home *** CD-ROM | disk | FTP | other *** search
| MacBinary | 1986-01-02 | 13.4 KB | [TEXT/RCMP] |
open in: 
MacOS 8.1
|
Win98
|
DOS
browse contents |
view JSON data
|
view as text
This file was processed as: MacBinary
(archive/macBinary).
| Confidence | Program | Detection | Match Type | Support
|
|---|
| 10%
| dexvert
| MacBinary (archive/macBinary)
| fallback
| Supported |
| 1%
| dexvert
| Text File (text/txt)
| fallback
| Supported |
| 100%
| file
| MacBinary II, Thu Jan 2 11:54:33 1986, modified Thu Jan 2 11:54:33 1986, creator 'RCMP', type ASCII, 13078 bytes "Billiard Parlour.Help" , at 0x3396 286 bytes resource
| default (weak)
| |
| 99%
| file
| data
| default
| |
| 74%
| TrID
| Macintosh plain text (MacBinary)
| default
| |
| 25%
| TrID
| MacBinary 2
| default (weak)
| |
| 100%
| siegfried
| fmt/1762 MacBinary (II)
| default
| |
| 100%
| lsar
| MacBinary
| default
|
|
| id metadata |
|---|
| key | value |
|---|
| macFileType | [TEXT] |
| macFileCreator | [RCMP] |
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 00 15 42 69 6c 6c 69 61 | 72 64 20 50 61 72 6c 6f |..Billia|rd Parlo|
|00000010| 75 72 2e 48 65 6c 70 00 | 00 00 00 00 00 00 00 00 |ur.Help.|........|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000040| 00 54 45 58 54 52 43 4d | 50 00 00 00 00 00 00 00 |.TEXTRCM|P.......|
|00000050| 00 00 00 00 00 33 16 00 | 00 01 1e 9a 40 6d c9 9a |.....3..|....@m..|
|00000060| 40 6d c9 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |@m......|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 7f 88 00 00 |........|........|
|00000080| 0d 47 65 6e 65 72 61 6c | 20 4f 70 65 72 61 74 69 |.General| Operati|
|00000090| 6f 6e 0d 0d 45 61 63 68 | 20 67 61 6d 65 20 68 61 |on..Each| game ha|
|000000a0| 73 20 61 20 43 55 45 20 | 42 41 4c 4c 2c 20 65 78 |s a CUE |BALL, ex|
|000000b0| 63 65 70 74 20 42 69 6c | 6c 69 61 72 64 73 20 68 |cept Bil|liards h|
|000000c0| 61 73 20 74 77 6f 2e 20 | 20 41 20 63 75 65 20 62 |as two. | A cue b|
|000000d0| 61 6c 6c 20 6d 61 79 20 | 62 65 0d 6c 61 75 6e 63 |all may |be.launc|
|000000e0| 68 65 64 20 77 69 74 68 | 20 74 68 65 20 6d 6f 75 |hed with| the mou|
|000000f0| 73 65 2e 20 20 54 68 69 | 73 20 69 73 20 64 6f 6e |se. Thi|s is don|
|00000100| 65 20 62 79 20 70 6c 61 | 63 69 6e 67 20 74 68 65 |e by pla|cing the|
|00000110| 20 6d 6f 75 73 65 20 6e | 65 61 72 20 74 68 65 20 | mouse n|ear the |
|00000120| 62 61 6c 6c 2c 0d 70 72 | 65 73 73 69 6e 67 2c 20 |ball,.pr|essing, |
|00000130| 74 68 65 6e 20 64 72 61 | 67 67 69 6e 67 20 6f 75 |then dra|gging ou|
|00000140| 74 20 61 20 63 75 65 20 | 6c 69 6e 65 2e 20 20 54 |t a cue |line. T|
|00000150| 68 65 20 62 61 6c 6c 20 | 69 73 20 6c 61 75 6e 63 |he ball |is launc|
|00000160| 68 65 64 20 75 70 6f 6e | 20 72 65 6c 65 61 73 65 |hed upon| release|
|00000170| 0d 6f 66 20 74 68 65 20 | 6d 6f 75 73 65 20 62 75 |.of the |mouse bu|
|00000180| 74 74 6f 6e 2c 20 77 69 | 74 68 20 73 70 65 65 64 |tton, wi|th speed|
|00000190| 20 70 72 6f 70 6f 72 74 | 69 6f 6e 61 6c 20 74 6f | proport|ional to|
|000001a0| 20 74 68 65 20 64 72 61 | 67 67 65 64 20 6c 65 6e | the dra|gged len|
|000001b0| 67 74 68 20 6f 66 20 74 | 68 65 0d 63 75 65 20 6c |gth of t|he.cue l|
|000001c0| 69 6e 65 20 61 6e 64 20 | 64 69 72 65 63 74 69 6f |ine and |directio|
|000001d0| 6e 20 64 65 74 65 72 6d | 69 6e 65 64 20 62 79 20 |n determ|ined by |
|000001e0| 74 68 65 20 6c 69 6e 65 | 2e 20 20 4e 6f 20 62 61 |the line|. No ba|
|000001f0| 6c 6c 20 6f 74 68 65 72 | 20 74 68 61 6e 20 63 75 |ll other| than cu|
|00000200| 65 20 0d 62 61 6c 6c 28 | 73 29 20 6d 61 79 20 62 |e .ball(|s) may b|
|00000210| 65 20 73 68 6f 74 3b 20 | 66 6f 72 20 42 69 6c 6c |e shot; |for Bill|
|00000220| 69 61 72 64 73 20 74 68 | 65 20 6c 61 75 6e 63 68 |iards th|e launch|
|00000230| 65 64 20 62 61 6c 6c 20 | 69 73 20 61 6c 77 61 79 |ed ball |is alway|
|00000240| 73 20 74 68 65 20 6f 6e | 65 20 0d 63 6c 6f 73 65 |s the on|e .close|
|00000250| 73 74 20 74 6f 20 74 68 | 65 20 69 6e 69 74 69 61 |st to th|e initia|
|00000260| 6c 20 70 72 65 73 73 2d | 64 6f 77 6e 20 70 6f 69 |l press-|down poi|
|00000270| 6e 74 20 6f 66 20 74 68 | 65 20 6d 6f 75 73 65 2e |nt of th|e mouse.|
|00000280| 0d 0d 42 65 20 63 61 72 | 65 66 75 6c 20 6e 6f 74 |..Be car|eful not|
|00000290| 20 74 6f 20 73 68 6f 6f | 74 20 74 6f 6f 20 68 61 | to shoo|t too ha|
|000002a0| 72 64 20 2d 20 69 66 20 | 79 6f 75 20 27 73 6c 61 |rd - if |you 'sla|
|000002b0| 6d 27 20 61 20 6e 65 61 | 72 62 79 20 6f 62 6a 65 |m' a nea|rby obje|
|000002c0| 63 74 20 62 61 6c 6c 2c | 20 79 6f 75 0d 6d 61 79 |ct ball,| you.may|
|000002d0| 20 67 65 74 20 61 20 27 | 68 6f 70 27 20 61 6e 64 | get a '|hop' and|
|000002e0| 20 6e 6f 74 20 68 69 74 | 20 74 68 65 20 6f 62 6a | not hit| the obj|
|000002f0| 65 63 74 20 73 6f 6c 69 | 64 6c 79 2e 20 20 41 20 |ect soli|dly. A |
|00000300| 6c 69 74 74 6c 65 20 70 | 72 61 63 74 69 63 65 20 |little p|ractice |
|00000310| 77 69 6c 6c 0d 72 65 76 | 65 61 6c 20 74 68 69 73 |will.rev|eal this|
|00000320| 2e 20 20 0d 0d 59 6f 75 | 20 63 61 6e 20 61 72 72 |. ..You| can arr|
|00000330| 61 6e 67 65 20 62 61 6c | 6c 73 20 62 79 20 68 6f |ange bal|ls by ho|
|00000340| 6c 64 69 6e 67 20 64 6f | 77 6e 20 74 68 65 20 4f |lding do|wn the O|
|00000350| 70 74 69 6f 6e 20 6b 65 | 79 20 6f 66 20 74 68 65 |ption ke|y of the|
|00000360| 20 6b 65 79 62 6f 61 72 | 64 20 77 68 69 6c 65 0d | keyboar|d while.|
|00000370| 79 6f 75 20 70 72 65 73 | 73 20 6f 6e 2c 20 61 6e |you pres|s on, an|
|00000380| 64 20 73 75 62 73 65 71 | 75 65 6e 74 6c 79 20 64 |d subseq|uently d|
|00000390| 72 61 67 2c 20 61 20 62 | 61 6c 6c 2e 20 20 41 20 |rag, a b|all. A |
|000003a0| 6d 65 6e 75 20 69 74 65 | 6d 20 27 41 72 72 61 6e |menu ite|m 'Arran|
|000003b0| 67 65 20 42 61 6c 6c 73 | 27 0d 61 6c 73 6f 20 70 |ge Balls|'.also p|
|000003c0| 65 72 66 6f 72 6d 73 20 | 74 68 69 73 20 66 75 6e |erforms |this fun|
|000003d0| 63 74 69 6f 6e 2c 20 62 | 75 74 20 6d 75 73 74 20 |ction, b|ut must |
|000003e0| 62 65 20 64 65 73 65 6c | 65 63 74 65 64 20 61 66 |be desel|ected af|
|000003f0| 74 65 72 20 61 72 72 61 | 6e 67 65 6d 65 6e 74 20 |ter arra|ngement |
|00000400| 69 73 0d 63 6f 6d 70 6c | 65 74 65 2e 20 20 0d 3e |is.compl|ete. .>|
|00000410| 3e 0d 41 20 68 61 6e 64 | 2d 63 75 72 73 6f 72 20 |>.A hand|-cursor |
|00000420| 72 65 73 75 6c 74 73 20 | 77 68 65 6e 65 76 65 72 |results |whenever|
|00000430| 20 62 61 6c 6c 73 20 6d | 61 79 20 62 65 20 61 72 | balls m|ay be ar|
|00000440| 72 61 6e 67 65 64 2e 20 | 20 53 75 6e 6b 20 0d 62 |ranged. | Sunk .b|
|00000450| 61 6c 6c 73 20 64 65 70 | 6f 73 69 74 65 64 20 6e |alls dep|osited n|
|00000460| 65 61 72 20 74 68 65 20 | 62 6f 74 74 6f 6d 20 6f |ear the |bottom o|
|00000470| 66 20 74 68 65 20 73 63 | 72 65 65 6e 20 63 61 6e |f the sc|reen can|
|00000480| 20 62 65 20 6d 6f 76 65 | 64 20 62 61 63 6b 20 6f | be move|d back o|
|00000490| 6e 74 6f 20 74 68 65 20 | 0d 74 61 62 6c 65 20 77 |nto the |.table w|
|000004a0| 69 74 68 6f 75 74 20 72 | 65 63 6f 75 72 73 65 20 |ithout r|ecourse |
|000004b0| 74 6f 20 74 68 65 20 4f | 70 74 69 6f 6e 20 6b 65 |to the O|ption ke|
|000004c0| 79 20 6f 72 20 6d 65 6e | 75 2e 0d 0d 45 4e 47 4c |y or men|u...ENGL|
|000004d0| 49 53 48 20 69 73 20 69 | 6e 76 6f 6b 65 64 20 62 |ISH is i|nvoked b|
|000004e0| 79 20 73 65 6c 65 63 74 | 69 6e 67 20 73 61 6d 65 |y select|ing same|
|000004f0| 20 6f 6e 20 74 68 65 20 | 4f 70 74 69 6f 6e 73 20 | on the |Options |
|00000500| 6d 65 6e 75 2c 20 75 70 | 6f 6e 20 77 68 69 63 68 |menu, up|on which|
|00000510| 20 61 20 0d 70 69 63 74 | 75 72 65 20 6f 66 20 74 | a .pict|ure of t|
|00000520| 68 65 20 63 75 65 20 62 | 61 6c 6c 20 66 61 63 65 |he cue b|all face|
|00000530| 20 61 70 70 65 61 72 73 | 20 74 6f 20 74 68 65 20 | appears| to the |
|00000540| 72 69 67 68 74 20 6f 66 | 20 74 68 65 20 74 61 62 |right of| the tab|
|00000550| 6c 65 2e 20 54 68 65 20 | 77 68 69 74 65 20 0d 73 |le. The |white .s|
|00000560| 70 6f 74 20 73 68 6f 77 | 73 20 77 68 65 72 65 20 |pot show|s where |
|00000570| 74 68 65 20 6e 65 78 74 | 20 73 68 6f 74 20 77 69 |the next| shot wi|
|00000580| 6c 6c 20 73 74 72 69 6b | 65 20 74 68 65 20 63 75 |ll strik|e the cu|
|00000590| 65 20 62 61 6c 6c 2e 20 | 20 4e 6f 74 65 20 74 77 |e ball. | Note tw|
|000005a0| 6f 20 74 68 69 6e 67 73 | 3a 20 0d 74 68 65 20 73 |o things|: .the s|
|000005b0| 70 6f 74 20 72 65 76 65 | 72 74 73 20 74 6f 20 74 |pot reve|rts to t|
|000005c0| 68 65 20 64 65 66 61 75 | 6c 74 20 70 6f 73 69 74 |he defau|lt posit|
|000005d0| 69 6f 6e 20 61 66 74 65 | 72 20 65 61 63 68 20 73 |ion afte|r each s|
|000005e0| 68 6f 74 2c 20 61 6e 64 | 20 74 68 69 73 20 64 65 |hot, and| this de|
|000005f0| 66 61 75 6c 74 20 0d 6c | 69 65 73 20 61 74 20 74 |fault .l|ies at t|
