttonclick buttonclick 4thisanim, ref syserrornumber = 0 ) <> mmplay clip stage "animationstage" hold a<> 0 animerror Repeat Animation Click on the background to return to Real Intersections. d@1J!)1 Dihedral Ang - 1 Descriptive Geometry Problems -- Basic Examples Dihedral Angle Example. Find the angle between planes ABC and ABD (the dihedral angle)............................. PostSc color schemes=W indows =WindowsY 0,C0C0C0,8 08080,0,C0 C0C0,8080, 0,C0C0C0,8 08080,0,C0 C0C0,8080, $x$h# $Z$0$Z$ $>&Z$>& &h#>& |1@'X1|' &|1M& <+` u backward forward To see the step-by-step solution, click the forward arrow below.ard arrow below. First, draw in the projection lines. Create view 1 parallel to line AB in view H. We choose line AB because it is the line of intersection of the two planes ABC and ABD. Draw in the projection lines...7 Draw the projection lines in view 1. (The lengths are obtained from view F.) Construct the planes in view 1. Notice that line AB is now in true length. Create view 2 perpendicular to line AB.C Draw in the projection lines... Draw the projection lines in view 2. Construct the planes in view 2. Now line AB is in point view, and you see the two planes ABC and ABD in edge view.I The dihedral angle is measured between the two planes in edge view. The solution is now complete. To see the solution again, click the forward arrow below..^! pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> DiAng- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("DiAng-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " DiAng- forward_silent update default buttonUp repeat_silent fwd_slnt update picture "2" ("DiAng-"&( default update B"forward_silent" = 11 normalgraphic = icon "repeat_silent" fwd_slnt" Dihedral angle (1) wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Dihedral Angle Quiz - 1/1 Quiz 9.14 The dihedral angle is shown when the intersecting line between two planes is in true length...h.insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.14. The dihedral angle is shown when the intersecting line between two planes is in true length.......... Button answer False. The intersecting line must be in point view, which puts both planes in edge view... misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference Distance Between Lines -- Plane Descriptive Geometry Problems -- Basic Examples Distance Between Two Lines -- Plane Method We have already covered finding the distance between two lines by the line method. The plane method allows you solve the problem without creating as many views. It will help you to find the shortest connector faster than the previous method allows. This method involves finding a view where both lines appear parallel, then measuring the perpendicular distance. This works because if the connector is in true length, and both lines are perpendicular to it, then those two lines should appear perpendicular to the connector. This means that the two original skew lines must appear parallel in this view. (Note that this view is not unique.) This is called the plane method because you must create a plane from one of the lines that is parallel to the other line. Finding the edge view of that plane will give you a view where both lines appear parallel. Pay careful attention to the example problems! Problems involving finding the distance between two lines may be more specific than simply asking for the shortest connector. They may ask for something more specific than the shortest horizontal connector, or the shortest connector 40 degrees from the horizontal. pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Distance (PlnMthd) - 1 Descriptive Geometry Problems -- Basic Examples Distance Between Two Lines -- Plane Method Example 1. Find the minimum distance between the skew lines AB and CD................................. t 1986 Microsoft C5 urier NCour CGM Import Filter *1 1*1 backward forward To see the step-by-step solution, click the forward arrow below............. Create a line (in green) in view F parallel to the view line. Make another line in view F parallel to CD. The intersection is point E. We have just created a plane ABE parallel to line CD. Line EA (in green) in view H must also be parallel to line CD in view H. We do not know its correct length yet. Draw in the projection line from point E to determine the length of EA in view H. From point E in view H, we can now draw in line BE, which is in true length (since it was drawn parallel to the view line in view F.) Draw in the projection lines...! Draw in the projection lines... View 1 is created perpendicular to line BE in view H. Since line BE lies on the plane ABE, view 1 is also perpendicular to that plane. Construct the edge view of plane ABC and line CD in view 1. Notice that line AB and CD appear parallel. Now the minimum distance can be found as the perpendicular connector in this view. The solution is now complete. To repeat this solution, click the forawrd arrow. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. DistPM-1- default update buttonUp "Press the arrow Bbelow." picture ( ("DistPM-1-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent update DistPM-1- default buttonUp repeat_silent fwd_slnt update picture "2" ("DistPM-1-"&( default update B"forward_silent" = 11 normalgraphic = icon "repeat_silent" fwd_slnt" Distance (PlnMthd) - 2 Descriptive Geometry Problems -- Basic Examples Distance Between Two Lines -- Plane Method Example 2. Find the shortest connector between lines AB and CD. Show it in all views............................... backward forward To see the step-by-step solution, click the forward arrow below.ard arrow below. First, draw a line in view H parallel to the view line. We will be creating a plane from this line. Draw a line in view H parallel to CD in view H. Where it intersects the first line is point E. We have just created plane ABE, parallel to line CD. Next, draw the edge of the plane parallel to CD in view F. To determine the length of this edge, we draw the projection line. Thus we have located point E in view F.i Connect points E and B to form the line EB, which is now in true length. It is in true length because EB was drawn parallel to the view line in the previous view.{ Draw in the projection lines... Create view 1 perpendicular to line EB in view F. We do this because we want to get the edge view of plane ABE in view 1. Draw the projection lines into view 1... Construct lines AB (edge view of plane ABE) and CD in view 1. Notice that the lines appear parallel in this view. The answer to the problem, the shortest connector, is found in this view.) View 2 is created parallel to line AB and CD in view 1. It is not necessary to create this view to solve the problem, but it is interesting to note that the shortest connector appears in point view in this view.. Now we create projection lines from view 1 back into view F in order to show the shortest connector in all the views, as the problem requests..u The shortest connector is drawn in view F. Projection lines for the shortest connector are drawn into view H. Finally, the shortest connector is drawn in view H. The solution is now complete. Click the forward arrow below to see it again. G/Courie (c) Copy right 1990 pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent DistPM-2- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("DistPM-2-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent DistPM-2- update default buttonUp repeat_silent fwd_slnt update picture "2" (fwd-1) ("DistPM-2-"&( default update B"forward_silent" r = 16 normalgraphic = icon "repeat_silent" fwd_slnt" Distance (PlnMthd) - 3 #F$ %2& 'B( ).* *T+B,>-D.j/ Descriptive Geometry Problems -- Basic Examples Distance Between Two Lines -- Plane Method Example 3. Find the shortest horizontal connector from AB to CD. L v"4 ck the for ward arrow below to Point Viu Access S oftek && M icrosoft C# poration ry Probl ihedral backward forward To see the step-by-step solution, click the forward arrow below.ard arrow below. First, draw a line in view F parallel to the view line. We will be creating a plane from this line. Draw a line in view F parallel to CD in view F. Where it intersects the first line is point E. We have just created plane ABE, parallel to line CD. Next, draw the edge of the plane parallel to CD in view H. To determine the length of this edge, we draw the projection line. Thus we have located point E in view H. Connect points E and B to form the line EB, which is now in true length. It is in true length because EB was drawn parallel to the view line in the previous view./& Draw in the projection lines... Create view 1 perpendicular to line EB in view H. We do this because we want to get the edge view of plane ABE in view 1. Draw the projection lines into view 1... Construct Lines AB and CD in view 1. We see the edge view of plane ABE and lines AB and CD appear parallel. In order to find the horizontal connector, we create view 2 perpendicular to view H. (Thus the horizontal connector should appear in point view in view 2.) Draw the projection lines... Draw the projection lines into view 2. Construct lines AB and CD in view 2. The horizontal connector is in point view at the apparent intersection of these lines. Project the horizontal connector into view 1. Since it is in point view in view 2, the connector lies along the projection line in view 1.;- Project the horizontal connector into view H. The line is created by the intersections between the projection lines and lines AB and CD in view H. The same is done for view F. The horizontal connector should appear horizontal in this view. The solution is now complete. Click the forward arrow to see the solution again.f/ pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> DistPM-3- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("DistPM-3-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " DistPM-3- forward_silent update default buttonUp repeat_silent fwd_slnt update picture "2" (fwd-1) ("DistPM-3-"&( default update B"forward_silent" r = 17 normalgraphic = icon "repeat_silent" fwd_slnt" Distance (PlnMthd) - 4 -X.