|00000600| 68 65 20 74 68 65 6f 72 | 65 74 69 63 61 6c 20 7a |he theor|etical z|
|00000610| 65 72 6f 2d 65 6e 67 6c | 69 73 68 20 68 65 69 67 |ero-engl|ish heig|
|00000620| 68 74 20 6f 66 20 37 2f | 35 20 72 61 64 69 75 73 |ht of 7/|5 radius|
|00000630| 2e 0d 0d 54 68 65 20 63 | 6f 6c 6c 69 73 69 6f 6e |...The c|ollision|
|00000640| 20 73 6f 75 6e 64 73 20 | 6d 61 79 20 62 65 20 74 | sounds |may be t|
|00000650| 75 72 6e 65 64 20 6f 6e | 20 6f 72 20 6f 66 66 20 |urned on| or off |
|00000660| 76 69 61 20 74 68 65 20 | 4f 70 74 69 6f 6e 73 20 |via the |Options |
|00000670| 6d 65 6e 75 20 69 74 65 | 6d 0d 27 53 6f 75 6e 64 |menu ite|m.'Sound|
|00000680| 27 2e 20 20 4c 69 6b 65 | 77 69 73 65 2c 20 27 45 |'. Like|wise, 'E|
|00000690| 6e 67 6c 69 73 68 27 20 | 68 61 73 20 74 68 65 20 |nglish' |has the |
|000006a0| 65 66 66 65 63 74 20 6f | 66 20 68 69 64 69 6e 67 |effect o|f hiding|
|000006b0| 20 6f 72 20 62 72 69 6e | 67 69 6e 67 0d 62 61 63 | or brin|ging.bac|
|000006c0| 6b 20 74 68 65 20 45 6e | 67 6c 69 73 68 20 64 69 |k the En|glish di|
|000006d0| 73 70 6c 61 79 2e 20 20 | 54 68 69 73 20 6d 65 6e |splay. |This men|
|000006e0| 75 20 69 74 65 6d 20 64 | 6f 65 73 20 6e 6f 74 20 |u item d|oes not |
|000006f0| 61 66 66 65 63 74 20 74 | 68 65 20 76 61 6c 75 65 |affect t|he value|
|00000700| 20 6f 66 0d 45 6e 67 6c | 69 73 68 2c 20 77 68 69 | of.Engl|ish, whi|
|00000710| 63 68 20 69 6e 20 61 6e | 79 20 63 61 73 65 20 61 |ch in an|y case a|
|00000720| 6c 77 61 79 73 20 72 65 | 76 65 72 74 73 20 74 6f |lways re|verts to|
|00000730| 20 7a 65 72 6f 20 61 66 | 74 65 72 20 61 6e 79 20 | zero af|ter any |
|00000740| 73 68 6f 74 2e 0d 3e 3e | 0d 53 63 6f 72 69 6e 67 |shot..>>|.Scoring|
|00000750| 20 6d 61 79 20 62 65 20 | 70 65 72 66 6f 72 6d 65 | may be |performe|
|00000760| 64 20 77 69 74 68 20 74 | 68 65 20 31 30 30 2d 63 |d with t|he 100-c|
|00000770| 61 72 72 6f 6d 20 73 63 | 6f 72 69 6e 67 20 72 61 |arrom sc|oring ra|
|00000780| 63 6b 20 61 74 6f 70 20 | 74 68 65 20 73 63 72 65 |ck atop |the scre|
|00000790| 65 6e 2e 20 20 0d 57 68 | 65 6e 20 75 73 69 6e 67 |en. .Wh|en using|
|000007a0| 20 74 68 65 20 63 61 72 | 72 6f 6d 73 2c 20 73 69 | the car|roms, si|
|000007b0| 6d 70 6c 79 20 64 72 61 | 67 20 63 61 72 72 6f 6d |mply dra|g carrom|
|000007c0| 73 20 74 6f 20 61 6e 64 | 20 66 72 6f 2e 20 20 54 |s to and| fro. T|
|000007d0| 68 65 20 54 55 52 4e 20 | 53 43 4f 52 45 20 69 73 |he TURN |SCORE is|
|000007e0| 20 0d 61 6c 77 61 79 73 | 20 72 65 70 6f 72 74 65 | .always| reporte|
|000007f0| 64 20 69 6e 20 74 68 65 | 20 63 65 6e 74 72 61 6c |d in the| central|
|00000800| 20 64 69 73 70 6c 61 79 | 20 6a 75 73 74 20 62 65 | display| just be|
|00000810| 6c 6f 77 20 74 68 65 20 | 63 61 72 72 6f 6d 20 72 |low the |carrom r|
|00000820| 61 63 6b 2e 20 20 54 68 | 69 73 20 0d 69 73 20 74 |ack. Th|is .is t|
|00000830| 68 65 20 6e 75 6d 62 65 | 72 20 6f 66 20 62 61 6c |he numbe|r of bal|
|00000840| 6c 73 20 73 75 6e 6b 20 | 6f 6e 20 74 68 65 20 70 |ls sunk |on the p|
|00000850| 72 65 76 69 6f 75 73 20 | 74 75 72 6e 2e 20 20 46 |revious |turn. F|
|00000860| 6f 72 20 73 74 72 61 69 | 67 68 74 66 6f 72 77 61 |or strai|ghtforwa|
|00000870| 72 64 20 0d 74 75 72 6e | 73 20 74 68 65 20 6e 75 |rd .turn|s the nu|
|00000880| 6d 62 65 72 20 77 69 6c | 6c 20 62 65 20 74 68 65 |mber wil|l be the|
|00000890| 20 61 6d 6f 75 6e 74 20 | 74 6f 20 61 64 64 20 69 | amount |to add i|
|000008a0| 6e 74 6f 20 74 68 65 20 | 63 75 72 72 65 6e 74 20 |nto the |current |
|000008b0| 70 6c 61 79 65 72 27 73 | 20 0d 63 75 6d 75 6c 61 |player's| .cumula|
|000008c0| 74 69 76 65 20 73 63 6f | 72 65 2e 20 20 46 6f 72 |tive sco|re. For|
|000008d0| 20 73 63 72 61 74 63 68 | 65 73 2c 20 65 74 63 2e | scratch|es, etc.|
|000008e0| 20 6f 6e 65 20 68 61 73 | 20 74 6f 20 63 61 72 65 | one has| to care|
|000008f0| 66 75 6c 6c 79 20 61 70 | 70 6c 79 20 77 68 61 74 |fully ap|ply what|
|00000900| 65 76 65 72 20 0d 73 63 | 6f 72 69 6e 67 20 72 75 |ever .sc|oring ru|
|00000910| 6c 65 73 20 68 61 76 65 | 20 62 65 65 6e 20 61 67 |les have| been ag|
|00000920| 72 65 65 64 20 75 70 6f | 6e 3b 20 69 6e 20 73 75 |reed upo|n; in su|
|00000930| 63 68 20 63 61 73 65 73 | 20 74 68 65 20 63 65 6e |ch cases| the cen|
|00000940| 74 72 61 6c 20 64 69 73 | 70 6c 61 79 20 69 73 20 |tral dis|play is |
|00000950| 0d 69 6e 74 65 6e 64 65 | 64 20 61 73 20 61 20 67 |.intende|d as a g|
|00000960| 75 69 64 65 2c 20 6e 6f | 74 20 61 6e 20 61 63 74 |uide, no|t an act|
|00000970| 75 61 6c 20 73 63 6f 72 | 65 2e 0d 0d 53 43 52 41 |ual scor|e...SCRA|
|00000980| 54 43 48 45 53 20 61 72 | 65 20 72 65 70 6f 72 74 |TCHES ar|e report|
|00000990| 65 64 20 28 61 73 20 62 | 65 65 70 73 29 20 77 68 |ed (as b|eeps) wh|
|000009a0| 65 6e 20 74 68 65 20 63 | 75 65 20 62 61 6c 6c 20 |en the c|ue ball |
|000009b0| 69 73 20 73 75 6e 6b 2c | 20 6f 72 20 69 6e 0d 38 |is sunk,| or in.8|
|000009c0| 2d 62 61 6c 6c 20 77 68 | 65 6e 20 74 68 65 20 38 |-ball wh|en the 8|
|000009d0| 20 69 73 20 73 75 6e 6b | 2e 20 20 46 6f 72 20 63 | is sunk|. For c|
|000009e0| 75 65 20 62 61 6c 6c 20 | 73 63 72 61 74 63 68 65 |ue ball |scratche|
|000009f0| 73 2c 20 74 68 65 20 62 | 61 6c 6c 20 69 73 20 70 |s, the b|all is p|
|00000a00| 6c 61 63 65 64 0d 69 6e | 20 74 68 65 20 72 69 67 |laced.in| the rig|
|00000a10| 68 74 2d 68 61 6e 64 20 | 68 61 6c 66 20 6f 66 20 |ht-hand |half of |
|00000a20| 74 68 65 20 74 61 62 6c | 65 2c 20 61 74 20 61 6e |the tabl|e, at an|
|00000a30| 20 6f 70 65 6e 20 6c 6f | 63 61 74 69 6f 6e 2e 20 | open lo|cation. |
|00000a40| 20 41 73 20 75 73 75 61 | 6c 20 74 68 65 0d 63 75 | As usua|l the.cu|
|00000a50| 65 20 62 61 6c 6c 20 6d | 61 79 20 62 65 20 6d 6f |e ball m|ay be mo|
|00000a60| 76 65 64 20 77 69 74 68 | 20 74 68 65 20 4f 70 74 |ved with| the Opt|
|00000a70| 69 6f 6e 20 6b 65 79 20 | 6f 72 20 74 68 65 20 4f |ion key |or the O|
|00000a80| 70 74 69 6f 6e 73 20 6d | 65 6e 75 20 65 6e 74 72 |ptions m|enu entr|
|00000a90| 79 0d 27 41 72 72 61 6e | 67 65 20 42 61 6c 6c 73 |y.'Arran|ge Balls|
|00000aa0| 27 2e 0d 3e 3e 0d 0d 54 | 68 65 20 47 61 6d 65 73 |'..>>..T|he Games|
|00000ab0| 0d 0d 49 6e 20 42 49 4c | 4c 49 41 52 44 53 20 74 |..In BIL|LIARDS t|
|00000ac0| 68 65 20 70 6c 61 79 65 | 72 73 20 61 6c 74 65 72 |he playe|rs alter|
|00000ad0| 6e 61 74 65 20 62 65 74 | 77 65 65 6e 20 74 68 65 |nate bet|ween the|
|00000ae0| 20 73 70 6f 74 74 65 64 | 20 61 6e 64 20 75 6e 73 | spotted| and uns|
|00000af0| 70 6f 74 74 65 64 20 63 | 75 65 0d 62 61 6c 6c 73 |potted c|ue.balls|
|00000b00| 2e 20 20 41 20 73 63 6f | 72 65 20 69 73 20 6c 6f |. A sco|re is lo|
|00000b10| 67 67 65 64 20 6f 6e 20 | 74 68 65 20 63 65 6e 74 |gged on |the cent|
|00000b20| 72 61 6c 20 64 69 73 70 | 6c 61 79 20 77 68 65 6e |ral disp|lay when|
|00000b30| 20 74 68 65 20 63 75 72 | 72 65 6e 74 20 63 75 65 | the cur|rent cue|
|00000b40| 20 62 61 6c 6c 0d 73 74 | 72 69 6b 65 73 20 74 68 | ball.st|rikes th|
|00000b50| 65 20 6f 74 68 65 72 20 | 74 77 6f 20 6f 62 6a 65 |e other |two obje|
|00000b60| 63 74 20 62 61 6c 6c 73 | 2c 20 62 75 74 20 6f 6e |ct balls|, but on|
|00000b70| 6c 79 20 69 66 20 74 68 | 72 65 65 20 72 61 69 6c |ly if th|ree rail|
|00000b80| 73 20 61 72 65 20 68 69 | 74 0d 62 79 20 74 68 65 |s are hi|t.by the|
|00000b90| 20 63 75 65 20 62 61 6c | 6c 20 62 65 66 6f 72 65 | cue bal|l before|
|00000ba0| 20 74 68 65 20 73 65 63 | 6f 6e 64 20 6f 62 6a 65 | the sec|ond obje|
|00000bb0| 63 74 20 62 61 6c 6c 20 | 69 73 20 73 74 72 75 63 |ct ball |is struc|
|00000bc0| 6b 2e 0d 0d 49 6e 20 53 | 54 52 41 49 47 48 54 20 |k...In S|TRAIGHT |
|00000bd0| 50 4f 4f 4c 20 74 68 65 | 20 72 61 63 6b 20 69 73 |POOL the| rack is|
|00000be0| 20 6e 75 6d 62 65 72 65 | 64 20 63 6f 6e 73 65 63 | numbere|d consec|
|00000bf0| 75 74 69 76 65 6c 79 20 | 66 72 6f 6d 20 31 20 74 |utively |from 1 t|
|00000c00| 68 72 6f 75 67 68 20 31 | 35 2c 20 61 6e 64 0d 73 |hrough 1|5, and.s|
|00000c10| 75 6e 6b 20 62 61 6c 6c | 73 20 77 69 6c 6c 20 62 |unk ball|s will b|
|00000c20| 65 20 64 65 70 6f 73 69 | 74 65 64 20 69 6e 20 6e |e deposi|ted in n|
|00000c30| 75 6d 65 72 69 63 61 6c | 20 6f 72 64 65 72 2e 0d |umerical| order..|
|00000c40| 0d 49 6e 20 38 2d 42 41 | 4c 4c 20 74 68 65 20 72 |.In 8-BA|LL the r|
|00000c50| 61 63 6b 20 68 61 73 20 | 61 20 63 65 6e 74 72 61 |ack has |a centra|
|00000c60| 6c 20 38 20 62 61 6c 6c | 2c 20 77 69 74 68 20 61 |l 8 ball|, with a|
|00000c70| 20 63 65 72 74 61 69 6e | 20 70 61 74 74 65 72 6e | certain| pattern|
|00000c80| 20 6f 66 20 73 6f 6c 69 | 64 73 0d 61 6e 64 20 73 | of soli|ds.and s|
|00000c90| 74 72 69 70 65 73 20 73 | 75 72 72 6f 75 6e 64 69 |tripes s|urroundi|
|00000ca0| 6e 67 2c 20 61 6e 64 20 | 73 75 6e 6b 20 62 61 6c |ng, and |sunk bal|