(/ Descriptive Geometry Problems -- Basic Examples Distance Between Two Lines -- Plane Method Example 4. Find the shortest connector 20 degrees from the horizontal between AB and CD, going downward from AB to CD................................ Solitaire INVERT RESURRECT TEUSEv TPIXEL ETBITMAPDI MENSIONEX FASTW INDOWFRAME CREATEP ATEPALETTE DMSCANL SELECT CLIPRG To see the step-by-step solution, click the forward arrow below.ard arrow below. First, draw a line in view F parallel to the view line. We will be creating a plane from this line. Draw a line in view F parallel to CD in view F. Where it intersects the first line is point E. We have just created plane ABE, parallel to line CD. Next, draw the edge of the plane parallel to CD in view H. To determine the length of this edge, we draw the projection line. Thus we have located point E in view H.q& Connect points E and B to form the line EB, which is now in true length. It is in true length because EB was drawn parallel to the view line in the previous view. Draw in the projection lines... Create view 1 perpendicular to line EB in view H. We do this because we want to get the edge view of plane ABE in view 1. Draw the projection lines into view 1... Construct Lines AB and CD in view 1. We see the edge view of plane ABE, and lines AB and CD appear parallel. In order to find the connector 20 degrees from the horizontal, we create view 2 at 20 degrees from the perpendicular to view H. q+ Draw the projection lines... Draw the projection lines into view 2. Construct lines AB and CD in view 2. Project the connector into view 1. Project the connector into view H. In view F, the connector appears 20 degrees from the horizontal. The solution is now complete.%/ backward forward pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. DistPM-4- default update buttonUp "Press the arrow Bbelow." picture ( ("DistPM-4-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " DistPM-4- forward_silent update default buttonUp repeat_silent fwd_slnt update picture "2" (fwd-1) ("DistPM-4-"&( default update B"forward_silent" r = 17 normalgraphic = icon "repeat_silent" fwd_slnt" 4E7Ne Ccs\\kmir_pp;SN.>:;@@OENOHT?IW6GU?HYLOaVSeUScYYfY\g]_g^`hbbkddmdcj`_f[Za^]d^]cZY_[Z`]\b[[^UTZUV]MNUHGM=:@LGK xutqoqegj@HLQ]d H^m`eq (_},Ke4I[Bae`~| .-cqt[t{;QZNW^cV[ FCZXK^ LinVis - 4 lity - 4 Line Visibility Another Example: A tetrahedron ABCD. Show the visibility of the edges................................................ Draw in the edges of the tetrahedron. Draw in a projection line from the apparent intersection in view H into view F. Since the projection line crosses AC first in view F, line AC must be on top in view H. Since AC is on top, line BD is dashed. Next, a projection line is drawn from the apparent intersection in view F. It hits line AD first in view H, so AD is on top in view F. Line BC is dashed in view F. The solution is now complete. Click the button below to see the example again. (k y'k G' s(;! f*10f*=..+=.`+ /.+10f*10 mouseLeave clearE xplanation && Microso ft Corp. All Righ All Righ To see the step-by-step solution, click the forward button below.e forward button below. (Click on the forward button to see the next step after each new construction and message.) backward forward pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&, " .&, " V, #> .&, " V, #> V, #> .&, " .&, #> LinVis-4- forward_silent Press the forward arrow button below. update buttonUp "Press the arrow Bbelow." picture "6" ("LinVis-4-"&( cfwd-1)) keep y" lock-out working "repeat" force take values that are valid -- clip references update B"forward_silent" forward_silent Basic Problem Solving - 1 BPS-1-2 false BPS-1-4 audioerror BPS-1-3 enterPage BPS-1-2 BPS-1-4 audioerror BPS-1-3 leavePage 4wavPlayable syserrornumber = 0 mmIsOpen clip "BPS-1-2" mmopen audioerror mmclose picture "2" Basic Problem Solving Now some simple problems will be solved using the 2 basic principles and 10 basic geometric relationships. Example 1. Locating a point. Point A is given in views 1 and 3. Find it in view 2............................ First draw a projection line from the point in view 1 into view 2. Remember that the projection line must be orthogonal to the view line between planes 1 and 2. To see the step-by-step solution, click the forward arrow button below.ow button below. Another orthogonal projection line is drawn from point A in view 3. Point A in view 2 is located where the projection lines cross. This must be true in order to satisfy the first principle of orthogonal projection. The solution is now complete. backward forward pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&, " V, #> .&, " .&, #> forward_silent BPS-1- Press the forward arrow button below. update buttonUp "Press the arrow Bbelow." picture ( ("BPS-1-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references update B"forward_silent" forward_silent .&+ +E .&, " forward_silent BPS-1- update default buttonUp repeat_silent fwd_slnt update picture "2" ("BPS-1-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" r"C r" ,`&i,I'i, 'k-I' .I'p/`&p/ BPS - 2 Basic Problem Solving Example 2. Plane ABC and line DE are parallel. Both objects are given in view F. Find D in view H................... b+U#b+w!!,w!P, #!,U#b+U# ge for t for the H eight. To see the step-by-step solution, click the forward arrow button below.ow button below. First, draw a line parallel to line DE anywhere on the plane ABC in view F. Since the problem states that line DE and the plane are parallel, you know that the line you have just drawn is also parallel line DE.lane.u Next, draw projection lines from the intersection of the new line and the edges of the plane. This will allow you to find the line in view H. Draw in the parallel line on the the plane in view H where the projection lines intersect the edges of the plane.S Draw line DE in view H from the point E, which was given. Remember that it must be parallel to the line you just drew on plane ABC in view H.c Draw a projection line from D in view F to locate the end of the line in view H. Finally, trim the line DE to its proper length. The solution is now complete.lick the forward arrow button below. backward forward pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " .&, " V, #> .&, " .&, #> BPS-2- forward_silent Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture "5" ("BPS-2-"&( keep y" lock-out working "repeat" force nam take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " .&, " forward_silent BPS-2- update default buttonUp repeat_silent fwd_slnt update picture "2" ("BPS-2-"&( default update B"forward_silent" normalgraphic = icon "repeat_silent" fwd_slnt" BPS - 3 !,# $ %N&b'\(R) Basic Problem Solving Example 3. Given line PQ and point R, construct a line through R that is perpendicular to PQ at an undetermined point S. Find the length of the connector RS... ge for the Dot &line R1E$)1 && Microso ft Corp. All Righ && Microso ft Corp. All Righ To see the step-by-step solution, click the forward arrow button below.ow button below.......k Draw view 1 parallel to PQ in view F. That way, you can get the true length of PQ in view 1. You will need the true length of PQ in order to find the perpendicular line. Draw the projection lines from view H into view F and up to the view line between F and 1. Remember that projection lines are always perpendicular to view lines. Construct the projection lines in view 1. By the second principle of orthogonal projection, the projection lines in view 1 must have the same lengths as the projection lines in view H. Draw in line PQ (which is now in true length) in view 1. Point R is also located. Line SR, which has not yet been constructed, will appear perpendicular to PQ in this view.)# The view line to view 2 is drawn perpendicular to line PQ in view 1 so as to find PQ in point view in view 2. Draw projection lines up to the view line between views 1 and 2........... 0&Z%-& Line RS is drawn. Point S is on the line PQ. RS must be in true length in this view because it is perpendicular to PQ, which is in point view. You can now measure the length of RS in view 2. Using the lengths between the points in view F and the view line between F and 1, the lengths of the projection lines are found in view 2. Point S is located at the intersection of the projection line and line PQ in view F. The connector RS is found in view F. The point view of line PQ and the point R are located. The next step is to draw in the connector between R and PQ. You solved the problem in the last step, but you should show the line RS in all views. Since RS is perpendicular to PQ (which is in true length in view 1), it will appear perpendicular in view 1. That is the only information you need to construct RS in view 1. The projection line for point S is drawn from view 1 into view F. The projection line from view F into view H is drawn.c, Finally, RS is drawn in view H. Notice that constructing line RS by "working backwards" was very easy. Since we knew that point S was on line PQ, it could simply be found at the intersections of its projection lines and PQ...... backward forward pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&, " V, #> .&, " .&, #> forward_silent Press the forward arrow button below. BPS-3- update buttonUp "Press the arrow Bbelow." picture ( ("BPS-3-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references update B"forward_silent" forward_silent .&+ +E .&, " forward_silent default update BPS-3- buttonUp repeat_silent fwd_slnt update picture "2" ("BPS-3-"&( default update B"forward_silent" c = 15 normalgraphic = icon "repeat_silent" fwd_slnt" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait D"EV&TS-2-12" playing a"EV&TS-2-12" u"EV&TS-2-12" picture "2" allow students click through the steps )their -- own pace ("EV&TS-2-"&(2)) volume cVolume -- control mmplay ("EV&TS-2-"&(2)) ("EV&TS-2-"&( ("EV&TS-2-"&( ("EV&TS-2-"&(fwd)) ("EV&TS-2-"&( +1)) -- ("EV&TS-2-"&( O+1)) ("EV&TS-2-"&( y+1)) -- ("EV&TS-2-"&( yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait D"EV&TS-3-11" playing a"EV&TS-3-11" u"EV&TS-3-11" picture "2" allow students click through the steps )their -- own pace ("EV&TS-3-"&(2)) volume cVolume -- control mmplay ("EV&TS-3-"&(2)) ("EV&TS-3-"&( ("EV&TS-3-"&( ("EV&TS-3-"&(fwd)) ("EV&TS-3-"&( +1)) -- ("EV&TS-3-"&( O+1)) ("EV&TS-3-"&( y+1)) -- ("EV&TS-3-"&( yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait D"DiAng-11" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait D"DistPM-1-11" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait D"DistPM-2-16" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"DistPM-3-2" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"DistPM-4-17" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"IntP&S-1-15" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() audioerror update default normalgraphic = icon "repeat" syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait C"IntS&S-1-10" playing picture "2" allow students click through the steps )their -- own pace "&(2)) volume cVolume -- control mmplay "&(2)) "&(fwd+1)) -- yieldApp() (fwd-1) audioerror update default normalgraphic = icon "repeat" 4wavPlayable syserrornumber = 0 mmIsOpen clip "Shad-3-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "Dvpmt(Con)-3-2" mmopen 1-3" P-4" o-5" audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "Dvpmt(Con)-2-2" mmopen 1-3" P-4" o-5" audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "Dvpmt(Con)-1-2" mmopen 1-3" P-4" o-5" audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "Dvpmt(Cyl)-2-2" mmopen 1-3" P-4" o-5" audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "Dvpmt(Pr)-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntS&S-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "IntS&S-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "DistPM-3-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "DistPM-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "DistPM-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "EV&TS-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "EV&TS-1-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "DistLM-2-2" mmopen audioerror mmclose picture "2" 4wavPlayable syserrornumber = 0 mmIsOpen clip "BPS-3-2" mmopen audioerror mmclose picture "2" 4wavPlayable audioenable syserrornumber = 0 mmIsOpen clip "LinVis-1-1" mmopen }<> 0 audioerror mmclose "Answer" "More" picture "2" 4wavplayable showVolume -- B"repeat" B"reset" B"Answer_silent" B"More_silent" B"reset_silent" clearVolume -- audiodisable -- -- J"Page Title" clearVolume 4wavPlayable, nam audioenable "p13-105" syserrornumber = 0 mmplay clip -<> 0 audioerror TO HANDLE THE ANIMATIONS 4thisanim, ref = "2planes" ) <> mmopen stage "animationstage" hold animerror , nam mmstatus % = "playing" < = "paused" mmstop V wait mmclose showVolume B"repeat" audiodisable 4wavPlayable syserrornumber = 0 mmIsOpen clip "10BasGeom-2" mmclose mmstatus 3p7-105" "playing" Mp7-105" "paused" mmstop kp7-105" wait audioerror picture "2" 4fwd, nam audioenable mmopen W = "p7-105" wavplayable mmplay showVolume -- B"repeat" B"Geometric2" B"Geometric2_silent" clearVolume -- audiodisable -- -- J"Page Title" 4wavPlayable, nam audioenable -- TEMPORARY "Stage" syserrornumber = 0 "p4-105" mmIsOpen clip "projection3-1" mmopen wavplayable mmplay audioerror TO HANDLE THE ANIMATIONS 4thisanim, ref = "2ndprinc" * <> stage "animationstage" hold animerror queue 0 PageId6 FALSE mmstatus 4-105" "playing" 3-105" "paused" mmstop 4-105" wait mmclose showVolume B"Show example" -- B"repeat" example_silent" tstep_silent" B"reset_silent" clearVolume audiodisable -- 4x, y, thiswav, vol, audioon, ref / = 0 x = 1 y = 1 -- @ = "tol24" -- yesplay = -- -- No fields }need be shown seek1 = noanim = x = 1 y = 50 -- = "shole1" -- x = 50 y = 60 -- = "shole2" -- num = 3 -- x = 150 -- y = 160 -- = "shole3" -- -- ("eq" & -- -- Start the sound -- mmvolume -- Always - either frame1 a segment mmseek mmshow Animationstage" Remove (num) dequeue -- ("eq" & J"Page Title" clearVolume 4wavPlayable, nam audioenable "p37-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref mmstatus = "playing" = "paused" mmstop wait showVolume B"repeat" audiodisable J"Page Title" clearVolume 4wavPlayable, nam audioenable "p48-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref mmstatus = "playing" = "paused" mmstop wait showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p60-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "cutplane" mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p64-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "rint" mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p70-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "vint" mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p84-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "rint" -- mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" -- mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p87-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "rint" -- mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" -- mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p93-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "rint" -- mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" -- mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p94-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "rint" -- mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" -- mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p101-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "rint" -- mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" -- mmclose showVolume B"repeat" audiodisable -- the 8will xprompt user leaving 8...WATCH OUT !! -0, -2, 641, 482 -- This stuff added HChris Casey integrated entire tutorial 4audioOn, ref, audioenabled, firstCD addtosysbooks "pagesys.sbk" menusys. statusBar = "Descriptive Geometry" statusbar statuscontrols --Sets CDMediaPath CD-ROM drive CDdrive = & ":\" disable emute evolume isopen 8"misc.tbk" = -- REMOVE final version -- Added try out mmSearchCD property clips allClips = resourceList(" It = -- END ref = windowRefFromHandle (windowHandle retain value returns -- "e28expls.exe" another 6, recall "projection2-1" used Hwidgets X"tb30win.dll" YieldApp() 4can play wave files -- adjust appropriately 4wavPlayable wavplayable = audioon "Title Page" "unavailable" /"2" /"2" clipList audioClip mmPlayable -- -- -- -- /"2" -- /"2" -- "Help" /"2" /"2" inform "The one more that"\ -- && "accompany on your"\ -- && " You may -- && "but voice narration be absent." "wrong" redefines default Toolbook "Print Pages "Control-P" keep printing "Sorry, are xallowed "Hahahahaha. I've broken FALSE syslocksreen= , pressed -- -- turning audion on update B"forward_silent" audioDisable audioEnable convert disables clearVolume -- Have condition... Is less than -- What them apart? they have their own -- scripts these two commands already. B"repeat" B"backward" B"backward_silent" "arrows" -- DO NOTHING "Still needs audiodisable implements showVolume -- DO "still ensure vol carries over -- mmVolume cVolume syserrornumber = 0 *<> 0 audioerror "volBoarder" /"2" "up" /"2" "down" /"2" B"volUp" /"2" B"volDown" /"2" B"speaker" /"2" /"2" /"2" /"2" /"2" "up" /"2" /"2" /"2" /"2" -- Messages "Strategy" "StrategyVw" .vwr" change -- a conducive %a separate -- aforementioned applications Examples 4examples windowOpen B"quit /"2" 8"e28revad. /"2" B"help" /"2" /"2" "title" /"2" /"2" "Main Menu" -- To initiate modified Beven Window. 4modifiedBack, interuptBack windowExit /"2" /"2" /"2" /"2" /"2" /"2" access ." function ! -- message should be placed handler each 4pageHistory[] 4pageShift[] 1] = (1] = dimensions( < 100 \i+1]= 1] = i+1]= 1] = modBack 4histPosition limit ,+2) > P --When clicks the segment 4fwd, mmClose waveAudio CDMediaPAth unlinkDLL " addToSysBooks newBook J"Page Title" clearVolume 4wavPlayable, nam audioenable "p57-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror TO HANDLE THE ANIMATIONS 4thisanim, ref = "linp" & <> mmopen stage "animationstage" hold animerror queue fwd mmstatus = "playing" = "paused" mmstop wait mmclose dequeue update B"Show example" showVolume B"repeat" audiodisable frame = 0 * = "p57a-105" D = "p57b-105" ^ = "p57c-105" cVolume nam = " reset J"Page Title" clearVolume 4wavPlayable, nam audioenable "p45-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror TO HANDLE THE ANIMATIONS 4thisanim, ref = "dihed" ' <> mmopen stage "animationstage" hold animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p74-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "pinp" mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p79-105" syserrornumber = 0 wavplayable mmplay clip D<> 0 audioerror 4thisanim, ref = "2solids" mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p97-105" syserrornumber = 0 wavplayable mmplay clip " E<> 0 audioerror 4thisanim, ref = "cutfill1" mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable "p98-105" syserrornumber = 0 wavplayable mmplay clip " E<> 0 audioerror 4thisanim, ref = "cutfill2" mmopen animerror mmstatus = "paused" = "playing" mmstop wait buttonclick "bg" "example" mmclose showVolume B"repeat" audiodisable clearVolume 4wavPlayable, nam audioenable syserrornumber = 0 "p96-105" wavplayable mmplay clip " U<> 0 audioerror 4thisanim, ref = "rint" -- mmopen animerror mmstatus = "playing" = "paused" mmstop wait buttonclick "bg" "example" -- mmclose showVolume B"repeat" audiodisable DG Problems - 1 forward es (Real Int (Ln & Pln) - 2 Cutting Pln Mthd - 1 Development (Cone) - 1 Point View of a Line Descriptive Geometry Problems -- Basic Examples Point View of a Line Finding the point view of a line is very important in solving many descriptive geometry problems. The point view of a line occurs when both endpoints of a line project to points on top of each other on the orthographic plane. This problem's importance will become more clear as we continue with more advanced problems. Method: 1. First you must find the true length of the line. This is done by creating an orthographic plane parallel to the line. 2. To get the point view, you must then create an orthographic plane perpendicular to the true length of the line. Remember: You must find the true length before you can find the point view! pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat Point View Ex. Descriptive Geometry Problems -- Basic Examples Point View of a Line Example. Find the point view of Line AB....... Arial roll sets creen roll sets roll sets5 PostScript Courier ourie T=yes MMCPL] mApps=12 W=430 && Microso ft Corp. All Righ -h . forward To see the step-by-step solution, click the forward arrow button below.utton below. First draw in the projection lines from view H to view F. Draw the view line between views F and 1 parallel to line AB in view F. Put in the projection lines... Construct the projection lines in view 1. The projection lines have the same lengths as those in view H. Draw line AB in view 1. Remember that it is now in true length.1 Draw view 2 perpendicular to AB in view 1. Draw in the projection line...i Find the length of the projection line into view 1. Notice that the lengths from points A and B in view 1 to the view line between F and 1 are the same. (Which is why there only appears to be one projection line.) Finally, draw in a point representing the point view of the line AB. The solution is now complete. Click the forward arrow to continue. backward pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat forward_silent .