|00000cb0| 6c 73 20 61 72 65 20 64 | 65 70 6f 73 69 74 65 64 |ls are d|eposited|
|00000cc0| 20 77 69 74 68 20 73 6f | 6c 69 64 73 20 74 6f 20 | with so|lids to |
|00000cd0| 74 68 65 0d 6c 65 66 74 | 20 61 6e 64 20 73 74 72 |the.left| and str|
|00000ce0| 69 70 65 73 20 74 6f 20 | 74 68 65 20 72 69 67 68 |ipes to |the righ|
|00000cf0| 74 2e 20 20 54 68 65 72 | 65 20 61 72 65 20 6d 61 |t. Ther|e are ma|
|00000d00| 6e 79 20 64 69 66 66 65 | 72 65 6e 74 20 27 66 61 |ny diffe|rent 'fa|
|00000d10| 76 6f 72 69 74 65 27 20 | 38 2d 42 61 6c 6c 20 0d |vorite' |8-Ball .|
|00000d20| 72 61 63 6b 20 63 6f 6e | 66 69 67 75 72 61 74 69 |rack con|figurati|
|00000d30| 6f 6e 73 3a 20 20 74 68 | 65 20 6f 6e 65 20 63 68 |ons: th|e one ch|
|00000d40| 6f 73 65 6e 20 66 6f 72 | 20 74 68 69 73 20 70 72 |osen for| this pr|
|00000d50| 6f 67 72 61 6d 20 67 75 | 61 72 61 6e 74 65 65 73 |ogram gu|arantees|
|00000d60| 20 61 20 66 61 69 72 6c | 79 20 0d 65 76 65 6e 20 | a fairl|y .even |
|00000d70| 64 69 73 74 72 69 62 75 | 74 69 6f 6e 20 6f 66 20 |distribu|tion of |
|00000d80| 73 74 72 69 70 65 2f 73 | 6f 6c 69 64 20 70 6c 61 |stripe/s|olid pla|
|00000d90| 63 65 6d 65 6e 74 20 6f | 76 65 72 20 61 20 6e 75 |cement o|ver a nu|
|00000da0| 6d 62 65 72 20 6f 66 20 | 62 72 65 61 6b 73 2e 20 |mber of |breaks. |
|00000db0| 0d 3e 3e 0d 49 6e 20 39 | 2d 42 41 4c 4c 20 74 68 |.>>.In 9|-BALL th|
|00000dc0| 65 20 72 61 63 6b 20 68 | 61 73 20 61 20 63 65 6e |e rack h|as a cen|
|00000dd0| 74 72 61 6c 20 39 20 62 | 61 6c 6c 2c 20 77 69 74 |tral 9 b|all, wit|
|00000de0| 68 20 61 20 63 65 72 74 | 61 69 6e 20 70 61 74 74 |h a cert|ain patt|
|00000df0| 65 72 6e 20 6f 66 20 62 | 61 6c 6c 73 20 31 0d 74 |ern of b|alls 1.t|
|00000e00| 68 72 6f 75 67 68 20 38 | 20 73 75 72 72 6f 75 6e |hrough 8| surroun|
|00000e10| 64 69 6e 67 2e 20 20 53 | 75 6e 6b 20 62 61 6c 6c |ding. S|unk ball|
|00000e20| 73 20 61 72 65 20 64 65 | 70 6f 73 69 74 65 64 20 |s are de|posited |
|00000e30| 69 6e 20 6e 75 6d 65 72 | 69 63 61 6c 20 6f 72 64 |in numer|ical ord|
|00000e40| 65 72 2e 0d 0d 49 6e 20 | 53 4e 4f 4f 4b 45 52 20 |er...In |SNOOKER |
|00000e50| 74 68 65 72 65 20 61 72 | 65 20 66 69 66 74 65 65 |there ar|e fiftee|
|00000e60| 6e 20 75 6e 6d 61 72 6b | 65 64 20 62 61 6c 6c 73 |n unmark|ed balls|
|00000e70| 20 69 6e 20 74 68 65 20 | 72 61 63 6b 2c 20 77 69 | in the |rack, wi|
|00000e80| 74 68 20 6e 75 6d 62 65 | 72 65 64 20 0d 62 61 6c |th numbe|red .bal|
|00000e90| 6c 73 20 32 2c 33 2c 34 | 2c 35 2c 36 2c 37 20 69 |ls 2,3,4|,5,6,7 i|
|00000ea0| 6e 20 73 70 65 63 69 66 | 69 63 20 70 6c 61 63 65 |n specif|ic place|
|00000eb0| 73 2e 20 20 53 75 6e 6b | 20 62 61 6c 6c 73 20 61 |s. Sunk| balls a|
|00000ec0| 72 65 20 64 65 70 6f 73 | 69 74 65 64 20 69 6e 20 |re depos|ited in |
|00000ed0| 74 77 6f 20 0d 67 72 6f | 75 70 73 3a 20 6e 75 6d |two .gro|ups: num|
|00000ee0| 62 65 72 65 64 20 61 6e | 64 20 75 6e 6d 61 72 6b |bered an|d unmark|
|00000ef0| 65 64 2e 0d 0d 49 6e 20 | 53 4c 4f 50 20 74 68 65 |ed...In |SLOP the|
|00000f00| 72 65 20 61 72 65 20 6f | 70 74 69 6f 6e 61 6c 20 |re are o|ptional |
|00000f10| 72 61 63 6b 20 73 69 7a | 65 73 2c 20 61 6e 64 20 |rack siz|es, and |
|00000f20| 61 6c 6c 20 6f 62 6a 65 | 63 74 20 62 61 6c 6c 73 |all obje|ct balls|
|00000f30| 20 61 72 65 20 75 6e 6d | 61 72 6b 65 64 2e 20 0d | are unm|arked. .|
|00000f40| 0d 54 68 65 20 4c 41 47 | 20 67 61 6d 65 20 73 69 |.The LAG| game si|
|00000f50| 6d 70 6c 79 20 61 75 74 | 6f 6d 61 74 65 73 20 74 |mply aut|omates t|
|00000f60| 68 65 20 27 6c 61 67 67 | 69 6e 67 27 20 70 72 6f |he 'lagg|ing' pro|
|00000f70| 63 65 73 73 20 69 6e 20 | 77 68 69 63 68 20 70 6c |cess in |which pl|
|00000f80| 61 79 65 72 73 20 0d 61 | 6c 74 65 72 6e 61 74 65 |ayers .a|lternate|
|00000f90| 6c 79 20 6c 61 75 6e 63 | 68 20 61 20 63 75 65 20 |ly launc|h a cue |
|00000fa0| 62 61 6c 6c 20 74 6f 20 | 73 65 65 20 77 68 6f 20 |ball to |see who |
|00000fb0| 63 61 6e 20 63 6f 6d 65 | 20 63 6c 6f 73 65 72 20 |can come| closer |
|00000fc0| 74 6f 20 61 20 70 6f 69 | 6e 74 20 6f 72 20 0d 72 |to a poi|nt or .r|
|00000fd0| 61 69 6c 2e 20 20 41 73 | 20 77 69 74 68 20 6f 74 |ail. As| with ot|
|00000fe0| 68 65 72 20 6f 70 74 69 | 6f 6e 73 2c 20 70 6c 61 |her opti|ons, pla|
|00000ff0| 79 65 72 73 20 6d 61 79 | 20 63 68 6f 6f 73 65 20 |yers may| choose |
|00001000| 74 68 65 69 72 20 6f 77 | 6e 20 6c 61 67 20 63 72 |their ow|n lag cr|
|00001010| 69 74 65 72 69 61 2c 20 | 0d 77 69 74 68 20 74 68 |iteria, |.with th|
|00001020| 65 20 70 72 6f 67 72 61 | 6d 20 70 72 6f 76 69 64 |e progra|m provid|
|00001030| 69 6e 67 20 64 65 63 69 | 73 69 6f 6e 20 61 69 64 |ing deci|sion aid|
|00001040| 20 2d 20 69 6e 20 74 68 | 69 73 20 63 61 73 65 20 | - in th|is case |
|00001050| 61 20 6c 61 67 20 6c 69 | 6e 65 20 69 73 20 64 72 |a lag li|ne is dr|
|00001060| 61 77 6e 20 0d 6f 6e 20 | 74 68 65 20 73 63 72 65 |awn .on |the scre|
|00001070| 65 6e 20 74 6f 20 69 6e | 64 69 63 61 74 65 20 66 |en to in|dicate f|
|00001080| 69 6e 61 6c 20 63 75 65 | 20 62 61 6c 6c 20 70 6f |inal cue| ball po|
|00001090| 73 69 74 69 6f 6e 2e 20 | 20 54 68 65 20 6c 61 67 |sition. | The lag|
|000010a0| 20 61 6c 73 6f 20 68 61 | 73 20 74 68 65 20 0d 66 | also ha|s the .f|
|000010b0| 65 61 74 75 72 65 20 74 | 68 61 74 20 74 68 65 20 |eature t|hat the |
|000010c0| 63 75 65 20 62 61 6c 6c | 20 6d 61 79 20 62 65 20 |cue ball| may be |
|000010d0| 65 69 74 68 65 72 20 64 | 72 61 67 67 65 64 20 6f |either d|ragged o|
|000010e0| 72 20 73 68 6f 74 20 77 | 68 69 6c 65 20 74 68 65 |r shot w|hile the|
|000010f0| 20 69 74 65 6d 20 69 73 | 20 0d 63 68 65 63 6b 65 | item is| .checke|
|00001100| 64 2e 20 20 4e 4f 54 45 | 3a 20 54 68 69 73 20 69 |d. NOTE|: This i|
|00001110| 74 65 6d 20 6d 75 73 74 | 20 62 65 20 64 65 73 65 |tem must| be dese|
|00001120| 6c 65 63 74 65 64 20 74 | 6f 20 65 6e 61 62 6c 65 |lected t|o enable|
|00001130| 20 61 6e 79 20 6f 74 68 | 65 72 20 67 61 6d 65 2e | any oth|er game.|
|00001140| 0d 3e 3e 0d 0d 54 68 65 | 20 52 61 63 6b 73 0d 0d |.>>..The| Racks..|
|00001150| 54 68 65 20 6d 65 6e 75 | 20 69 74 65 6d 73 20 27 |The menu| items '|
|00001160| 43 6f 6d 70 6c 65 74 65 | 20 52 61 63 6b 27 20 61 |Complete| Rack' a|
|00001170| 6e 64 20 27 43 6f 6e 74 | 69 6e 75 61 74 69 6f 6e |nd 'Cont|inuation|
|00001180| 20 52 61 63 6b 27 20 70 | 72 6f 76 69 64 65 20 6d | Rack' p|rovide m|
|00001190| 65 61 6e 73 20 66 6f 72 | 0d 73 65 74 74 69 6e 67 |eans for|.setting|
|000011a0| 20 75 70 20 67 61 6d 65 | 73 2e 20 20 27 43 6f 6d | up game|s. 'Com|
|000011b0| 70 6c 65 74 65 20 52 61 | 63 6b 27 20 69 73 20 75 |plete Ra|ck' is u|
|000011c0| 73 65 64 20 74 6f 20 73 | 74 61 72 74 20 61 66 72 |sed to s|tart afr|
|000011d0| 65 73 68 2e 20 20 27 43 | 6f 6e 74 69 6e 75 61 74 |esh. 'C|ontinuat|
|000011e0| 69 6f 6e 0d 52 61 63 6b | 27 20 6d 61 6b 65 73 20 |ion.Rack|' makes |
|000011f0| 74 68 65 20 6d 6f 73 74 | 20 73 65 6e 73 65 20 69 |the most| sense i|
|00001200| 6e 20 53 74 72 61 69 67 | 68 74 20 50 6f 6f 6c 20 |n Straig|ht Pool |
|00001210| 76 61 72 69 61 74 69 6f | 6e 73 2c 20 62 79 20 72 |variatio|ns, by r|
|00001220| 61 63 6b 69 6e 67 20 61 | 6c 6c 20 62 75 74 0d 74 |acking a|ll but.t|
|00001230| 68 65 20 66 69 6e 61 6c | 20 62 61 6c 6c 20 6c 65 |he final| ball le|
|00001240| 66 74 20 6f 6e 20 74 68 | 65 20 74 61 62 6c 65 2e |ft on th|e table.|
|00001250| 20 20 49 66 20 74 68 65 | 20 6e 75 6d 62 65 72 20 | If the| number |
|00001260| 6f 66 20 6f 62 6a 65 63 | 74 20 62 61 6c 6c 73 20 |of objec|t balls |
|00001270| 6c 65 66 74 20 69 73 20 | 0d 6c 65 73 73 20 74 68 |left is |.less th|
|00001280| 61 6e 20 6f 72 20 67 72 | 65 61 74 65 72 20 74 68 |an or gr|eater th|
|00001290| 61 6e 20 6f 6e 65 2c 20 | 6f 72 20 69 66 20 74 68 |an one, |or if th|
|000012a0| 65 20 73 69 6e 67 6c 65 | 20 62 61 6c 6c 20 6c 65 |e single| ball le|
|000012b0| 66 74 20 69 73 20 77 69 | 74 68 69 6e 20 74 68 65 |ft is wi|thin the|
|000012c0| 20 0d 31 35 2d 62 61 6c | 6c 20 72 61 63 6b 69 6e | .15-bal|l rackin|
|000012d0| 67 20 74 72 69 61 6e 67 | 6c 65 20 74 68 65 20 43 |g triang|le the C|
|000012e0| 6f 6d 70 6c 65 74 65 20 | 52 61 63 6b 20 72 65 73 |omplete |Rack res|
|000012f0| 75 6c 74 73 20 61 73 20 | 61 20 64 65 66 61 75 6c |ults as |a defaul|
|00001300| 74 2e 0d 3e 3e 0d 4d 61 | 67 6e 69 66 69 63 61 74 |t..>>.Ma|gnificat|
|00001310| 69 6f 6e 0d 0d 54 68 69 | 73 20 69 73 20 74 6f 20 |ion..Thi|s is to |
|00001320| 61 69 64 20 69 6e 20 72 | 65 61 64 69 6e 67 20 62 |aid in r|eading b|
|00001330| 61 6c 6c 20 6e 75 6d 62 | 65 72 73 20 61 6e 64 20 |all numb|ers and |
|00001340| 61 73 73 65 73 73 69 6e | 67 20 63 6f 6d 70 6c 65 |assessin|g comple|
|00001350| 78 20 70 6f 73 69 74 69 | 6f 6e 73 2e 0d 0d 20 20 |x positi|ons... |