&+ +E .&, " forward_silent ptView- update default buttonUp repeat_silent fwd_slnt update picture "2" ("ptView-"&( default update B"forward_silent" = 10 normalgraphic = icon "repeat_silent" fwd_slnt" backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent ptView- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ("ptView-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" Point View of a Line (2) wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Point View of a Line Quiz - 1/2 Quiz 9.6 Any view orthogonal to the point view of a line will show the line in true length...............plicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the ques Quiz 8.6. Any view orthogonal to the point view of a line will show the line in true length................. Button answer True. All views perpendicular to the view with the line in point view are also parallel to the line itself.self.... misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Point View of a Line Quiz - 2/2 Quiz 9.7 Given the front and horizontal views of a line, two additional views are required to establish the point view of the line................... determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.7. Given the front and horizontal views of a line, two additional views are required to establish the point view of the line.......... Button answer - If one view shows the line in true length, only one additional view is required. - If one view shows the line in point view, no additional views are required................ misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" Inconclusive reference Distance Between Lines -- Line M pause repeat Repeat Descriptive Geometry Problems -- Basic Examples Distance Between Lines -- Line Method This method is the first way you will learn to find the distance between two lines. The shortest connector is one that is perpendicular to both lines. Finding the distance between two lines is an application of the point view of a line. This method involves putting one of the original lines in point view, so the connector will appear in true length. Since the connector is in true length, it will also appear perpendicular to the second line. Finding angles between lines by the line method: To find the angle between two skew lines, put both lines in true length. Any view off the point view of a line yields the true length of the line. So create a view from the point view of the first line which also gives the true length of the second line. You will see more clearly how to do this by looking at the following example problems........ audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Distance (LinMthd) - 1 %L)p- Descriptive Geometry Problems -- Basic Examples Distance Between Lines -- Line Method Example 1. Determine the minimum distance between skew lines AB and CD.. AB and CD. nt to Dot & lines Default &Color cotan Courier To see the step-by-step solution, click the forward arrow below.ard arrow below. First, draw in the projection lines in views H and F. Create view 1 parallel to line AB in view H. Draw in the projection lines. Construct the projection lines into view 1 using the lengths from view F. Draw in lines AB and CD. Note that AB is now in true length.+ Create view 2 perpendicular to line AB in view 1. Draw in the projection lines.W Construct the projection lines in view 2 using the lengths of the projection lines between views H and 1./ Draw in line CD and the point view of line AB. The minimum distance, PQ, is in true length in this view, perpendicular to both lines. Line PQ can now be measured. The solution is now complete. backward forward pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent DistLM-1- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("DistLM-1-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent DistLM-1- update default buttonUp repeat_silent fwd_slnt update picture "2" ("DistLM-1-"&( default update B"forward_silent" = 11 normalgraphic = icon "repeat_silent" fwd_slnt" Distance (LinMthd) - 2 Descriptive Geometry Problems -- Basic Examples Distance Between Lines -- Line Method Example 2. Determine the angle between skew lines AB and CD....... backward forward ic Geomet ric - 6 Are you s ure you wa nt toW "e!C"G! ll be repl aced by th e default Substituti served CREATECOMPATIBLEBITMAP3 To see the step-by-step solution, click the forward arrow below..rd arrow below. |#6#y# First draw in the projection lines from view H to view F. Construct view 1 parallel to line AB in view F.A$ Draw in the projection lines... Construct the projection lines into view 1. The lengths of the these projection lines are the same as those in view H. Draw in lines AB and CD in view 1. Note that AB is in true length because view 1 was constructed parallel to AB in view F. Construct view 2 perpendicular to line AB in view 1. Draw in the projection lines... Draw the projection lines into view 2. They have the same lengths as the projection lines in view F. Construct lines CD and AB. Notice that Line AB is in point view.W) Make view 3 parallel to line CD in view 2. r*F*o* Draw in the projection lines... Create the projection lines in view 3. Note that points A and B are along the same line.M+ Construct lines CD and AB in view 3. Now both lines are in true length. The answer to the problem is the acute angle shown when both lines are in true length. Click the forward arrow below to see the solution again. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&+ +E .&, " V, #> .&, " .&, #> forward_silent DistLM-2- Press the forward arrow button below. default update buttonUp "Press the arrow Bbelow." picture ( ("DistLM-2-"&( keep y" lock-out working "repeat" force take values that are valid -- clip references default update B"forward_silent" forward_silent .&+ +E .&, " forward_silent DistLM-2- update default buttonUp repeat_silent fwd_slnt update picture "2" ("DistLM-2-"&( default update B"forward_silent" f = 15 normalgraphic = icon "repeat_silent" fwd_slnt" Distance Between Lines (line Me wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Distance Between Lines (Line Method) Quiz - 1/2 Quiz 9.8 The minimum distance between two skew lines can be determined from a point view of one of the lines...ficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.8. The minimum distance between two skew lines can be determined from a point view of one of the lines.......... Button answer True. When one of the lines is in point view, the shortest connecter is a line from the point to the other line. The connnector is also perpendicular to the latter line.... misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference Distance Between Lines (line Met Distance Between Lines -- Plane LinVis - 4 Distance (PlnMthd) - 2 wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Distance Between Lines (Line Method) Quiz - 2/2 Quiz 9.9 The true angle between two intersecting lines can be seen when one line is in true length.....................nsufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.9. The true angle between two intersecting lines can be seen when one line is in true length.......... Button answer Inconclusive. This is only true if the angle happens to be 90 degrees. Otherwise, both lines must be in true length. misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" Inconclusive reference nms:7==GKV|{i NUU\WWYWT {nmibb ?E GV 7IKm}n Yt{Tmti {ok~tp y|zskid |w}yw :?E=N\ 10 Basic Geometric Int (Pln & Sld) - 2 10 Basic Geometric - 6 ' )n* 607h7 10 Basic Geometric RelationshipsQ 6. Skew lines are lines that are neither parallel nor intersecting. Clicking the button below rotates the skew lines around the y axis to show that they do not actually intersect (it is obvious that they are not parallel).ot parallel.) Skew lines may appear to intersect, but one is always in front of the other at the apparent intersection point. Skew lines do not exist in two dimensions....... Geometric6 Rotate Skew Lines served served served served Skew lines may appear to intersect, but one is always in front of the other at the apparent intersection point. Skew lines do not exist in two dimensions..............llel.) pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat p11-105 paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume nam = "p11-105" audioerror Repeat Geometric6_silent .&+ +E .&, " .&, " default buttonUp picture ( 0"36" default Rotate Skew Lines 10 Basic Geometric - 7 10 Basic Geometric RelationshipsI 7. If two lines are perpendicular, they will appear to be perpendicular in any view in which one or the other is in true length..... Geometric7 Create Views t#%"1 ordfield polygon Notice that the two lines do not necessarily intersect. In this case they do not because they do not have a point in common. Lines a and b appear perpendicular in view 1... pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume p12-105 closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume nam = "p12-105" audioerror Repeat Geometric7_silent .