|00001360| 47 6c 61 73 73 3a 20 20 | 41 20 72 65 63 74 61 6e |Glass: |A rectan|
|00001370| 67 6c 65 20 77 69 6c 6c | 20 66 6f 6c 6c 6f 77 20 |gle will| follow |
|00001380| 74 68 65 20 6d 6f 75 73 | 65 20 6d 6f 76 65 6d 65 |the mous|e moveme|
|00001390| 6e 74 73 2e 20 20 48 6f | 6c 64 20 64 6f 77 6e 20 |nts. Ho|ld down |
|000013a0| 74 68 65 0d 20 20 20 20 | 20 20 20 20 20 20 6d 6f |the. | mo|
|000013b0| 75 73 65 20 62 75 74 74 | 6f 6e 20 74 6f 20 6d 61 |use butt|on to ma|
|000013c0| 67 6e 69 66 79 20 74 68 | 65 20 73 65 6c 65 63 74 |gnify th|e select|
|000013d0| 65 64 20 61 72 65 61 2e | 20 20 41 6e 20 3c 4f 70 |ed area.| An <Op|
|000013e0| 74 69 6f 6e 3e 2d 43 6c | 69 63 6b 0d 20 20 20 20 |tion>-Cl|ick. |
|000013f0| 20 20 20 20 20 20 6f 72 | 20 61 20 44 6f 75 62 6c | or| a Doubl|
|00001400| 65 2d 63 6c 69 63 6b 20 | 77 69 6c 6c 20 63 61 75 |e-click |will cau|
|00001410| 73 65 20 74 68 65 20 6d | 61 67 6e 69 66 79 69 6e |se the m|agnifyin|
|00001420| 67 20 67 6c 61 73 73 20 | 74 6f 20 64 69 73 61 70 |g glass |to disap|
|00001430| 70 65 61 72 2e 0d 20 20 | 46 75 6c 6c 53 63 72 65 |pear.. |FullScre|
|00001440| 65 6e 3a 20 20 54 68 65 | 20 74 61 62 6c 65 20 69 |en: The| table i|
|00001450| 73 20 62 6c 6f 77 6e 20 | 75 70 20 74 6f 20 67 72 |s blown |up to gr|
|00001460| 65 61 74 65 72 20 74 68 | 61 6e 20 66 75 6c 6c 2d |eater th|an full-|
|00001470| 73 63 72 65 65 6e 20 73 | 69 7a 65 2e 20 20 0d 20 |screen s|ize. . |
|00001480| 20 20 20 20 20 20 20 20 | 20 44 72 61 67 20 74 68 | | Drag th|
|00001490| 65 20 6d 6f 75 73 65 2c | 20 77 69 74 68 20 74 68 |e mouse,| with th|
|000014a0| 65 20 62 75 74 74 6f 6e | 20 68 65 6c 64 20 64 6f |e button| held do|
|000014b0| 77 6e 2c 20 74 6f 20 73 | 63 72 6f 6c 6c 20 74 68 |wn, to s|croll th|
|000014c0| 65 20 0d 20 20 20 20 20 | 20 20 20 20 20 66 75 6c |e . | ful|
|000014d0| 6c 20 73 63 72 65 65 6e | 20 64 69 73 70 6c 61 79 |l screen| display|
|000014e0| 20 28 61 73 20 69 6e 20 | 4d 61 63 50 61 69 6e 74 | (as in |MacPaint|
|000014f0| 20 27 53 68 6f 77 50 61 | 67 65 27 20 6d 6f 64 65 | 'ShowPa|ge' mode|
|00001500| 29 2e 20 41 6e 20 0d 20 | 20 20 20 20 20 20 20 20 |). An . | |
|00001510| 20 3c 4f 70 74 69 6f 6e | 3e 2d 43 6c 69 63 6b 20 | <Option|>-Click |
|00001520| 6f 72 20 61 20 44 6f 75 | 62 6c 65 2d 63 6c 69 63 |or a Dou|ble-clic|
|00001530| 6b 20 77 69 6c 6c 20 63 | 61 75 73 65 20 74 68 65 |k will c|ause the|
|00001540| 20 73 63 72 65 65 6e 0d | 20 20 20 20 20 20 20 20 | screen.| |
|00001550| 20 20 74 6f 20 72 65 76 | 65 72 74 20 74 6f 20 6e | to rev|ert to n|
|00001560| 6f 72 6d 61 6c 2e 0d 0d | 0d 4e 6f 74 65 3a 20 20 |ormal...|.Note: |
|00001570| 54 68 65 20 73 74 61 72 | 74 75 70 20 64 69 73 70 |The star|tup disp|
|00001580| 6c 61 79 20 28 77 69 74 | 68 20 61 6e 69 6d 61 74 |lay (wit|h animat|
|00001590| 65 64 20 42 69 6c 6c 69 | 61 72 64 20 50 61 72 6c |ed Billi|ard Parl|
|000015a0| 6f 75 72 20 73 63 65 6e | 65 29 20 6d 61 79 20 62 |our scen|e) may b|
|000015b0| 65 0d 20 20 20 20 20 20 | 20 73 70 65 65 64 65 64 |e. | speeded|
|000015c0| 20 75 70 20 62 79 20 68 | 6f 6c 64 69 6e 67 20 64 | up by h|olding d|
|000015d0| 6f 77 6e 20 74 68 65 20 | 3c 4f 70 74 69 6f 6e 3e |own the |<Option>|
|000015e0| 20 6b 65 79 2e 0d 7e 7e | 0d 0d 4f 72 69 67 69 6e | key..~~|..Origin|
|000015f0| 73 20 6f 66 20 42 69 6c | 6c 69 61 72 64 20 50 61 |s of Bil|liard Pa|
|00001600| 72 6c 6f 75 72 0d 0d 54 | 68 65 20 70 72 6f 6a 65 |rlour..T|he proje|
|00001610| 63 74 20 77 61 73 20 73 | 74 61 72 74 65 64 20 61 |ct was s|tarted a|
|00001620| 73 20 61 20 73 68 61 72 | 70 20 74 65 73 74 20 6f |s a shar|p test o|
|00001630| 66 20 52 61 73 63 61 6c | 20 61 6e 69 6d 61 74 69 |f Rascal| animati|
|00001640| 6f 6e 2e 20 20 57 65 20 | 68 61 64 0d 77 6f 72 6b |on. We |had.work|
|00001650| 65 64 20 6f 75 74 20 66 | 61 73 74 20 27 69 6e 74 |ed out f|ast 'int|
|00001660| 65 67 65 72 20 63 61 6c | 63 75 6c 75 73 27 20 72 |eger cal|culus' r|
|00001670| 6f 75 74 69 6e 65 73 20 | 66 6f 72 20 63 6f 6c 6c |outines |for coll|
|00001680| 69 64 69 6e 67 20 62 6f | 64 69 65 73 20 61 6e 64 |iding bo|dies and|
|00001690| 0d 70 65 72 66 6f 72 6d | 69 6e 67 20 76 61 72 69 |.perform|ing vari|
|000016a0| 6f 75 73 20 72 61 70 69 | 64 20 67 72 61 70 68 69 |ous rapi|d graphi|
|000016b0| 63 73 20 66 75 6e 63 74 | 69 6f 6e 73 2e 20 54 68 |cs funct|ions. Th|
|000016c0| 65 73 65 20 66 6f 72 6d | 75 6c 61 73 20 61 6e 64 |ese form|ulas and|
|000016d0| 20 74 65 63 68 6e 69 71 | 75 65 73 0d 63 6f 75 70 | techniq|ues.coup|
|000016e0| 6c 65 64 20 77 69 74 68 | 20 62 69 74 2d 63 6f 70 |led with| bit-cop|
|000016f0| 79 69 6e 67 20 6f 66 20 | 62 61 6c 6c 20 69 6d 61 |ying of |ball ima|
|00001700| 67 65 73 20 66 6f 72 6d | 65 64 20 74 68 65 20 62 |ges form|ed the b|
|00001710| 61 73 69 73 20 66 6f 72 | 0d 74 68 65 20 72 65 61 |asis for|.the rea|
|00001720| 73 6f 6e 61 62 6c 79 20 | 72 65 61 6c 69 73 74 69 |sonably |realisti|
|00001730| 63 20 62 69 6c 6c 69 61 | 72 64 20 65 66 66 65 63 |c billia|rd effec|
|00001740| 74 73 2e 20 20 54 68 65 | 20 66 69 6e 61 6c 20 61 |ts. The| final a|
|00001750| 70 70 6c 69 63 61 74 69 | 6f 6e 20 77 61 73 20 74 |pplicati|on was t|
|00001760| 68 75 73 0d 77 72 69 74 | 74 65 6e 20 65 6e 74 69 |hus.writ|ten enti|
|00001770| 72 65 6c 79 20 77 69 74 | 68 69 6e 20 74 68 65 20 |rely wit|hin the |
|00001780| 52 61 73 63 61 6c 20 63 | 6f 6d 70 69 6c 65 72 2f |Rascal c|ompiler/|
|00001790| 64 65 76 65 6c 6f 70 6d | 65 6e 74 20 73 79 73 74 |developm|ent syst|
|000017a0| 65 6d 20 0d 65 6e 76 69 | 72 6f 6e 6d 65 6e 74 2e |em .envi|ronment.|
|000017b0| 0d 0d 54 68 65 20 66 6f | 6c 6c 6f 77 69 6e 67 20 |..The fo|llowing |
|000017c0| 74 65 63 68 6e 69 63 61 | 6c 20 72 65 6d 61 72 6b |technica|l remark|
|000017d0| 73 20 6d 61 79 20 62 65 | 20 6f 66 20 69 6e 74 65 |s may be| of inte|
|000017e0| 72 65 73 74 20 74 6f 20 | 74 68 65 20 73 65 72 69 |rest to |the seri|
|000017f0| 6f 75 73 20 0d 70 72 6f | 67 72 61 6d 6d 65 72 2e |ous .pro|grammer.|
|00001800| 0d 3e 3e 0d 50 65 72 68 | 61 70 73 20 74 68 65 20 |.>>.Perh|aps the |
|00001810| 6d 6f 73 74 20 73 61 6c | 69 65 6e 74 20 66 61 63 |most sal|ient fac|
|00001820| 74 20 61 62 6f 75 74 20 | 74 68 65 20 62 69 6c 6c |t about |the bill|
|00001830| 69 61 72 64 73 20 61 6c | 67 6f 72 69 74 68 6d 73 |iards al|gorithms|
|00001840| 20 69 73 20 74 68 61 74 | 20 6e 6f 0d 66 6c 6f 61 | is that| no.floa|
|00001850| 74 69 6e 67 20 70 6f 69 | 6e 74 20 69 73 20 75 73 |ting poi|nt is us|
|00001860| 65 64 20 77 68 61 74 73 | 6f 65 76 65 72 2e 20 20 |ed whats|oever. |
|00001870| 41 6c 6c 20 63 61 6c 63 | 75 6c 61 74 69 6f 6e 73 |All calc|ulations|
|00001880| 20 61 72 65 20 64 6f 6e | 65 20 69 6e 20 31 36 2d | are don|e in 16-|
|00001890| 62 69 74 0d 69 6e 74 65 | 67 65 72 20 66 6f 72 6d |bit.inte|ger form|
|000018a0| 61 74 2e 20 20 54 68 65 | 20 72 65 61 73 6f 6e 2c |at. The| reason,|
|000018b0| 20 6f 66 20 63 6f 75 72 | 73 65 2c 20 69 73 20 74 | of cour|se, is t|
|000018c0| 68 65 20 71 75 65 73 74 | 20 66 6f 72 20 73 70 65 |he quest| for spe|
|000018d0| 65 64 2e 20 20 54 68 6f | 75 67 68 0d 66 6c 6f 61 |ed. Tho|ugh.floa|
|000018e0| 74 69 6e 67 20 70 6f 69 | 6e 74 20 76 61 72 69 61 |ting poi|nt varia|
|000018f0| 62 6c 65 73 20 61 72 65 | 20 65 61 73 69 65 72 20 |bles are| easier |
|00001900| 74 6f 20 77 6f 72 6b 20 | 77 69 74 68 20 66 6f 72 |to work |with for|
|00001910| 20 64 79 6e 61 6d 69 63 | 61 6c 20 70 72 6f 62 6c | dynamic|al probl|
|00001920| 65 6d 73 2c 0d 74 68 65 | 72 65 20 69 73 20 6e 6f |ems,.the|re is no|
|00001930| 20 68 6f 70 65 20 66 6f | 72 20 66 75 6c 6c 20 70 | hope fo|r full p|
|00001940| 6f 6f 6c 20 74 61 62 6c | 65 20 64 79 6e 61 6d 69 |ool tabl|e dynami|
|00001950| 63 73 20 6f 6e 20 74 68 | 65 20 4d 61 63 69 6e 74 |cs on th|e Macint|
|00001960| 6f 73 68 20 75 6e 6c 65 | 73 73 0d 69 6e 74 65 67 |osh unle|ss.integ|
|00001970| 65 72 20 63 61 6c 63 75 | 6c 61 74 69 6f 6e 73 20 |er calcu|lations |
|00001980| 70 72 65 64 6f 6d 69 6e | 61 74 65 2e 0d 3e 3e 0d |predomin|ate..>>.|
|00001990| 54 68 65 20 73 70 65 65 | 64 20 6f 66 20 74 68 65 |The spee|d of the|
|000019a0| 20 69 6e 74 65 67 65 72 | 20 64 79 6e 61 6d 69 63 | integer| dynamic|
|000019b0| 61 6c 20 72 6f 75 74 69 | 6e 65 73 20 73 68 6f 75 |al routi|nes shou|
|000019c0| 6c 64 20 62 65 20 65 76 | 69 64 65 6e 74 20 66 72 |ld be ev|ident fr|
|000019d0| 6f 6d 20 61 0d 63 6f 6e | 73 69 64 65 72 61 74 69 |om a.con|siderati|
|000019e0| 6f 6e 20 6f 66 20 77 68 | 61 74 20 6d 75 73 74 20 |on of wh|at must |
|000019f0| 62 65 20 64 6f 6e 65 20 | 74 6f 20 69 74 65 72 61 |be done |to itera|
|00001a00| 74 65 20 61 6e 20 65 6e | 74 69 72 65 20 65 6e 73 |te an en|tire ens|
|00001a10| 65 6d 62 6c 65 20 6f 66 | 20 68 61 72 64 0d 73 70 |emble of| hard.sp|
|00001a20| 68 65 72 65 73 2e 20 20 | 53 61 79 20 74 68 65 72 |heres. |Say ther|
|00001a30| 65 20 61 72 65 20 4e 20 | 73 70 68 65 72 65 73 20 |e are N |spheres |
|00001a40| 74 6f 74 61 6c 20 69 6e | 20 6d 6f 74 69 6f 6e 20 |total in| motion |
|00001a50| 6f 6e 20 74 68 65 20 74 | 61 62 6c 65 2e 20 20 4f |on the t|able. O|
|00001a60| 6e 65 20 6d 75 73 74 0d | 6f 6e 20 65 76 65 72 79 |ne must.|on every|
|00001a70| 20 70 61 73 73 20 6f 66 | 20 74 68 65 20 6d 61 69 | pass of| the mai|
|00001a80| 6e 20 69 74 65 72 61 74 | 69 6f 6e 20 6c 6f 6f 70 |n iterat|ion loop|
|00001a90| 0d 0d 20 20 20 20 20 31 | 29 20 55 70 64 61 74 65 |.. 1|) Update|
|00001aa0| 20 32 4e 20 63 6f 6f 72 | 64 69 6e 61 74 65 20 76 | 2N coor|dinate v|
|00001ab0| 61 6c 75 65 73 2e 0d 20 | 20 20 20 20 32 29 20 55 |alues.. | 2) U|
|00001ac0| 70 64 61 74 65 20 32 4e | 20 76 65 6c 6f 63 69 74 |pdate 2N| velocit|
|00001ad0| 79 20 76 61 6c 75 65 73 | 2e 0d 20 20 20 20 20 33 |y values|.. 3|
|00001ae0| 29 20 53 65 65 6b 20 61 | 6e 64 20 61 6e 61 6c 79 |) Seek a|nd analy|
|00001af0| 7a 65 20 63 6f 6c 6c 69 | 73 69 6f 6e 73 2c 20 72 |ze colli|sions, r|
|00001b00| 65 71 75 69 72 69 6e 67 | 20 4e 2a 4e 2f 32 20 63 |equiring| N*N/2 c|
|00001b10| 68 65 63 6b 73 2e 0d 20 | 20 20 20 20 34 29 20 48 |hecks.. | 4) H|
|00001b20| 61 6e 64 6c 65 20 64 61 | 6d 70 69 6e 67 20 61 6e |andle da|mping an|
|00001b30| 64 20 45 6e 67 6c 69 73 | 68 2e 0d 20 20 20 20 20 |d Englis|h.. |
|00001b40| 35 29 20 46 6f 72 20 6d | 6f 73 74 20 67 61 6d 65 |5) For m|ost game|
|00001b50| 73 2c 20 63 68 65 63 6b | 20 66 6f 72 20 70 6f 63 |s, check| for poc|
|00001b60| 6b 65 74 20 73 69 6e 6b | 69 6e 67 20 66 6f 72 20 |ket sink|ing for |
|00001b70| 65 61 63 68 20 6f 66 20 | 74 68 65 20 4e 20 62 61 |each of |the N ba|
|00001b80| 6c 6c 73 2e 0d 20 20 20 | 20 20 36 29 20 43 68 65 |lls.. | 6) Che|
|00001b90| 63 6b 20 66 6f 72 20 72 | 61 69 6c 20 62 6f 75 6e |ck for r|ail boun|
|00001ba0| 63 65 73 20 66 6f 72 20 | 65 61 63 68 20 6f 66 20 |ces for |each of |
|00001bb0| 4e 20 62 61 6c 6c 73 2e | 0d 20 20 20 20 20 0d 4e |N balls.|. .N|
|00001bc0| 61 74 75 72 61 6c 6c 79 | 2c 20 73 6f 6d 65 20 6f |aturally|, some o|
|00001bd0| 66 20 74 68 65 20 61 62 | 6f 76 65 20 61 72 65 20 |f the ab|ove are |
|00001be0| 69 6e 74 65 72 72 65 6c | 61 74 65 64 20 2d 20 66 |interrel|ated - f|
|00001bf0| 6f 72 20 65 78 61 6d 70 | 6c 65 20 63 6f 6c 6c 69 |or examp|le colli|
|00001c00| 73 69 6f 6e 20 61 6e 64 | 0d 64 61 6d 70 69 6e 67 |sion and|.damping|
|00001c10| 20 61 72 65 20 77 68 61 | 74 20 69 6d 70 6c 79 20 | are wha|t imply |
|00001c20| 74 68 65 20 6e 65 65 64 | 20 66 6f 72 20 75 70 64 |the need| for upd|
|00001c30| 61 74 69 6e 67 20 76 65 | 6c 6f 63 69 74 69 65 73 |ating ve|locities|
|00001c40| 2e 20 20 54 68 65 20 66 | 61 63 74 20 74 68 61 74 |. The f|act that|
|00001c50| 0d 4e 2a 4e 2f 32 20 63 | 68 65 63 6b 73 20 61 72 |.N*N/2 c|hecks ar|
|00001c60| 65 20 75 73 65 64 20 74 | 6f 20 73 65 65 6b 20 61 |e used t|o seek a|
|00001c70| 6c 6c 20 63 6f 6c 6c 69 | 73 69 6f 6e 73 20 69 73 |ll colli|sions is|
|00001c80| 20 65 73 70 65 63 69 61 | 6c 6c 79 20 63 75 6d 62 | especia|lly cumb|
|00001c90| 65 72 73 6f 6d 65 20 77 | 68 65 6e 0d 74 68 65 20 |ersome w|hen.the |
|00001ca0| 6e 75 6d 62 65 72 20 4e | 20 69 6e 20 74 68 65 20 |number N| in the |
|00001cb0| 65 6e 73 65 6d 62 6c 65 | 20 69 73 20 6c 61 72 67 |ensemble| is larg|
|00001cc0| 65 2e 20 20 46 6f 72 20 | 61 20 66 75 6c 6c 20 70 |e. For |a full p|
|00001cd0| 6f 6f 6c 20 74 61 62 6c | 65 2c 20 74 68 69 73 20 |ool tabl|e, this |
|00001ce0| 6d 65 61 6e 73 0d 31 32 | 38 20 63 68 65 63 6b 73 |means.12|8 checks|
|00001cf0| 20 66 6f 72 20 63 6f 6c | 6c 69 73 69 6f 6e 73 20 | for col|lisions |
|00001d00| 61 72 65 20 6d 61 64 65 | 20 61 74 20 65 61 63 68 |are made| at each|
|00001d10| 20 69 74 65 72 61 74 69 | 6f 6e 2e 0d 3e 3e 0d 41 | iterati|on..>>.A|
|00001d20| 6e 20 65 78 61 6d 70 6c | 65 20 6f 66 20 74 72 69 |n exampl|e of tri|
|00001d30| 63 6b 65 72 79 20 69 6e | 74 65 6e 64 65 64 20 74 |ckery in|tended t|
|00001d40| 6f 20 6f 70 74 69 6d 69 | 7a 65 20 73 70 65 65 64 |o optimi|ze speed|
|00001d50| 20 69 73 20 74 68 61 74 | 20 75 73 65 64 20 74 6f | is that| used to|
|00001d60| 20 63 68 65 63 6b 20 0d | 66 6f 72 20 63 6f 6c 6c | check .|for coll|
|00001d70| 69 73 69 6f 6e 73 2e 20 | 20 54 68 65 20 52 61 73 |isions. | The Ras|
|00001d80| 63 61 6c 20 73 6f 75 72 | 63 65 20 68 61 73 20 61 |cal sour|ce has a|
|00001d90| 20 63 6f 6c 6c 69 73 69 | 6f 6e 20 61 6c 67 6f 72 | collisi|on algor|
|00001da0| 69 74 68 6d 20 65 73 73 | 65 6e 74 69 61 6c 6c 79 |ithm ess|entially|
|00001db0| 20 0d 6c 69 6b 65 20 73 | 6f 3a 0d 0d 20 20 20 20 | .like s|o:.. |
|00001dc0| 20 73 20 3a 3d 20 34 2a | 72 61 64 69 75 73 2a 72 | s := 4*|radius*r|
|00001dd0| 61 64 69 75 73 3b 0d 20 | 20 20 20 20 6c 6f 6f 70 |adius;. | loop|
|00001de0| 28 2c 69 3a 3d 30 2c 2b | 2b 69 2c 69 3e 6e 75 6d |(,i:=0,+|+i,i>num|
|00001df0| 62 61 6c 6c 73 2d 31 29 | 0d 20 20 20 20 20 7b 0d |balls-1)|. {.|
|00001e00| 20 20 20 20 20 20 20 6c | 6f 6f 70 28 69 3c 6e 75 | l|oop(i<nu|
|00001e10| 6d 62 61 6c 6c 73 2d 31 | 2c 20 6a 3a 3d 69 2b 31 |mballs-1|, j:=i+1|
|00001e20| 2c 20 2b 2b 6a 2c 20 6a | 3e 6e 75 6d 62 61 6c 6c |, ++j, j|>numball|
|00001e30| 73 2d 31 29 0d 20 20 20 | 20 20 20 20 7b 0d 20 20 |s-1). | {. |
|00001e40| 20 20 20 20 20 20 20 20 | 20 64 78 20 3a 3d 20 78 | | dx := x|
|00001e50| 5b 69 5d 20 2d 20 78 5b | 6a 5d 3b 0d 20 20 20 20 |[i] - x[|j];. |
|00001e60| 20 20 20 20 20 20 20 69 | 66 20 64 78 2a 64 78 20 | i|f dx*dx |
|00001e70| 3c 3d 20 73 20 74 68 65 | 6e 0d 20 20 20 20 20 20 |<= s the|n. |
|00001e80| 20 20 20 20 20 20 20 20 | 7b 20 64 79 3a 3d 20 79 | |{ dy:= y|
|00001e90| 5b 69 5d 20 2d 20 79 5b | 6a 5d 3b 0d 20 20 20 20 |[i] - y[|j];. |
|00001ea0| 20 20 20 20 20 20 20 20 | 20 20 20 20 69 66 20 64 | | if d|
|00001eb0| 78 2a 64 78 20 2b 20 64 | 79 2a 64 79 20 3c 3d 20 |x*dx + d|y*dy <= |
|00001ec0| 73 20 74 68 65 6e 0d 20 | 20 20 20 20 20 20 20 20 |s then. | |
|00001ed0| 20 20 20 20 20 20 20 20 | 20 20 63 6f 6c 6c 69 64 | | collid|
|00001ee0| 65 28 69 2c 6a 29 3b 0d | 20 20 20 20 20 20 20 20 |e(i,j);.| |
|00001ef0| 20 20 20 20 20 20 7d 3b | 0d 20 20 20 20 20 20 20 | };|. |
|00001f00| 7d 3b 0d 20 20 20 20 20 | 7d 3b 0d 3e 3e 0d 0d 54 |};. |};.>>..T|
|00001f10| 68 65 20 74 77 6f 20 6c | 6f 6f 70 73 20 61 72 65 |he two l|oops are|
|00001f20| 20 73 74 72 61 69 67 68 | 74 66 6f 72 77 61 72 64 | straigh|tforward|
|00001f30| 2c 20 64 69 63 74 61 74 | 69 6e 67 20 74 68 61 74 |, dictat|ing that|
|00001f40| 20 77 65 20 61 72 65 20 | 63 68 65 63 6b 69 6e 67 | we are |checking|
|00001f50| 20 66 6f 72 0d 70 61 69 | 72 20 28 69 2c 6a 29 20 | for.pai|r (i,j) |
|00001f60| 63 6f 6c 6c 69 73 69 6f | 6e 73 20 77 68 65 72 65 |collisio|ns where|
|00001f70| 20 69 20 69 73 20 6e 6f | 74 20 65 71 75 61 6c 20 | i is no|t equal |
|00001f80| 74 6f 20 6a 2e 20 20 42 | 75 74 20 74 68 65 20 70 |to j. B|ut the p|
|00001f90| 72 69 6d 61 72 79 20 70 | 6f 69 6e 74 20 69 73 20 |rimary p|oint is |
|00001fa0| 0d 74 68 61 74 20 74 68 | 65 20 63 68 65 63 6b 20 |.that th|e check |
|00001fb0| 64 78 2a 64 78 3c 73 20 | 69 73 20 6d 61 64 65 20 |dx*dx<s |is made |
|00001fc0| 66 69 72 73 74 20 74 6f | 20 73 61 76 65 20 74 69 |first to| save ti|
|00001fd0| 6d 65 2e 20 20 4e 6f 74 | 65 20 74 68 61 74 20 74 |me. Not|e that t|
|00001fe0| 77 6f 20 62 61 6c 6c 73 | 20 0d 68 61 76 65 20 63 |wo balls| .have c|
|00001ff0| 6f 6c 6c 69 64 65 64 20 | 28 74 68 61 74 20 69 73 |ollided |(that is|
|00002000| 2c 20 70 65 6e 65 74 72 | 61 74 65 20 65 61 63 68 |, penetr|ate each|
|00002010| 20 6f 74 68 65 72 29 20 | 77 68 65 6e 65 76 65 72 | other) |whenever|
|00002020| 0d 0d 20 20 20 20 73 71 | 72 74 28 64 78 2a 64 78 |.. sq|rt(dx*dx|
|00002030| 20 2b 20 64 79 2a 64 79 | 29 20 3c 3d 20 32 2a 72 | + dy*dy|) <= 2*r|
|00002040| 61 64 69 75 73 0d 20 20 | 20 20 0d 73 6f 20 63 6f |adius. | .so co|
|00002050| 6c 6c 69 73 69 6f 6e 20 | 61 6c 73 6f 20 69 6d 70 |llision |also imp|
|00002060| 6c 69 65 73 20 73 71 72 | 74 28 64 78 2a 64 78 29 |lies sqr|t(dx*dx)|
|00002070| 3c 20 32 2a 72 61 64 69 | 75 73 2e 20 20 54 68 65 |< 2*radi|us. The|
|00002080| 20 27 73 71 72 74 27 20 | 66 75 6e 63 74 69 6f 6e | 'sqrt' |function|
|00002090| 20 63 61 6e 0d 62 65 20 | 64 72 6f 70 70 65 64 2c | can.be |dropped,|
|000020a0| 20 61 73 20 69 6e 20 74 | 68 65 20 65 78 70 6c 69 | as in t|he expli|
|000020b0| 63 69 74 20 6c 6f 6f 70 | 20 61 62 6f 76 65 2c 20 |cit loop| above, |
|000020c0| 69 6e 20 74 68 65 20 69 | 6e 74 65 72 65 73 74 20 |in the i|nterest |
|000020d0| 6f 66 20 73 70 65 65 64 | 2e 0d 0d 4d 61 6e 79 20 |of speed|...Many |
|000020e0| 73 75 63 68 20 69 6e 74 | 65 67 65 72 20 63 61 6c |such int|eger cal|