&+ +E default buttonUp picture "2" default Create Views 10 Basic Geometric - 8 10 Basic Geometric Relationships 8. A plane is defined by three points, two intersecting lines, 2 parallel lines, or a point and a line (if the point does not lie on the line). The four pictures below show how these objects can define a plane:::I pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat 10 Basic Geometric - 8 Distance (LinMthd) - 2 10 Basic Geometric - 9 10 Basic Geometric RelationshipsQ 9. A line is parallel to a plane if it is parallel to any line that lies on that plane. To find a line called "m" parallel to the plane ABC and show it in views H and F, click the button "Create Views" below....................................................... First, create a line, called "a," parallel to line "m" on the plane ABC in view H. Then find line "a" in view F. Finally, draw line "m" in view F so that it begins at the given point and is parallel to line "a" in view F..... H. Then find line "a" in view F. Finally, draw line "m" in view F so that it begins at the given point and is parallel to line "a" in view F.e "a" in view F. . 0 -- Handle errors audioerror Repeat Orthogonal Projection and Geomet wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Orthogonal Projection and Geometric Relationships Quiz - 1/5C Quiz 9.1 A plane is defined by two lines. Quiz 8.1. A plane is defined by two lines. ble) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.1. A plane is defined by two lines. real exam, you would be required to write this down.) Go to the next page after you have tried answering the question. Quiz 8.1. A plane is defined by two lines. 1. A plane is defined by two lines. Button answer Inconclusive. A plane can be defined by two parallel or intersecting lines, but not by two skew lines. There is insufficient information to be sure of the answer... wrong buttonUp "wrong" wrong buttonUp "wrong" answer right buttonUp "answer" wrong misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false wrong misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" Inconclusive reference Orthogonal Projection and Geomet LinVis - 2 Dihedral angle (1) Dihedral angle (1) wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Orthogonal Projection and Geometric Relationships Quiz - 2/5G Quiz 9.2 A line is perpendicular to a plane if it is only perpendicular to one line contained in that plane.sufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.2. A line is perpendicular to a plane if it is perpendicular to one line contained in that plane.......... Button answer False. A line must be perpendicular to 2 intersecting lines lying on a plane to be perpendicular to that plane... wrong buttonUp "wrong" answer right buttonUp "answer" wrong misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" reference False inconclusive wrong misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive wrong buttonUp "wrong" wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Orthogonal Projection and Geometric Relationships Quiz - 3/5I Quiz 9.3 Two parallel lines have no points in common..atement is false, or "Inconclusive" (if applicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.3. Two Parallel lines have no points in common.......... Button answer True. Parallel lines can be viewed as two lines, two points, or one line, but they never have a point in common....u wrong buttonUp "wrong" answer right buttonUp "answer" misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Orthogonal Projection and Geometric Relationships Quiz - 4/5[ Quiz 9.4 Two skew lines have one point in common... statement is false, or "Inconclusive" (if applicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.4. Two skew lines have one point in common.......... Button answer False. Skew lines have no points in common.n.I misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal false misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference wrong answer right clearVolume enterPage wrong answer right leavePage audioenable audiodisable clearVolume Hide "wrong" "answer" audioenable audiodisable Orthogonal Projection and Geometric Relationships Quiz - 5/5O Quiz 9.5 A line is parallel to a plane if it is parallel to one line in that plane.............ve" (if applicable) if insufficient information is provided to determine if the statement is true or false. Go to the next page after you have tried answering the question. Quiz 8.5. A line is parallel to a plane if it is parallel to one line in that plane.......... Button answer True. This is Rule 9 of the 10 Basic Geometric Relationships.... misc.tbk correct buttonUp "wrong" "answer" "correct" 8"misc.tbk" false misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal False inconclusive misc.tbk incorrect buttonUp "wrong" "answer" "incorrect" 8"misc.tbk" %modal Inconclusive reference Line Visibility - 1 Line Visibility Line Visibility can easily be determined using descriptive geometry. Using only graphical techniques one can determine which line segments in a drawing are visible and which are not. Lines m and n are shown in two views below. Do they intersect???????????????????????????????????????????????????????? .&+ +E LinVis-1-1 }gyieldApp reset paused playing FcVolume default LinVis-1-2 buttonUp mmstatus clip paused mmstop mmrewind F wait :"LinVis-1-1" playing cVolume mmplay yieldApp() picture "2" "More" B"reset" default The projection line starting at P in view H crosses line n before line m in view F. This means that n is above m in view H.s Answer Lines m and n do not intersect. By taking the projection at the apparent intersection points, we can see that at P, n is above m. At Q, n is in front of m. Answer .&+ +E LinVis-1-1 }gyieldApp Answer paused audioerror FcVolume default buttonUp syserrornumber = 0 mmstatus clip paused mmstop mmrewind s wait "LinVis-1-1" cVolume mmplay audioerror yieldApp() picture "2" "Answer" B"More" default Answer pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat reset .&+ +E Answer paused playing reset default LinVis-1-2 buttonUp mmstatus clip paused mmstop mmrewind M wait :"LinVis-1-2" playing "Answer" picture "2" "More" B"reset" default Reset Answer_silent Answer Answer_silent More_silent buttonUp picture "2" "Answer" B"Answer_silent" B"More_silent" Answer More_silent reset_silent More_silent buttonUp picture "2" "More" B"More_silent" B"reset_silent" reset_silent .&+ +E Answer Answer_silent reset_silent More_silent default buttonUp "Answer" picture "2" "More" B"More_silent" B"reset_silent" B"Answer_silent" default Reset cannot ru n this app lication. *[ [* ![*+! )&&k)g&k) LinVis - 2 lity - 2 Line Visibility Example of Application Show the visibility of the sides of a cube. Click on the cube to see hidden lines. Without visibility (e.g. the hidden lines shown as dashed) it is impossible to tell which side of the cube is in front. By using visibility, the answer is obvious. Using visibility is very important to solving many descriptive geometry problems. Pay close attention to the "visibility test" used in the following examples, as it is used extensively in more complicated intersection problems......... pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat }gyieldApp LinVis-2 paused playing FcVolume wavPlayable buttonUp 4wavPlayable mmstatus clip paused mmstop mmrewind S wait ?"LinVis-2" playing cVolume mmplay yieldApp() "one" "two" }gyieldApp LinVis-2 paused playing FcVolume wavPlayable buttonUp 4wavPlayable mmstatus clip paused mmstop mmrewind S wait ?"LinVis-2" playing cVolume mmplay yieldApp() "two" "one" }gyieldApp LinVis-2 paused playing FcVolume wavPlayable buttonUp 4wavPlayable mmstatus clip paused mmstop mmrewind S wait ?"LinVis-2" playing cVolume mmplay yieldApp() }gyieldApp LinVis-2 paused playing FcVolume wavPlayable buttonUp 4wavPlayable mmstatus clip paused mmstop mmrewind S wait ?"LinVis-2" playing cVolume mmplay yieldApp() LinVis - 3 lity - 3 Line Visibility A tetrahedron is a 4-sided solid. You can visualize it as a simple pyramid. Ex. Problem: The tetrahedron shown below has vertices A, B, C, D. Show the visibility of the edges.................................................................. r)~0r) .r*)0?*~0r)~0 uired XMS memory. Decre PermSR To see the step-by-step solution, click the forward button below............ (Click on the forward button to see the next step after each new construction and message.))))))))))))) Draw in the lines representing the edges of the intersecting planes that make up the sides of the tetrahedron. Dash out line BD in view H to show that it is not visible, as we determined in the last step. Draw a projection line from the apparent intersection in view H at point P. Since the projection line crosses AC before BD in view F, line AC must be on top in view H. Since line AC is on top in view F, line BD is dashed to show that it is not visible. The solution is now complete. Click the button below to see the example again.. backward forward o 8"I Now we do the same thing in view F. An orthogonal projection line is drawn from Q, the apparent intersection in view F. It crosses AC before BD in view H, so AC is on top in view F. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&, " .&, " V, #> .&, " V, #> V, #> .&, " .&, #> forward_silent Press the forward arrow button below. LinVis-3- update buttonUp "Press the arrow Bbelow." picture "6" ("LinVis-3-"&( @-1)) keep y" lock-out working "repeat" force take values that are valid -- clip references update B"forward_silent" forward_silent line. PermS DC1RMECCHIN1.SFL SFLX. The Meaning of Orthogonal 2 Basic Principles of Orthogonal Projection The term orthogonal means "at right angles." Therefore, orthogonal planes are at right angles to each other: Orthogonal projection is the projection of an object onto two viewing planes at right angles. There are 2 basic principles of Orthogonal Projection which are essential to your understanding of descriptive geometry. orward arrow button at the top of the page to continue to the next page. 90 degrees} animationstage animationstage thisanim animerror buttonclick buttonclick 4thisanim, ref syserrornumber = 0 ) <> mmplay clip stage "animationstage" hold a<> 0 animerror Repeat Animation pause audioOn paused audioerror playing buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmStatus clip S = "playing" mmvolume mmPause = "paused" mmPlay notify -- Handle errors audioerror repeat audioOn audioerror buttonClick buttonClick 4nam, audioOn, vol syserrornumber = 0 mmvolume clip mmPlay 0 notify Q<> 0 -- Handle errors audioerror Repeat The Meaning of Orthogonal Development of Prismatic Surface Int (Pln & Pln) Virt - 2 Cut & Fill - 2 Projection -- 2 2 Basic Principles of Orthogonal Projection Basic Principle 1. The projections of a point in space onto two orthogonal projection planes lie on a line that is perpendicular to the intersection of the two planes. Next step projection2-1 Field2 }gyieldApp Last step Next step Field1 paused queue projection2-2 playing FcVolume buttonClick buttonClick mmstatus clip paused mmstop mmrewind 8 wait :"projection2-1" = "playing" 62" -- volume cVolume --control mmplay 2" -- yieldApp() '"Object1" "Field1" "Object2" "Field2" B"Next B"Last queue 2 Next step Object1 Show example projection2-1 }gyieldApp Next step Field1 paused queue Show example audioerror playing Object1 FcVolume buttonUp 4fwd, nam syserrornumber = 0 mmstatus clip "playing" "paused" mmstop f wait "projection2-1" cVolume mmplay audioerror yieldApp() '"Object1" "Field1" B"Show example" B"Next queue 1 Show example Field1 A point in three-dimensional space is projected onto planes H and 1. On plane H it becomes point AH and on plane 1 it becomes A1.................................... Field2 Watch as Plane 1 is folded upwards...... Field3 This is how the planes would appear in a typical descriptive geometry problem. You can see that the line between the two points is perpendicular to the view line............. Last step Field2 }gyieldApp Reset Last step paused queue projection2-3 Field3 projection2-2 playing FcVolume buttonClick buttonClick mmstatus clip paused mmstop mmrewind 8 wait :"projection2-2" = "playing" 63" -- volume cVolume --control mmplay 3" -- yieldApp() picture "Object3" "Object2" "Field2" "Field3" '"Object1" B"Last B"Reset" queue 3 Last step Reset show example pause paused projection2-3 stage repeat playing queue buttonClick buttonClick mmstatus clip paused mmstop mmrewind J wait :"projection2-3" playing example" B"repeat" "stage" queue 0 Reset pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused p3-105 audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume nam = "p3-105" audioerror Repeat Audio show example_silent next step_silent Field1 Object1 queue show example_silent buttonUp '"Object1" "Field1" example_silent" tstep_silent" queue 1 Show example next step_silent next step_silent Field2 last step_silent Field1 queue buttonUp '"Object1" "Field1" "Object2" "Field2" tstep_silent" queue 2 Next step last step_silent Field2 last step_silent reset_silent Field3 queue buttonUp picture "Object3" "Object2" "Field2" "Field3" '"Object1" Jstep_silent" B"reset_silent" queue 3 Last step reset_silent stage queue show example_silent buttonUp example_silent" "stage" queue 0 Reset ,%H.% ,%H.% button pause buttons buttonclick buttonclick buttons = getobjectlist ( &Button stage animationstage animationstage thisanim animerror buttonclick buttonclick 4thisanim, x, y, ref syserrornumber = 0 / <> mmplay clip stage "animationstage" hold d<> 0 animerror Repeat Animation Projection -- 2 Intersection of Two Planes -- Re Intersection of Two Planes -- Vi Intersections of Planes and Soli Projection -- 3 2 Basic Principles of Orthogonal Projection Basic Principle 2. When two orthogonal projection planes are orthogonal to a third projection plane, the distance that a point lies from the third projection plane can be seen twice, each time as the distance along the projection line in each of the first two projection planes......................... Object1 Next step Next step Field2 }gyieldApp Reset Field1 paused queue projection3-2 projection3-1 playing FcVolume buttonUp mmstatus clip paused mmstop mmrewind 8 wait :"projection3-1" = "playing" 62" -- volume cVolume --control mmplay 2" -- yieldApp() '"Object1" "Field1" '"Object2" "Field2" B"Next B"Reset" queue 2 Next step Show example Next step }gyieldApp Field1 paused queue projection3-1 audioerror playing Object1 FcVolume buttonUp mmstatus clip "playing" "paused" mmstop ? wait "projection3-1" -- volume cVolume --control syserrornumber = 0 mmPlay (<> 0 audioerror yieldApp() B"Next '"Object1" "Field1" queue 1 Show example Field1 Planes F and 1 are both orthogonal to horizontal plane H. Note that the projection lines f and f' are the same length. Field2 This is how the planes would appear on paper in a typical descriptive geometry problem. Note that lengths f and f' are the same. Reset repeat field2 pause field1 paused projection3-2 stage Show example playing queue buttonUp 4nam, ref mmstatus clip paused mmstop mmrewind O wait :"projection3-2" playing "field1" "field2" B"Show example" B"repeat" "stage" queue 0 Reset pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat p4-105 paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume nam = "p4-105" audioerror Repeat Audio show example_silent next step_silent Field1 Object1 queue buttonUp tstep_silent" '"Object1" "Field1" queue 1 Show example next step_silent next step_silent Field2 reset_silent Field1 queue buttonUp '"Object1" "Field1" '"Object2" "Field2" tstep_silent" B"reset_silent" queue 2 Next step reset_silent field2 field1 queue show example_silent buttonUp "field2" "field1" example_silent" queue 0 Reset stage animationstage animationstage thisanim animerror buttonclick buttonclick 4thisanim, x, y, ref syserrornumber = 0 / <> mmplay clip stage "animationstage" hold ^<> 0 animerror Repeat Animation Projection -- 3 Distance Between Lines -- Line M Profiles Int (Ln & Pln) - 1 Int (Pln & Pln) - 1 pointProjection 2 Basic Principles of Orthogonal Projection How to Project a Point Point A is shown below in views H and F. We want to project it into view 1, which is adjacent to view H......................... $u" &u" $s% &s% Click the forward button below to see the step-by-step solution to this problem. n the forward arrow button below. ime you click on the forward arrow, a new part of the drawing and new text explaining the next step will be shown. Clicking on the backward arrow will take you back one step. backward forward Step 1: Draw a line connecting point A in view H to point A in view F. The projection line (dashed) should be perpedicular to the view line (solid blue). The first step is always to draw the projection lines for points in adjacent views......3 Step 2: The projection line in view F (from the view line to point A in view F) is labelled f, and the projection line in view H is labelled h. Note: You don't have to label or name projection lines in solving these problems, but it helps in this explanation....... Step 3: Next, draw the projection line between point A in view H and the viewline between views H and 1. Notice that projection lines are always perpendicular to view lines...... Step 4: The next step is to take a record of the length of projection line f. In this example, we created a circle (dashed green) with radius f. This is one of the most accurate methods. You could also use the measure command and record the length on paper. Step 5: A copy of the circle is made and placed so that its center is at the intersection of the projection line between A and the view line between views H and 1. We did this because the projection line into view 1 will have the same length as f. Step 6: Draw projection line f ' perpendicular to the view line. Extend it to the circle so that it will have the same length as the radius of the circle. Thus f ' = f. Step 7: Finally, draw and label point A in view 1. The projection is now complete. Note that this is the projection of only a single point. If you were projecting a line, you would have to go through this process for each of the endpoints. Clicking the forward arrow now will start the example again from the beginning. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat backward_silent .&, " V, #> .&, " .&, #> ptproj- forward_silent There are no previous steps. Press the forward arrow button below. update buttonUp "There are no steps. Press the arrow Bbelow." picture ( ("ptproj-"&( keep y" lock-out working "repeat" force nam take values that valid -- clip references update B"forward_silent" forward_silent .&+ +E .&, " forward_silent ptproj- update default buttonUp repeat_silent fwd_slnt update picture "2" - 1) ("ptproj-"&( update B"forward_silent" default normalgraphic = icon "repeat_silent" fwd_slnt" 10 Basic Geometric - 1 10 Basic Geometric RelationshipsU The 10 Basic Geometric Relationships are used in combination with the 2 Basic Principles of Orthogonal Projection in solving all descriptive geometry problems. It is important that you can visualize and understand these relationships. We will discuss each of the 10 relationships with examples and figures. 1. Two points determine a straight line. Line AB in views H and F is defined by the two points at its ends. The projection lines are drawn from those points. By clicking the button below, you can see the orthogonal planes unfold to give you the flat descriptive geometry picture you see now................... F*E.F* Dot &li GETKERN INGPAIRSL Geometric1 Unfold Orthogonal Planes pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume audioerror Repeat Geometric1_silent .&+ +E default buttonUp picture "5" "perp" default Unfold Orthogonal Planes 10 Basic Geometric - 1 10 Basic Geometric - 10 Line Visibility - 1 Cut-and-Fill Devlopment (Cylin) - 1 Intersection of Two Planes (Rea 10 Basic Geometric - 2 10 Basic Geometric Relationshipso 2. A straight line appears straight, however it is viewed. In the four different views below, the line AB always appears straight... LPT1: strSto Geometric2 Create Views The four views in the descriptive geometry on the left were created using orthogonal viewing planes. The 2 Basic Principles of orthogonal projection were used to find the line in views 1 and 2 from the original views H and F. Clicking the button "Create Views" shows how the process by which line AB is found in views 1 and 2.. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat p7-105 paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume nam = "p7-105" audioerror Repeat Geometric2_silent .&+ +E default buttonUp picture "2" default Create Views 10 Basic Geometric - 2 10 Basic Geometric - 6 Basic Problem Solving - 1 Line Visibility - 2 10 Basic Geometric - 3 10 Basic Geometric RelationshipsG 3. The true length of a line will show in a view where the projection plane and the line are parallel. The views below demonstrate this relationship. The view line between 1 and H is drawn parallel to the line AB in view H. The line in view 1 is then in True Length (TL)..... 7*9"7*h %F#G& $F#8% of field " Geometric3 Create Views pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat p8-105 paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume nam = "p8-105" audioerror Repeat Geometric3_silent .&+ +E default buttonUp picture "2" default Create Views The view line between 1 and H is drawn parallel to the line AB in view H. The line in view 1 is then in True Length (TL)............The four views in the descriptive geometry on the left were created using orthogonal viewing planes. The 2 Basic Principles of orthogonal projection were used to find the line in views 1 and 2 from the original views H and F. Clicking the button "Create Views" shows how the process by which line AB is found in views 1 and 2. 10 Basic Geometric - 3 Edge View and True Shape of a Pl Int (Sld & Sld) - 1 Profiles - 1 Shadow - 1 10 Basic Geometric - 4 10 Basic Geometric Relationshipse 4. Orthogonal projections of parallel lines will always appear as parallel lines, one line, or 2 points. Views constructed below will demonstrate this principle.Note that view 1 shows both lines in true length, and view 2 shows both lines in point view.... Olivetti P G 303 Geometric4 Create Views The true length of a line is found by taking a view parallel to that line, and the point view of a line is found by taking a view perpendicular to the line in true length. At the left, view 1 shows both lines in true length, and view 2 shows both lines in point view. True length and point views will be discussed later in this tutorial...............................................................................................................................................................................views will be discussed further later in this tutorial. pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat paused p9-105 audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume nam = "p9-105" audioerror Repeat Geometric4_silent .&+ +E default buttonUp picture "2" default Create Views 10 Basic Geometric - 4 Intersection of a Line and a Pla Int (Pln & Pln) Real - 2 10 Basic Geometric-5 10 Basic Geometric RelationshipsY 5. Intersecting lines will have a point in common in all viewing planes. This rule can be used to determine if lines intersect. Lines m and n intersect at P..................... )3 K( Remember that the same point projected into two different views must have a projection line that is perpendicular to the view line.K g * g Geometric5 Create Views Since point P is an intersection point, it can be found at the intersection of lines m and n in view 1 without actually projecting point P itself from view H. Also, view 1 was not created at any significant place, it is only one of an infinite number of possible adjacent views.))))) pause paused audioerror playing FcVolume buttonClick buttonClick syserrornumber = 0 mmstatus clip playing mmpause paused mmplay cVolume audioerror repeat p10-105 paused audioerror playing FcVolume closed buttonClick buttonClick syserrornumber = 0 mmstatus clip paused mmstop mmrewind [ wait playing closed mmplay cVolume nam = "p10-105" audioerror Repeat Geometric5_silent .&+ +E default buttonUp picture "2" default Create Views QZ T^ LZ3m}F }%&"v <+U!8 statusBox enterbook Page Title leavePage -0, -2, 641, 482 FALSE J"Page Title" System Arial :CDMEDIAPATH Arial Arial Arial TBKWidgets Arial Arial Arial' Arial System Arial Arial Arial Arial Times New Roman Arial Arial Arial :HDMEDIAPATH System Times New Roman Arial cVolume volume volDown volUp speaker clearVolume -0, -2, 641, 482 up the stuff used Hwidgets X"tbkwin.dll" YieldApp() FALSE J"Page Title" ensure that |value carries over -- mmVolume tclip cVolume volume controls )appropriate clearVolume "up" /"2" "down" /"2" B"volUp" /"2" B"volDown" /"2" B"speaker" /"2" /"2" Graphics Interactive metry DG Help NavBar Page id 9 DG Help Basic Descriptive Geometry Page id 1 pageScrolled pageScrolled currentPage focusWindow scrollPosition > 4470 0,4470 a > 6720 0,6720 &File E&xit Alt+F4 Exit the program &Navigate navigate &First Page Ctrl+Home first &Next Page Ctrl+N &Previous Page Ctrl+P previous &Go to Page... Ctrl+G Introduction intro Go to Introduction chapter Objectives intro1 History intro2 Usefulness intro3 Sketching sketch Go to Sketching chapter Objectives Techniques Objects Cartooning Engineering Drawings formDraw Go to Formal Drawings chapter Objectives Format Working Drawings Othogonal Projection ortho Go to Orthogonal Projection chapter Objectives orth1 Theory orth2 Standard Views orth3 Auxiliary Views orth5 Common Practices orth4 orth6 Pictorials pictorials Go to Pictorials chapter Objectives pict1 Oblique View pict3 Isometric View pict2 Perspective View pict4 pict5 Sections sections Go to Sections chpater Objectives Full Section Half Section Offset Section Broken-Out Section Revolved Section Removed Section Common Practices Dimensioning dimension Go to Dimensioning chapter Objectives Definitions Guidelines Common Shorthand Tolerancing tolerance Go to Tolerancing chapter Objectives Definitions Practical Fabrication Tolerances True Position Datums Surface Features Descriptive Geometry descGeom Go to Descriptive Geometry chapter Objectives Basic Principles and Relationships Line Visibility Distance Between Lines Edge Views and True Shapes Dihedral Angles Intersection of a Line and a Plane Intersection of Two Planes Intersection of a Plane and a Solid Intersection of Solids Surface Developments Contours and Cut-and-Fill Shadows &Main Menu Ctrl+Alt+Home Go to the main menu &Options options &Audio audio On Ctrl+M OnOff Turns audio on or off Volume... setVolume Set the volume of audio Animation... setAnimation Sets the animation speed &Help Instructions F1 tutor How to use the program About the Authors authors Information about the authors Prof. Dennis K. Lieu Chris Casey Su Shien Pang Paul Krueger Acknowledgments others Copyright Info copyright &File E&xit Alt+F4 Exit the program &Navigate navigate &First Page Ctrl+Home first &Next Page Page Down &Previous Page Page Up previous &Go to Page... Ctrl+G Introduction intro Go to Introduction chapter Objectives intro1 History intro2 Usefulness intro3 Sketching sketch Go to Sketching chapter Objectives Techniques Objects Cartooning Engineering Drawings formDraw Go to Formal Drawings chapter Objectives Format Working Drawings Othogonal Projection ortho Go to Orthogonal Projection chapter Objectives orth1 Theory orth2 Standard Views orth3 Auxiliary Views orth4 Common Practices orth5 orth6 Pictorials pictorials Go to Pictorials chapter Objectives pict1 Oblique View pict2 Isometric View pict3 Perspective View pict4 pict5 Sections sections Go to Sections chpater Objectives Full Section Half Section Offset Section Broken-Out Section Revolved Section Removed Section Common Practices Dimensioning dimension Go to Dimensioning chapter Objectives Definitions Guidelines Common Shorthand Tolerancing tolerance Go to Tolerancing chapter Objectives Definitions Practical Fabrication Tolerances True Position Datums Surface Features Descriptive Geometry descGeom Go to Descriptive Geometry chapter Objectives Basic Principles and Relationships Line Visibility Distance Between Lines Edge Views and True Shapes Dihedral Angles Intersection of a Line and a Plane Intersection of Two Planes Intersection of a Plane and a Solid Intersection of Solids Surface Developments Contours and Cut-and-Fill Shadows &Main Menu Ctrl+Alt+Home Go to the main menu &Options options &Audio Mute Ctrl+M OnOff Turns audio on or off Volume... setVolume Set the volume of audio &Page Controls controls Displays/Hides the Navigation Control Bar &Help Instructions F1 tutor How to use the program About the Authors authors Information about the authors Prof. Dennis K. Lieu Chris Casey Su Shien Pang Paul Krueger Allison Okamura Acknowledgments others Copyright Info copyright Dvpmt(Pr)-1-13 Dvpmt(Pr)-1-3 false Dvpmt(Pr)-1-12 Dvpmt(Pr)-1-9 Dvpmt(Pr)-1-2 Dvpmt(Pr)-1-4 Dvpmt(Pr)-1-11 Dvpmt(Pr)-1-10 audioerror Dvpmt(Pr)-1-8 Dvpmt(Pr)-1-5 Dvpmt(Pr)-1-7 Dvpmt(Pr)-1-6 enterPage Dvpmt(Pr)-1-13 Dvpmt(Pr)-1-3 Dvpmt(Pr)-1-12 Dvpmt(Pr)-1-9 Dvpmt(Pr)-1-2 Dvpmt(Pr)-1-4 Dvpmt(Pr)-1-11 Dvpmt(Pr)-1-10 audioerror Dvpmt(Pr)-1-8 Dvpmt(Pr)-1-5 Dvpmt(Pr)-1-7 Dvpmt(Pr)-1-6 leavePage IntS&S-1-7 IntS&S-1-6 false IntS&S-1-3 IntS&S-1-9 IntS&S-1-2 IntS&S-1-4 audioerror IntS&S-1-10 IntS&S-1-8 IntS&S-1-5 enterPage IntS&S-1-7 IntS&S-1-6 IntS&S-1-3 IntS&S-1-9 IntS&S-1-2 IntS&S-1-4 audioerror IntS&S-1-10 IntS&S-1-8 IntS&S-1-5 leavePage DistPM-3-8 DistPM-3-12 false DistPM-3-14 DistPM-3-7 DistPM-3-6 DistPM-3-11 DistPM-3-3 DistPM-3-5 DistPM-3-10 DistPM-3-15 DistPM-3-17 DistPM-3-16 audioerror DistPM-3-13 DistPM-3-9 DistPM-3-2 DistPM-3-4 enterPage DistPM-3-8 DistPM-3-12 DistPM-3-5 DistPM-3-14 DistPM-3-7 DistPM-3-6 DistPM-3-11 DistPM-3-3 DistPM-3-10 DistPM-3-15 DistPM-3-17 DistPM-3-16 audioerror DistPM-3-13 DistPM-3-9 DistPM-3-2 DistPM-3-4 leavePage p84-105 clearVolume audioerror audioenable wavPlayable enterPage p84-105 paused audioerror playing leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable clearVolume p87-105 audioerror audioenable wavPlayable enterPage p87-105 paused audioerror playing leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable p93-105 clearVolume audioerror audioenable wavPlayable enterPage p93-105 paused audioerror playing leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable clearVolume p94-105 audioerror audioenable wavPlayable enterPage paused p94-105 audioerror playing leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable p101-105 clearVolume audioerror audioenable wavPlayable enterPage p101-105 paused audioerror playing leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable <+U!8 <+U!8 <+U!8 ,%H.