|000020f0| 63 75 6c 61 74 69 6f 6e | 73 20 77 65 72 65 20 6e |culation|s were n|
|00002100| 65 63 65 73 73 61 72 79 | 20 74 6f 20 61 63 68 69 |ecessary| to achi|
|00002110| 65 76 65 20 61 20 63 65 | 72 74 61 69 6e 20 0d 72 |eve a ce|rtain .r|
|00002120| 65 61 6c 69 73 6d 2e 20 | 20 0d 3e 3e 0d 4f 74 68 |ealism. | .>>.Oth|
|00002130| 65 72 20 65 78 61 6d 70 | 6c 65 73 20 77 68 69 63 |er examp|les whic|
|00002140| 68 20 6d 69 67 68 74 20 | 69 6e 74 65 72 65 73 74 |h might |interest|
|00002150| 20 74 68 65 20 70 72 6f | 67 72 61 6d 6d 65 72 20 | the pro|grammer |
|00002160| 61 72 65 3a 0d 0d 20 20 | 20 20 20 31 29 20 45 61 |are:.. | 1) Ea|
|00002170| 63 68 20 62 61 6c 6c 20 | 68 61 73 20 74 77 6f 20 |ch ball |has two |
|00002180| 70 69 63 74 75 72 65 73 | 2c 20 77 68 69 63 68 20 |pictures|, which |
|00002190| 61 6c 74 65 72 6e 61 74 | 65 20 61 66 74 65 72 20 |alternat|e after |
|000021a0| 65 76 65 72 79 20 6d 75 | 6c 74 69 70 6c 65 0d 20 |every mu|ltiple. |
|000021b0| 20 20 20 20 20 20 20 6f | 66 20 70 69 2a 72 61 64 | o|f pi*rad|
|000021c0| 69 75 73 20 69 73 20 6d | 6f 76 65 64 20 6f 6e 20 |ius is m|oved on |
|000021d0| 74 68 65 20 73 63 72 65 | 65 6e 2e 20 20 54 68 69 |the scre|en. Thi|
|000021e0| 73 20 67 69 76 65 73 20 | 61 6e 20 69 6d 70 72 65 |s gives |an impre|
|000021f0| 73 73 69 6f 6e 20 6f 66 | 0d 20 20 20 20 20 20 20 |ssion of|. |
|00002200| 20 72 6f 6c 6c 69 6e 67 | 2e 0d 20 20 20 20 20 32 | rolling|.. 2|
|00002210| 29 20 44 61 6d 70 69 6e | 67 20 69 73 20 68 61 72 |) Dampin|g is har|
|00002220| 64 20 74 6f 20 61 63 63 | 6f 6d 70 6c 69 73 68 20 |d to acc|omplish |
|00002230| 77 69 74 68 20 69 6e 74 | 65 67 65 72 73 2e 20 20 |with int|egers. |
|00002240| 54 68 65 20 70 72 69 6d | 61 72 79 20 70 72 6f 62 |The prim|ary prob|
|00002250| 6c 65 6d 0d 20 20 20 20 | 20 20 20 20 69 73 20 74 |lem. | is t|
|00002260| 68 61 74 20 69 66 20 77 | 65 20 61 74 74 65 6d 70 |hat if w|e attemp|
|00002270| 74 20 61 74 20 65 61 63 | 68 20 69 74 65 72 61 74 |t at eac|h iterat|
|00002280| 69 6f 6e 20 73 6f 6d 65 | 74 68 69 6e 67 20 6c 69 |ion some|thing li|
|00002290| 6b 65 3a 20 20 20 20 20 | 20 20 20 0d 20 20 20 20 |ke: | . |
|000022a0| 20 20 20 20 20 20 20 20 | 20 20 76 78 5b 69 5d 3a | | vx[i]:|
|000022b0| 3d 20 28 76 78 5b 69 5d | 2a 39 39 39 29 2f 31 30 |= (vx[i]|*999)/10|
|000022c0| 30 30 3b 0d 20 20 20 20 | 20 20 20 20 20 20 20 20 |00;. | |
|000022d0| 20 20 76 79 5b 69 5d 3a | 3d 20 28 76 79 5b 69 5d | vy[i]:|= (vy[i]|
|000022e0| 2a 39 39 39 29 2f 31 30 | 30 30 3b 20 20 20 20 20 |*999)/10|00; |
|000022f0| 20 20 20 20 20 20 20 20 | 20 0d 20 20 20 20 20 20 | | . |
|00002300| 20 20 74 68 65 6e 2c 20 | 69 6e 20 67 65 6e 65 72 | then, |in gener|
|00002310| 61 6c 2c 20 6f 6e 65 20 | 6f 66 20 76 78 20 6f 72 |al, one |of vx or|
|00002320| 20 76 79 20 77 69 6c 6c | 20 76 61 6e 69 73 68 20 | vy will| vanish |
|00002330| 63 6f 6d 70 6c 65 74 65 | 6c 79 20 62 65 66 6f 72 |complete|ly befor|
|00002340| 65 20 0d 20 20 20 20 20 | 20 20 20 74 68 65 20 6f |e . | the o|
|00002350| 74 68 65 72 2c 20 61 74 | 20 74 68 65 20 74 61 69 |ther, at| the tai|
|00002360| 6c 20 65 6e 64 20 6f 66 | 20 61 20 62 61 6c 6c 27 |l end of| a ball'|
|00002370| 73 20 6d 6f 74 69 6f 6e | 2e 20 20 54 68 69 73 20 |s motion|. This |
|00002380| 63 61 75 73 65 73 20 0d | 20 20 20 20 20 20 20 20 |causes .| |
|00002390| 73 77 65 72 76 69 6e 67 | 20 61 74 20 74 68 65 20 |swerving| at the |
|000023a0| 65 6e 64 20 6f 66 20 74 | 68 65 20 74 72 61 6a 65 |end of t|he traje|
|000023b0| 63 74 6f 72 79 2c 20 61 | 73 20 61 20 62 61 6c 6c |ctory, a|s a ball|
|000023c0| 20 64 69 73 61 70 70 6f | 69 6e 74 69 6e 67 6c 79 | disappo|intingly|
|000023d0| 20 0d 20 20 20 20 20 20 | 20 20 66 6f 6c 6c 6f 77 | . | follow|
|000023e0| 73 20 6f 6e 65 20 61 78 | 69 73 20 6f 72 20 74 68 |s one ax|is or th|
|000023f0| 65 20 6f 74 68 65 72 2e | 20 20 54 68 65 20 73 6f |e other.| The so|
|00002400| 6c 75 74 69 6f 6e 20 77 | 61 73 20 74 6f 20 61 70 |lution w|as to ap|
|00002410| 70 6c 79 20 74 68 65 20 | 0d 20 20 20 20 20 20 20 |ply the |. |
|00002420| 20 66 6f 72 6d 75 6c 61 | 20 6f 6e 6c 79 20 61 74 | formula| only at|
|00002430| 20 63 65 72 74 61 69 6e | 20 74 69 6d 65 73 20 2d | certain| times -|
|00002440| 20 6e 6f 74 20 69 6e 20 | 65 61 63 68 20 69 74 65 | not in |each ite|
|00002450| 72 61 74 69 6f 6e 20 2d | 20 61 6e 64 20 6d 61 6b |ration -| and mak|
|00002460| 65 20 0d 20 20 20 20 20 | 20 20 20 73 75 72 65 20 |e . | sure |
|00002470| 74 68 61 74 20 74 6f 74 | 61 6c 20 64 61 6d 70 69 |that tot|al dampi|
|00002480| 6e 67 20 69 73 20 61 63 | 68 69 65 76 65 64 20 62 |ng is ac|hieved b|
|00002490| 65 66 6f 72 65 20 74 68 | 65 20 66 69 6e 61 6c 20 |efore th|e final |
|000024a0| 73 77 65 72 76 65 2e 20 | 20 54 68 69 73 20 0d 20 |swerve. | This . |
|000024b0| 20 20 20 20 20 20 20 6c | 61 73 74 20 65 66 66 65 | l|ast effe|
|000024c0| 63 74 20 69 73 20 64 6f | 6e 65 20 62 79 20 73 69 |ct is do|ne by si|
|000024d0| 6d 70 6c 79 20 73 74 6f | 70 70 69 6e 67 20 74 68 |mply sto|pping th|
|000024e0| 65 20 6d 6f 74 69 6f 6e | 20 61 66 74 65 72 20 61 |e motion| after a|
|000024f0| 20 63 65 72 74 61 69 6e | 20 0d 20 20 20 20 20 20 | certain| . |
|00002500| 20 20 69 74 65 72 61 74 | 69 6f 6e 20 63 6f 75 6e | iterat|ion coun|
|00002510| 74 20 77 68 69 63 68 20 | 64 65 70 65 6e 64 73 20 |t which |depends |
|00002520| 69 6e 20 74 75 72 6e 20 | 6f 6e 20 74 68 65 20 67 |in turn |on the g|
|00002530| 61 6d 65 20 70 6c 61 79 | 65 64 20 61 6e 64 20 6f |ame play|ed and o|
|00002540| 6e 20 0d 20 20 20 20 20 | 20 20 20 6f 74 68 65 72 |n . | other|
|00002550| 20 63 6f 6e 64 69 74 69 | 6f 6e 73 2e 0d 3e 3e 0d | conditi|ons..>>.|
|00002560| 20 20 20 20 20 33 29 20 | 54 68 65 20 64 69 66 66 | 3) |The diff|
|00002570| 69 63 75 6c 74 79 20 77 | 69 74 68 20 69 6e 74 65 |iculty w|ith inte|
|00002580| 67 65 72 20 63 61 6c 63 | 75 6c 75 73 20 69 73 20 |ger calc|ulus is |
|00002590| 65 76 69 64 65 6e 74 20 | 77 68 65 6e 20 6f 6e 65 |evident |when one|
|000025a0| 20 63 6f 6e 73 69 64 65 | 72 73 0d 20 20 20 20 20 | conside|rs. |
|000025b0| 20 20 20 74 68 65 20 62 | 61 73 69 63 20 4e 65 77 | the b|asic New|
|000025c0| 74 6f 6e 69 61 6e 20 69 | 74 65 72 61 74 69 6f 6e |tonian i|teration|
|000025d0| 3a 0d 20 20 20 20 20 20 | 20 20 0d 20 20 20 20 20 |:. | . |
|000025e0| 20 20 20 20 20 20 20 20 | 78 5b 69 5d 3a 3d 20 78 | |x[i]:= x|
|000025f0| 5b 69 5d 20 2b 20 76 78 | 5b 69 5d 3b 0d 20 20 20 |[i] + vx|[i];. |
|00002600| 20 20 20 20 20 20 20 20 | 20 20 79 5b 69 5d 3a 3d | | y[i]:=|
|00002610| 20 79 5b 69 5d 20 2b 20 | 76 79 5b 69 5d 3b 0d 20 | y[i] + |vy[i];. |
|00002620| 20 20 20 20 20 20 20 20 | 20 20 20 20 0d 20 20 20 | | . |
|00002630| 20 20 20 20 20 6e 6f 74 | 69 6e 67 20 74 68 61 74 | not|ing that|
|00002640| 20 69 6e 20 72 65 61 6c | 2d 6e 75 6d 62 65 72 20 | in real|-number |
|00002650| 63 61 6c 63 75 6c 75 73 | 20 6f 6e 65 20 77 6f 75 |calculus| one wou|
|00002660| 6c 64 20 68 61 76 65 20 | 65 61 63 68 20 76 65 6c |ld have |each vel|
|00002670| 6f 63 69 74 79 0d 20 20 | 20 20 20 20 20 20 74 65 |ocity. | te|
|00002680| 72 6d 20 6d 75 6c 74 69 | 70 6c 69 65 64 20 62 79 |rm multi|plied by|
|00002690| 20 61 20 73 6d 61 6c 6c | 20 74 69 6d 65 20 69 6e | a small| time in|
|000026a0| 63 72 65 6d 65 6e 74 20 | 64 74 2e 20 20 42 65 63 |crement |dt. Bec|
|000026b0| 61 75 73 65 20 77 65 20 | 63 61 6e 6e 6f 74 0d 20 |ause we |cannot. |
|000026c0| 20 20 20 20 20 20 20 64 | 6f 20 74 68 69 73 20 77 | d|o this w|
|000026d0| 69 74 68 20 69 6e 74 65 | 67 65 72 73 20 28 74 68 |ith inte|gers (th|
|000026e0| 65 20 73 6d 61 6c 6c 65 | 73 74 20 69 6e 63 72 65 |e smalle|st incre|
|000026f0| 6d 65 6e 74 20 62 65 69 | 6e 67 20 31 29 20 74 68 |ment bei|ng 1) th|
|00002700| 65 72 65 20 69 73 0d 20 | 20 20 20 20 20 20 20 74 |ere is. | t|
|00002710| 68 65 20 74 68 72 65 61 | 74 20 74 68 61 74 20 62 |he threa|t that b|
|00002720| 61 6c 6c 73 20 77 69 6c | 6c 20 6d 6f 76 65 20 76 |alls wil|l move v|
|00002730| 65 72 79 20 66 61 72 20 | 61 74 20 65 61 63 68 20 |ery far |at each |
|00002740| 69 74 65 72 61 74 69 6f | 6e 2e 20 20 54 68 65 0d |iteratio|n. The.|
|00002750| 20 20 20 20 20 20 20 20 | 73 6f 6c 75 74 69 6f 6e | |solution|
|00002760| 20 69 73 20 65 61 73 79 | 20 65 6e 6f 75 67 68 3a | is easy| enough:|
|00002770| 20 68 6f 6c 64 20 61 6c | 6c 20 63 6f 6f 72 64 69 | hold al|l coordi|
|00002780| 6e 61 74 65 73 20 61 6e | 64 20 76 65 6c 6f 63 69 |nates an|d veloci|
|00002790| 74 69 65 73 20 61 73 20 | 0d 20 20 20 20 20 20 20 |ties as |. |
|000027a0| 20 6c 61 72 67 65 20 69 | 6e 74 65 67 65 72 73 2c | large i|ntegers,|
|000027b0| 20 61 6e 64 20 64 69 76 | 69 64 65 20 62 79 20 61 | and div|ide by a|
|000027c0| 20 63 6f 6e 73 74 61 6e | 74 20 6f 6e 6c 79 20 77 | constan|t only w|