% projection2-1 pagesys.sbk =^addtosysbooks audioOn wrong misc.tbk false statuscontrols controls Descriptive Geometry firstCD page controls CDdrive allClips recall statusbar wavPlayable audioenabled statusBox right statusBar YieldApp volume tb30win.dll menusys.sbk enterbook Sorry, you are not allowed to print pages from this book. printPages Page Title leavePage false retain forward forward_silent audioEnable syslocksreen audioDisable pressed wavPlayable update enterPage forward forward_silent pause clearVolume repeat backward backward_silent update audioDisable showVolume forward forward_silent pause repeat backward backward_silent update audioEnable audioerror cVolume clearVolume showVolume modifiedBack e28revad.exe quit window interuptBack title windowOpen modifiedBack e28revad.exe quit window title windowExit ,!Jd" ,%H.% ,%H.% pageShift pageHistory pages newPage limit false pageHistory interuptBack histPosition modBack waveAudio tb30win.dll recall wavPlayable leaveBook addToSysBooks p97-105 clearVolume thisanim audioerror cutfill1 audioenable animerror wavPlayable enterPage p97-105 thisanim paused audioerror playing animerror example leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable clearVolume thisanim cutfill2 audioerror audioenable animerror wavPlayable p98-105 enterPage thisanim paused audioerror playing animerror p98-105 example leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable p96-105 clearVolume audioerror audioenable wavPlayable enterPage p96-105 paused audioerror playing leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable 4thisanim, ref = "rint" objectives thisWav audioerror wavplayable enterpage paused thisWav audioerror playing leavepage 4thisWav, vol, wavplayable = "objectives" syserrornumber = 0 mmvolume clip thiswav = mmplay S<> 0 audioerror (mmstatus x"playing" "paused") mmstop Chapter 9: Descriptive Geometryng The objectives of this chapter are to: Generate an understanding of the relationships between lines and planes in space.ce. Demonstrate the solution of 3-dimensional geometry problems by graphical means. Encourage the development of spatial reasoning skills for engineering design. buttonclick buttonclick Begin Lesson Title Page Contours Int (Sld & Sld) - 4 Main Menu 10 Basic Geometric - 7 10 Basic Geometric - 9 Point View of a Line (2) The edge view and true shape of Dihedral Angle Intersection of Two Solids Int (Sld & Sld) - 3 Shadow - 3 Development (Prsm) - 1 Point View of a Line (2) volume Volume: % .&+ +E playing default buttonUp mmstatus clip playing mmstop mmrewind A wait "help" default currentPage focusWindow = "Help" clearExplanation quit window playing buttonUp 4examples "help" mmstatus clip playing mmstop mmclose W wait *targetWindow "Strategy" .tbk" currentPage focusWindow 8"e28revad.exe" clearExplanation buttonClick buttonClick Press the "Quit" button to return to the previous application. click here to remove title Basic Descriptive Geometry unavailable Audio is Un-availablee wrong Again! right You are Correct! .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward IntS&S-3- paused Press the forward arrow button below. playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp Forward paused DistPM-2- Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> DistPM-3- }gyieldApp forward paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward paused Press the forward arrow button below. 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IntS&S-2- audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp Forward IntS&S-3- IntS&S-3-5 paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp Forward paused update audioerror IntS&S-4- playing FcVolume default IntS&S-4-6 buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> .&, " .&, " Dvpmt(Pr)-1-13 }gyieldApp forward paused update audioerror Dvpmt(Pr)-1- playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> .&, " .&, " }gyieldApp forward paused Press the forward arrow button below. audioerror Dvpmt(Pr)-1- playing FcVolume update default buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward Dvpmt(Pr)-2-4 paused Dvpmt(Pr)-2- update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> }gyieldApp forward Dvpmt(Cyl)-1- paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> Dvpmt(Cyl)-2- }gyieldApp forward paused Press the forward arrow button below. audioerror playing FcVolume default update buttonUp .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward paused Dvpmt(Con)-1- update Dvpmt(Con)-1-7 audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> }gyieldApp forward Dvpmt(Con)-2- Dvpmt(Con)-2-6 paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> Dvpmt(Con)-3-6 }gyieldApp forward paused default update audioerror playing FcVolume Dvpmt(Con)-3- buttonUp forward repeat update .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> Shad-2-3 }gyieldApp forward paused update audioerror Shad-2- playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " .&, " .&, " forward_silent update IntP&P(v)-2- default buttonUp repeat_silent fwd_slnt update .&+ +E .&, " .&, " .&, " .&, " .&, " forward_silent IntP&S-1- update default buttonUp repeat_silent fwd_slnt update .&+ +E .&, " .&, " .&, " .&, " .&, " forward_silent IntP&S-2- update default buttonUp repeat_silent fwd_slnt update .&+ +E .&, " .&, " .&, " .&, " forward_silent update default IntS&S-1- buttonUp repeat_silent fwd_slnt update .&+ +E .&, " .&, " .&, " forward_silent update Dvpmt(Pr)-1- default buttonUp repeat_silent fwd_slnt update false Profile-1-5 Profile-1-3 audioerror Profile-1-2 Profile-1-4 enterPage Profile-1-5 Profile-1-3 audioerror Profile-1-2 Profile-1-4 leavePage IntL&P-2-7 IntL&P-2-6 IntL&P-2-13 IntL&P-2-3 false IntL&P-2-12 IntL&P-2-9 IntL&P-2-2 IntL&P-2-4 IntL&P-2-11 audioerror IntL&P-2-10 IntL&P-2-8 IntL&P-2-5 enterPage IntL&P-2-7 IntL&P-2-6 IntL&P-2-13 IntL&P-2-3 IntL&P-2-12 IntL&P-2-9 IntL&P-2-2 IntL&P-2-4 IntL&P-2-11 audioerror IntL&P-2-10 IntL&P-2-8 IntL&P-2-5 leavePage DistPM-1-11 DistPM-1-3 DistPM-1-10 false DistPM-1-9 DistPM-1-2 DistPM-1-4 audioerror DistPM-1-8 DistPM-1-5 DistPM-1-7 DistPM-1-6 enterPage DistPM-1-11 DistPM-1-3 DistPM-1-10 DistPM-1-9 DistPM-1-2 DistPM-1-4 audioerror DistPM-1-8 DistPM-1-5 DistPM-1-7 DistPM-1-6 leavePage false LinVis-3-2 LinVis-3-4 LinVis-3-5 audioerror LinVis-3-6 LinVis-3-3 enterPage LinVis-3-2 LinVis-3-4 LinVis-3-5 audioerror LinVis-3-6 LinVis-3-3 leavePage LinVis-1-1 false audioenable audioerror LinVis-1-2 enterPage LinVis-1-1 Answer audioerror LinVis-1-2 leavePage showVolume false Answer Answer_silent reset_silent pause clearVolume repeat More_silent reset wavplayable audioenable showVolume false Answer Answer_silent reset_silent pause clearVolume repeat More_silent reset wavplayable audiodisable ptproj-4 false ptproj-8 ptproj-5 ptproj-7 ptproj-6 ptproj-3 syslockscren audioerror ptproj-2 leavePage ptproj-4 showVolume false ptproj-8 ptproj-5 clearVolume ptproj-7 ptproj-6 ptproj-3 audioerror wavPlayable ptproj-2 enterPage .&+ +E .&, " .&, #> .&, #> V, #> V, #> V, #> V, #> Dvpmt(Cyl)-1-2 }gyieldApp forward Dvpmt(Cyl)-1- paused update audioerror playing FcVolume default buttonUp forward repeat update .&+ +E .&, " .&, " V, #> V, #> V, #> V, #> .&, " .&, " .&, " .&, " .&, " }gYieldApp forward paused Press the forward arrow button below. audioerror }gyieldApp playing FcVolume default IntS&S-1- update buttonUp animationstage clearVolume p13-105 thisanim audioerror 2planes audioenable animerror enterPage paused thisanim audioerror playing animerror leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable animationstage p15-105 clearVolume thisanim audioerror 2planes audioenable animerror enterPage paused thisanim audioerror playing animerror leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable p8-105 paused audioerror 10BasGeom-3 playing leavePage false p8-105 audioenable audioerror 10BasGeom-3 wavPlayable enterPage Geometric3_silent Geometric3 showVolume false pause clearVolume repeat wavplayable audioenable Geometric3_silent Geometric3 showVolume false pause clearVolume repeat wavplayable audiodisable p10-105 paused 10BasGeom-5 audioerror playing leavePage p10-105 false audioenable 10BasGeom-5 audioerror wavPlayable enterPage showVolume false pause clearVolume repeat Geometric5_silent Geometric5 wavplayable audioenable showVolume false pause clearVolume repeat Geometric5_silent Geometric5 wavplayable audiodisable 10BasGeom-9 paused audioerror playing p14-105 leavePage 10BasGeom-9 false audioenable audioerror wavPlayable p14-105 enterPage showVolume false pause clearVolume repeat Geometric9 Geometric9_silent wavplayable audioenable showVolume false pause clearVolume repeat Geometric9 Geometric9_silent wavplayable audiodisable p32-105 clearVolume audioerror audioenable wavPlayable enterPage p32-105 paused audioerror playing leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable clearVolume audioerror p37-105 audioenable wavPlayable enterPage paused audioerror p37-105 playing leavepage showVolume false pause clearVolume repeat wavPlayable audioenable audioenable audiodisable Point View of a Line ?@A>DDDD UUUVUU eeUUQT @A?>Q ?@?>A=C=FEF9E7:8 ADADD @?>>A=C=FEF9E7:8 ?@A>de ffYUED@@@ EEUUU ?@A>TeUYUUUUUEUU UUUUYUUUQUUQUU% D?@=>A=C=FEF9E7:8 !C@B=> C@A>> @B>>A=C=FEF9E7:8 MECGAUNR MECGAUNR.SFL SFLX`+ zstusrrronomfhiebcic_bacZXd`YYT[`TVcYXgYShgSYf`b^VnnIc}[Yonnrjkuorypwyn~ wnnlnw{ku Je;XgQz -J:2@HGJPST VZ^^cmm} 9KbFy ^<>3%* 6_=2+ 0FOX`][aely ~qmosrgr^ ntfXX]^`afy`2D\e xrtz| U3SPqp711 q]M$O ~@Z(x r!$4_ w}P\+ WowV{w wTpHqrQ QuI>N ovv\?Ol v7ww? 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