|000027d0| 68 65 6e 20 61 63 74 75 | 61 6c 6c 79 20 0d 20 20 |hen actu|ally . |
|000027e0| 20 20 20 20 20 20 67 72 | 61 70 68 69 6e 67 2e 20 | gr|aphing. |
|000027f0| 20 54 68 75 73 20 69 6e | 20 42 69 6c 6c 69 61 72 | Thus in| Billiar|
|00002800| 64 20 50 61 72 6c 6f 75 | 72 20 74 68 65 20 74 79 |d Parlou|r the ty|
|00002810| 70 69 63 61 6c 20 63 6f | 6f 72 64 69 6e 61 74 65 |pical co|ordinate|
|00002820| 73 20 61 72 65 20 6f 6e | 20 0d 20 20 20 20 20 20 |s are on| . |
|00002830| 20 20 74 68 65 20 6f 72 | 64 65 72 20 6f 66 20 31 | the or|der of 1|
|00002840| 30 30 30 30 20 61 6e 64 | 20 64 69 76 69 73 69 6f |0000 and| divisio|
|00002850| 6e 73 20 62 79 20 31 30 | 30 20 61 72 65 20 74 79 |ns by 10|0 are ty|
|00002860| 70 69 63 61 6c 20 61 74 | 20 67 72 61 70 68 20 74 |pical at| graph t|
|00002870| 69 6d 65 2e 0d 3e 3e 0d | 20 20 20 20 20 34 29 20 |ime..>>.| 4) |
|00002880| 54 68 65 20 70 72 6f 62 | 6c 65 6d 20 6f 66 20 45 |The prob|lem of E|
|00002890| 6e 67 6c 69 73 68 20 69 | 73 20 61 20 67 6f 6f 64 |nglish i|s a good|
|000028a0| 20 65 78 61 6d 70 6c 65 | 20 6f 66 20 61 20 74 6f | example| of a to|
|000028b0| 75 67 68 2d 73 6f 75 6e | 64 69 6e 67 20 0d 20 20 |ugh-soun|ding . |
|000028c0| 20 20 20 70 72 6f 62 6c | 65 6d 20 77 68 69 63 68 | probl|em which|
|000028d0| 20 74 75 72 6e 73 20 6f | 75 74 20 74 6f 20 62 65 | turns o|ut to be|
|000028e0| 20 72 61 74 68 65 72 20 | 74 72 69 76 69 61 6c 20 | rather |trivial |
|000028f0| 74 6f 20 73 6f 6c 76 65 | 2e 20 20 46 6f 72 20 45 |to solve|. For E|
|00002900| 6e 67 6c 69 73 68 20 0d | 20 20 20 20 20 65 66 66 |nglish .| eff|
|00002910| 65 63 74 73 20 61 74 20 | 61 20 72 61 69 6c 2c 20 |ects at |a rail, |
|00002920| 77 65 20 61 64 64 20 74 | 6f 20 74 68 65 20 72 65 |we add t|o the re|
|00002930| 66 6c 65 63 74 65 64 20 | 76 65 6c 6f 63 69 74 79 |flected |velocity|
|00002940| 20 74 68 65 20 66 6f 6c | 6c 6f 77 69 6e 67 20 0d | the fol|lowing .|
|00002950| 20 20 20 20 20 63 72 6f | 73 73 2d 20 70 72 6f 64 | cro|ss- prod|
|00002960| 75 63 74 20 65 78 70 72 | 65 73 73 69 6f 6e 3a 0d |uct expr|ession:.|
|00002970| 20 20 20 20 20 20 20 20 | 0d 20 20 20 20 20 20 20 | |. |
|00002980| 20 20 20 20 20 20 20 6b | 28 6f 6d 65 67 61 20 58 | k|(omega X|
|00002990| 20 76 65 6c 6f 63 69 74 | 79 29 0d 20 20 20 20 20 | velocit|y). |
|000029a0| 20 20 20 20 20 20 20 20 | 20 0d 20 20 20 20 20 77 | | . w|
|000029b0| 68 65 72 65 20 6f 6d 65 | 67 61 20 69 73 20 61 20 |here ome|ga is a |
|000029c0| 75 6e 69 74 20 76 65 63 | 74 6f 72 20 6e 6f 72 6d |unit vec|tor norm|
|000029d0| 61 6c 20 74 6f 20 74 68 | 65 20 70 6c 61 6e 65 20 |al to th|e plane |
|000029e0| 6f 66 20 74 68 65 20 74 | 61 62 6c 65 20 61 6e 64 |of the t|able and|
|000029f0| 20 0d 20 20 20 20 20 69 | 6e 64 69 63 61 74 69 6e | . i|ndicatin|
|00002a00| 67 20 61 6e 67 75 6c 61 | 72 20 72 6f 74 61 74 69 |g angula|r rotati|
|00002a10| 6f 6e 2c 20 77 68 69 6c | 65 20 6b 20 69 73 20 74 |on, whil|e k is t|
|00002a20| 68 65 20 76 61 6c 75 65 | 20 6f 66 20 28 68 6f 72 |he value| of (hor|
|00002a30| 69 7a 6f 6e 74 61 6c 29 | 0d 20 20 20 20 20 45 6e |izontal)|. En|
|00002a40| 67 6c 69 73 68 2e 20 20 | 46 6f 72 20 76 65 72 74 |glish. |For vert|
|00002a50| 69 63 61 6c 20 45 6e 67 | 6c 69 73 68 20 61 74 20 |ical Eng|lish at |
|00002a60| 61 20 72 61 69 6c 2c 20 | 77 65 20 73 69 6d 70 6c |a rail, |we simpl|
|00002a70| 79 20 61 64 64 20 74 6f | 20 74 68 65 20 6e 6f 72 |y add to| the nor|
|00002a80| 6d 61 6c 20 0d 20 20 20 | 20 20 72 65 66 6c 65 63 |mal . | reflec|
|00002a90| 74 65 64 20 63 6f 6d 70 | 6f 6e 65 6e 74 20 56 6e |ted comp|onent Vn|
|00002aa0| 20 74 68 65 20 71 75 61 | 6e 74 69 74 79 20 68 2a | the qua|ntity h*|
|00002ab0| 56 6e 20 77 68 65 72 65 | 20 68 20 69 73 20 6e 6f |Vn where| h is no|
|00002ac0| 77 20 74 68 65 20 76 65 | 72 74 69 63 61 6c 20 0d |w the ve|rtical .|
|00002ad0| 20 20 20 20 20 45 6e 67 | 6c 69 73 68 2e 20 20 54 | Eng|lish. T|
|00002ae0| 68 65 73 65 20 72 75 6c | 65 73 20 61 72 65 20 6e |hese rul|es are n|
|00002af0| 6f 74 20 63 6f 6d 70 6c | 65 74 65 6c 79 20 65 78 |ot compl|etely ex|
|00002b00| 61 63 74 20 70 68 79 73 | 69 63 61 6c 6c 79 2c 20 |act phys|ically, |
|00002b10| 62 75 74 20 69 74 20 69 | 73 20 0d 20 20 20 20 20 |but it i|s . |
|00002b20| 65 61 73 79 20 74 6f 20 | 73 68 6f 77 20 74 68 61 |easy to |show tha|
|00002b30| 74 20 74 68 65 20 6d 61 | 6a 6f 72 20 71 75 61 6c |t the ma|jor qual|
|00002b40| 69 74 61 74 69 76 65 20 | 62 65 68 61 76 69 6f 72 |itative |behavior|
|00002b50| 20 6f 66 20 45 6e 67 6c | 69 73 68 20 61 74 20 72 | of Engl|ish at r|
|00002b60| 61 69 6c 73 20 0d 20 20 | 20 20 20 69 73 20 68 61 |ails . | is ha|
|00002b70| 6e 64 6c 65 64 20 63 6f | 72 72 65 63 74 6c 79 20 |ndled co|rrectly |
|00002b80| 77 69 74 68 20 74 68 65 | 73 65 20 73 69 6d 70 6c |with the|se simpl|
|00002b90| 65 20 63 61 6c 63 75 6c | 61 74 69 6f 6e 73 2e 20 |e calcul|ations. |
|00002ba0| 20 46 6f 72 20 45 6e 67 | 6c 69 73 68 20 0d 20 20 | For Eng|lish . |
|00002bb0| 20 20 20 64 75 72 69 6e | 67 20 62 61 6c 6c 2d 62 | durin|g ball-b|
|00002bc0| 61 6c 6c 20 65 6e 63 6f | 75 6e 74 65 72 73 2c 20 |all enco|unters, |
|00002bd0| 74 68 65 20 73 61 6d 65 | 20 66 6f 72 6d 75 6c 61 |the same| formula|
|00002be0| 20 61 72 65 20 75 73 65 | 64 2c 20 62 75 74 20 72 | are use|d, but r|
|00002bf0| 65 6c 65 67 61 74 65 64 | 20 0d 20 20 20 20 20 6f |elegated| . o|
|00002c00| 66 20 63 6f 75 72 73 65 | 20 74 6f 20 74 68 65 20 |f course| to the |
|00002c10| 63 65 6e 74 65 72 2d 6f | 66 2d 6d 6f 6d 65 6e 74 |center-o|f-moment|
|00002c20| 75 6d 20 66 72 61 6d 65 | 2c 20 77 68 65 72 65 20 |um frame|, where |
|00002c30| 65 61 63 68 20 62 61 6c | 6c 20 73 65 65 73 20 69 |each bal|l sees i|
|00002c40| 6e 20 0d 20 20 20 20 20 | 65 66 66 65 63 74 20 74 |n . |effect t|
|00002c50| 68 65 20 6f 74 68 65 72 | 20 62 61 6c 6c 20 61 73 |he other| ball as|
|00002c60| 20 61 20 27 72 61 69 6c | 27 2e 0d 3e 3e 0d 20 20 | a 'rail|'..>>. |
|00002c70| 20 20 20 35 29 20 42 69 | 6c 6c 69 61 72 64 20 50 | 5) Bi|lliard P|
|00002c80| 61 72 6c 6f 75 72 20 64 | 79 6e 61 6d 69 63 61 6c |arlour d|ynamical|
|00002c90| 20 63 61 6c 63 75 6c 61 | 74 69 6f 6e 73 20 61 72 | calcula|tions ar|
|00002ca0| 65 20 6e 6f 74 20 65 78 | 61 63 74 2c 20 61 6e 64 |e not ex|act, and|
|00002cb0| 20 66 6f 72 20 74 68 65 | 0d 20 20 20 20 20 20 20 | for the|. |
|00002cc0| 20 73 61 6b 65 20 6f 66 | 20 73 70 65 65 64 20 73 | sake of| speed s|
|00002cd0| 6f 6d 65 20 27 6d 6f 6c | 65 63 75 6c 61 72 27 20 |ome 'mol|ecular' |
|00002ce0| 65 66 66 65 63 74 73 20 | 2d 20 69 6e 20 77 68 69 |effects |- in whi|
|00002cf0| 63 68 20 62 61 6c 6c 73 | 20 73 74 69 63 6b 20 0d |ch balls| stick .|
|00002d00| 20 20 20 20 20 20 20 20 | 74 6f 67 65 74 68 65 72 | |together|
|00002d10| 20 6d 6f 6d 65 6e 74 61 | 72 69 6c 79 20 2d 20 68 | momenta|rily - h|
|00002d20| 61 76 65 20 62 65 65 6e | 20 6c 65 66 74 20 69 6e |ave been| left in|
|00002d30| 2e 20 20 54 68 65 73 65 | 20 65 66 66 65 63 74 73 |. These| effects|
|00002d40| 20 6f 63 63 75 72 20 0d | 20 20 20 20 20 20 20 20 | occur .| |
|00002d50| 70 72 69 6d 61 72 69 6c | 79 20 62 65 63 61 75 73 |primaril|y becaus|
|00002d60| 65 20 6f 66 20 74 68 65 | 20 61 6d 62 69 67 75 69 |e of the| ambigui|
|00002d70| 74 79 20 62 65 74 77 65 | 65 6e 20 69 6e 63 6f 6d |ty betwe|en incom|
|00002d80| 69 6e 67 20 61 6e 64 20 | 6f 75 74 67 6f 69 6e 67 |ing and |outgoing|
|00002d90| 20 0d 20 20 20 20 20 20 | 20 20 63 6f 6c 6c 69 73 | . | collis|
|00002da0| 69 6f 6e 73 3a 20 69 66 | 20 74 77 6f 20 62 61 6c |ions: if| two bal|
|00002db0| 6c 73 20 6d 75 74 75 61 | 6c 6c 79 20 70 65 6e 65 |ls mutua|lly pene|
|00002dc0| 74 72 61 74 65 2c 20 69 | 74 20 69 73 20 6e 6f 74 |trate, i|t is not|
|00002dd0| 20 65 61 73 79 20 74 6f | 20 0d 20 20 20 20 20 20 | easy to| . |
|00002de0| 20 20 66 69 6e 64 20 6f | 75 74 20 77 68 65 74 68 | find o|ut wheth|
|00002df0| 65 72 20 74 68 65 79 20 | 68 61 76 65 20 6a 75 73 |er they |have jus|
|00002e00| 74 20 68 61 64 20 74 68 | 65 69 72 20 76 65 6c 6f |t had th|eir velo|
|00002e10| 63 69 74 69 65 73 20 72 | 65 66 6c 65 63 74 65 64 |cities r|eflected|
|00002e20| 2c 20 6f 72 20 0d 20 20 | 20 20 20 20 20 20 77 68 |, or . | wh|
|00002e30| 65 74 68 65 72 20 6e 6f | 77 20 69 73 20 74 68 65 |ether no|w is the|
|00002e40| 20 74 69 6d 65 20 74 6f | 20 73 6f 20 72 65 66 6c | time to| so refl|
|00002e50| 65 63 74 2e 20 20 54 68 | 65 20 61 6d 62 69 67 75 |ect. Th|e ambigu|
|00002e60| 69 74 79 20 69 73 20 0d | 20 20 20 20 20 20 20 20 |ity is .| |
|00002e70| 65 73 70 65 63 69 61 6c | 6c 79 20 66 69 65 72 63 |especial|ly fierc|
|00002e80| 65 20 77 68 65 6e 20 6d | 61 6e 79 20 62 61 6c 6c |e when m|any ball|
|00002e90| 73 20 61 72 65 20 62 61 | 6e 67 69 6e 67 20 61 72 |s are ba|nging ar|
|00002ea0| 6f 75 6e 64 20 69 6e 20 | 61 20 63 6c 75 74 63 68 |ound in |a clutch|
|00002eb0| 2e 20 20 0d 20 20 20 20 | 20 20 20 20 53 6f 20 74 |. . | So t|
|00002ec0| 68 65 20 61 70 70 6c 69 | 63 61 74 69 6f 6e 20 77 |he appli|cation w|
|00002ed0| 61 73 20 64 65 73 69 67 | 6e 65 64 20 66 6f 72 20 |as desig|ned for |
|00002ee0| 73 70 65 65 64 3a 20 74 | 68 65 72 65 20 69 73 20 |speed: t|here is |
|00002ef0| 61 20 6d 6f 6c 65 63 75 | 6c 65 20 0d 20 20 20 20 |a molecu|le . |
|00002f00| 20 20 20 20 66 72 6f 6d | 20 74 69 6d 65 20 74 6f | from| time to|
|00002f10| 20 74 69 6d 65 2c 20 62 | 75 74 20 74 68 65 20 6d | time, b|ut the m|
|00002f20| 6f 6c 65 63 75 6c 65 20 | 64 6f 65 73 20 6e 6f 74 |olecule |does not|
|00002f30| 20 73 74 61 79 20 74 6f | 67 65 74 68 65 72 2e 20 | stay to|gether. |
|00002f40| 20 0d 20 20 20 20 20 20 | 20 20 52 65 6d 6f 76 69 | . | Removi|
|00002f50| 6e 67 20 61 6c 6c 20 75 | 6e 72 65 61 6c 69 73 74 |ng all u|nrealist|
|00002f60| 69 63 20 65 66 66 65 63 | 74 73 20 70 72 6f 76 65 |ic effec|ts prove|
|00002f70| 73 20 74 6f 20 74 61 6b | 65 20 74 6f 6f 20 6d 75 |s to tak|e too mu|
|00002f80| 63 68 20 63 6f 6d 70 75 | 74 65 20 0d 20 20 20 20 |ch compu|te . |
|00002f90| 20 20 20 20 74 69 6d 65 | 20 61 77 61 79 20 66 72 | time| away fr|
|00002fa0| 6f 6d 20 74 68 65 20 6f | 74 68 65 72 77 69 73 65 |om the o|therwise|
|00002fb0| 20 70 6c 65 61 73 69 6e | 67 20 6d 6f 74 69 6f 6e | pleasin|g motion|
|00002fc0| 2e 0d 3e 3e 0d 54 68 65 | 20 73 65 72 69 6f 75 73 |..>>.The| serious|
|00002fd0| 20 70 72 6f 67 72 61 6d | 6d 65 72 20 6d 61 79 20 | program|mer may |
|00002fe0| 61 6c 73 6f 20 62 65 20 | 69 6e 74 65 72 65 73 74 |also be |interest|
|00002ff0| 65 64 20 69 6e 20 74 68 | 65 20 76 61 72 69 6f 75 |ed in th|e variou|
|00003000| 73 20 75 74 69 6c 69 74 | 69 65 73 20 61 6e 64 0d |s utilit|ies and.|
|00003010| 6d 65 74 68 6f 64 73 20 | 75 6e 72 65 6c 61 74 65 |methods |unrelate|
|00003020| 64 20 74 6f 20 64 79 6e | 61 6d 69 63 73 20 74 68 |d to dyn|amics th|
|00003030| 61 74 20 77 65 6e 74 20 | 69 6e 74 6f 20 74 68 65 |at went |into the|
|00003040| 20 70 72 6f 6a 65 63 74 | 2e 20 20 54 68 65 20 0d | project|. The .|
|00003050| 6d 61 67 6e 69 66 69 63 | 61 74 69 6f 6e 20 66 65 |magnific|ation fe|
|00003060| 61 74 75 72 65 20 66 6f | 72 20 72 65 61 64 69 6e |ature fo|r readin|
|00003070| 67 20 62 61 6c 6c 73 20 | 61 6e 64 20 70 6f 73 69 |g balls |and posi|
|00003080| 74 69 6f 6e 73 20 65 61 | 73 69 6c 79 20 69 73 20 |tions ea|sily is |
|00003090| 61 20 67 6f 6f 64 20 0d | 65 78 61 6d 70 6c 65 20 |a good .|example |
|000030a0| 6f 66 20 52 61 73 63 61 | 6c 20 6f 66 66 2d 73 63 |of Rasca|l off-sc|
|000030b0| 72 65 65 6e 20 70 6f 72 | 74 20 67 72 61 70 68 69 |reen por|t graphi|
|000030c0| 63 73 2e 20 20 54 68 65 | 20 73 6f 75 6e 64 20 6f |cs. The| sound o|
|000030d0| 66 20 62 61 6c 6c 20 63 | 6c 69 63 6b 73 20 69 73 |f ball c|licks is|
|000030e0| 20 0d 61 63 68 69 65 76 | 65 64 20 62 79 20 66 72 | .achiev|ed by fr|
|000030f0| 65 65 2d 66 6f 72 6d 20 | 73 79 6e 74 68 65 73 69 |ee-form |synthesi|
|00003100| 73 20 6f 66 20 27 63 68 | 69 72 70 27 20 77 61 76 |s of 'ch|irp' wav|
|00003110| 65 73 20 2d 20 69 2e 65 | 2e 20 68 69 67 68 2d 66 |es - i.e|. high-f|
|00003120| 72 65 71 75 65 6e 63 79 | 2c 20 0d 62 72 69 65 66 |requency|, .brief|
|00003130| 20 74 6f 6e 65 20 62 75 | 72 73 74 73 2e 20 20 54 | tone bu|rsts. T|
|00003140| 68 65 20 67 72 61 70 68 | 69 63 73 20 70 72 6f 62 |he graph|ics prob|
|00003150| 6c 65 6d 20 70 72 65 73 | 65 6e 74 65 64 20 62 79 |lem pres|ented by|
|00003160| 20 74 68 65 20 63 61 72 | 72 6f 6d 73 20 73 63 6f | the car|roms sco|
|00003170| 72 69 6e 67 20 0d 72 61 | 63 6b 20 69 73 20 73 75 |ring .ra|ck is su|
|00003180| 72 70 72 69 73 69 6e 67 | 6c 79 20 64 69 66 66 69 |rprising|ly diffi|
|00003190| 63 75 6c 74 2c 20 61 6e | 64 20 73 74 61 6e 64 73 |cult, an|d stands|
|000031a0| 20 61 73 20 61 20 67 6f | 6f 64 20 65 78 61 6d 70 | as a go|od examp|
|000031b0| 6c 65 20 6f 66 20 73 74 | 72 61 69 67 68 74 20 0d |le of st|raight .|
|000031c0| 71 75 69 63 6b 64 72 61 | 77 20 6d 65 74 68 6f 64 |quickdra|w method|
|000031d0| 73 2e 0d 0d 54 68 65 20 | 6b 65 79 20 67 72 61 70 |s...The |key grap|
|000031e0| 68 69 63 73 20 70 72 6f | 63 65 64 75 72 65 73 20 |hics pro|cedures |
|000031f0| 61 72 65 20 66 6f 75 6e | 64 20 6f 6e 20 74 68 65 |are foun|d on the|
|00003200| 20 73 74 61 6e 64 61 72 | 64 20 52 61 73 63 61 6c | standar|d Rascal|
|00003210| 20 4a 61 6e 20 31 39 38 | 36 0d 72 65 6c 65 61 73 | Jan 198|6.releas|
|00003220| 65 20 61 73 20 6c 69 62 | 72 61 72 79 20 65 6e 74 |e as lib|rary ent|
|00003230| 72 69 65 73 2e 20 20 54 | 68 65 20 6b 65 79 20 6c |ries. T|he key l|
|00003240| 69 62 72 61 72 79 20 69 | 73 20 63 61 6c 6c 65 64 |ibrary i|s called|
|00003250| 20 5f 5f 47 72 61 70 68 | 55 74 69 6c 73 2c 20 61 | __Graph|Utils, a|
|00003260| 6e 64 0d 68 61 73 20 6d | 61 6e 79 20 74 68 69 6e |nd.has m|any thin|
|00003270| 67 73 20 66 72 6f 6d 20 | 73 63 72 65 65 6e 20 69 |gs from |screen i|
|00003280| 6e 69 74 69 61 6c 69 7a | 61 74 69 6f 6e 20 74 6f |nitializ|ation to|
|00003290| 20 68 69 67 68 2d 73 70 | 65 65 64 20 73 69 6e 65 | high-sp|eed sine|
|000032a0| 2c 20 63 6f 73 69 6e 65 | 2c 20 61 6e 64 0d 73 71 |, cosine|, and.sq|
|000032b0| 75 61 72 65 20 72 6f 6f | 74 20 66 75 6e 63 74 69 |uare roo|t functi|
|000032c0| 6f 6e 73 3b 20 69 6e 20 | 67 65 6e 65 72 61 6c 20 |ons; in |general |
|000032d0| 69 6e 74 65 67 65 72 20 | 74 65 63 68 6e 69 71 75 |integer |techniqu|
|000032e0| 65 73 20 66 6f 72 20 66 | 61 73 74 20 67 72 61 70 |es for f|ast grap|
|000032f0| 68 69 63 73 2e 0d 42 75 | 74 20 6f 74 68 65 72 20 |hics..Bu|t other |
|00003300| 6c 69 62 72 61 72 69 65 | 73 20 61 72 65 20 69 6e |librarie|s are in|
|00003310| 76 6f 6c 76 65 64 20 68 | 65 61 76 69 6c 79 20 2d |volved h|eavily -|
|00003320| 20 74 68 65 20 69 6e 74 | 65 72 65 73 74 65 64 20 | the int|erested |
|00003330| 70 72 6f 67 72 61 6d 6d | 65 72 20 63 61 6e 0d 63 |programm|er can.c|
|00003340| 6f 6e 73 75 6c 74 20 74 | 68 65 20 42 69 6c 6c 69 |onsult t|he Billi|
|00003350| 61 72 64 20 50 61 72 6c | 6f 75 72 20 73 6f 75 72 |ard Parl|our sour|
|00003360| 63 65 20 6c 69 73 74 69 | 6e 67 20 69 6e 20 63 6f |ce listi|ng in co|
|00003370| 6e 6a 75 6e 63 74 69 6f | 6e 20 77 69 74 68 20 74 |njunctio|n with t|
|00003380| 68 65 20 52 61 73 63 61 | 6c 0d 55 73 65 72 20 4d |he Rasca|l.User M|
|00003390| 61 6e 75 61 6c 2e 00 00 | 00 00 00 00 00 00 00 00 |anual...|........|
|000033a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000033b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000033c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000033d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000033e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000033f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003400| 00 00 01 00 00 00 01 00 | 00 00 00 00 00 00 00 1e |........|........|
|00003410| e4 20 00 54 ac 84 81 00 | 89 52 22 19 49 10 42 05 |. .T....|.R".I.B.|
|00003420| e4 49 4a 52 88 a4 89 24 | a2 4d 14 45 29 22 21 02 |.IJR...$|.M.E)"!.|
|00003430| 15 42 69 6c 6c 69 61 72 | 64 20 50 61 72 6c 6f 75 |.Billiar|d Parlou|
|00003440| 72 2e 48 65 6c 70 02 00 | 00 00 50 61 72 74 53 49 |r.Help..|..PartSI|
|00003450| 00 00 50 61 72 74 53 49 | 54 78 00 00 00 00 00 00 |..PartSI|Tx......|
|00003460| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003470| 00 00 a9 7f d2 3a 00 00 | 00 00 00 00 01 1e 0e fe |.....:..|........|
|00003480| 37 bf c7 77 cb bf f7 ec | ee 3b be 71 c1 02 8d bb |7..w....|.;.q....|
|00003490| e1 47 e3 d9 9c df dd f7 | 7f 6f b6 73 bb 8b 48 53 |.G......|.o.s..HS|
|000034a0| 64 f5 41 df b9 bf d9 c7 | 1d dd dd d9 99 9b ff fb |d.A.....|........|
|000034b0| 66 66 63 4d 34 d0 1d e9 | 05 a7 38 00 ef b8 40 07 |ffcM4...|..8...@.|
|000034c0| cc 69 69 5e fd dc fe d8 | 00 00 08 20 87 e0 00 10 |.ii^....|... ....|
|000034d0| 00 03 00 20 00 00 c0 c0 | 00 44 00 01 e0 00 00 00 |... ....|.D......|
|000034e0| 00 00 08 00 00 00 00 10 | 00 00 00 00 00 00 30 c0 |........|......0.|
|000034f0| 00 00 00 02 20 04 00 00 | 00 40 80 00 00 00 08 03 |.... ...|.@......|
|00003500| 00 00 01 00 00 00 01 00 | 00 00 00 00 00 00 00 1e |........|........|
|00003510| 00 00 00 00 00 00 00 00 | 00 1c 00 1e ff ff 00 00 |........|........|
|00003520| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003530| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003540| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003550| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003560| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003570| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
+--------+-------------------------+-------------------------+--------+--------+
