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|00000b20| 6e 74 20 43 6f 6e 74 65 | 6e 74 73 20 6f 66 20 41 |nt Conte|nts of A|
|00000b30| 72 63 68 69 76 65 20 66 | 74 70 2e 63 73 68 2e 72 |rchive f|tp.csh.r|
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|00000b70| 68 61 74 27 73 20 6e 65 | 77 3f 0a 0a 20 20 20 20 |hat's ne|w?..    |
|00000b80| 20 44 65 73 63 72 69 70 | 74 69 6f 6e 20 6f 66 20 | Descrip|tion of |
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|00000cb0| 64 20 69 74 20 74 6f 6f | 2e 20 20 42 75 74 2e 2e |d it too|.  But..|
|00000cc0| 2e 0a 72 65 67 61 72 64 | 6c 65 73 73 2c 20 74 68 |..regard|less, th|
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|00003650| 20 20 20 20 20 20 6d 61 | 74 72 69 78 20 6d 72 2c |      ma|trix mr,|
|00003660| 20 6d 70 2c 20 6d 79 3b | 20 20 20 20 20 20 2f 2a | mp, my;|      /*|
|00003670| 20 69 6e 64 69 76 69 64 | 75 61 6c 20 74 72 61 6e | individ|ual tran|
|00003680| 73 66 6f 72 6d 61 74 69 | 6f 6e 73 20 2a 2f 0a 20 |sformati|ons */. |
|00003690| 20 20 20 20 20 20 20 6d | 61 74 72 69 78 20 73 3b |       m|atrix s;|
|000036a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 2f |        |       /|
|000036b0| 2a 20 66 69 6e 61 6c 20 | 6d 61 74 72 69 78 20 2a |* final |matrix *|
|000036c0| 2f 0a 0a 20 20 20 20 20 | 20 20 20 73 72 20 3d 20 |/..     |   sr = |
|000036d0| 73 69 6e 28 20 72 6f 6c | 6c 20 29 3b 20 20 20 20 |sin( rol|l );    |
|000036e0| 20 63 72 20 3d 20 63 6f | 73 28 20 72 6f 6c 6c 20 | cr = co|s( roll |
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|00003700| 73 69 6e 28 20 70 69 74 | 63 68 20 29 3b 20 20 20 |sin( pit|ch );   |
|00003710| 20 63 70 20 3d 20 63 6f | 73 28 20 70 69 74 63 68 | cp = co|s( pitch|
|00003720| 20 29 3b 0a 20 20 20 20 | 20 20 20 20 73 79 20 3d | );.    |    sy =|
|00003730| 20 73 69 6e 28 20 79 61 | 77 20 29 3b 20 20 20 20 | sin( ya|w );    |
|00003740| 20 20 63 79 20 3d 20 63 | 6f 73 28 20 79 61 77 20 |  cy = c|os( yaw |
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|00003760| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003770| 20 20 20 20 2f 2a 20 63 | 6c 65 61 72 20 61 6c 6c |    /* c|lear all|
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|00003790| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|000037e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 2a 2f |        |      */|
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|00003880| 5d 20 3d 20 63 72 3b 0a | 20 20 20 20 20 20 20 20 |] = cr;.|        |
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|000038b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00003930| 3b 0a 0a 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |;..     |        |
|00003940| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00005f20| 6f 6e 74 2d 4f 66 20 6f | 72 20 42 65 68 69 6e 64 |ont-Of o|r Behind|
|00005f30| 0a 20 20 20 20 20 20 20 | 20 74 68 65 20 72 6f 6f |.       | the roo|
|00005f40| 74 20 6e 6f 64 65 2e 20 | 20 28 54 68 69 73 20 69 |t node. | (This i|
|00005f50| 73 20 74 68 65 20 74 72 | 69 63 6b 79 20 62 69 74 |s the tr|icky bit|
|00005f60| 29 2e 0a 20 20 20 20 34 | 29 20 52 65 70 65 61 74 |)..    4|) Repeat|
|00005f70| 20 74 68 65 73 65 20 73 | 74 65 70 73 20 77 69 74 | these s|teps wit|
|00005f80| 68 20 74 68 65 20 27 46 | 72 6f 6e 74 20 48 65 61 |h the 'F|ront Hea|
|00005f90| 70 27 20 61 6e 64 20 74 | 68 65 20 27 42 61 63 6b |p' and t|he 'Back|
|00005fa0| 20 48 65 61 70 27 2e 0a | 41 73 20 61 6e 20 69 6e | Heap'..|As an in|
|00005fb0| 74 65 72 65 73 74 69 6e | 67 20 6e 6f 74 65 2c 20 |terestin|g note, |
|00005fc0| 49 20 63 61 6e 20 73 65 | 65 20 6e 6f 20 61 64 76 |I can se|e no adv|
|00005fd0| 61 6e 74 61 67 65 20 61 | 74 20 61 6c 6c 20 74 6f |antage a|t all to|
|00005fe0| 20 74 72 79 69 6e 67 20 | 74 6f 20 6b 65 65 70 0a | trying |to keep.|
|00005ff0| 61 20 72 65 6c 61 74 69 | 76 65 6c 79 20 62 61 6c |a relati|vely bal|
|00006000| 61 6e 63 65 64 20 74 72 | 65 65 2e 0a 0a 20 20 20 |anced tr|ee...   |
|00006010| 20 20 4e 6f 77 20 63 6f | 6d 65 73 20 74 68 65 20 |  Now co|mes the |
|00006020| 69 6e 74 65 72 65 73 74 | 69 6e 67 20 62 69 74 2e |interest|ing bit.|
|00006030| 20 20 4e 6f 77 20 74 68 | 61 74 20 74 68 65 20 6f |  Now th|at the o|
|00006040| 62 6a 65 63 74 20 69 73 | 20 61 20 27 67 6f 6f 64 |bject is| a 'good|
|00006050| 27 0a 42 53 50 2d 74 72 | 65 65 20 6f 62 6a 65 63 |'.BSP-tr|ee objec|
|00006060| 74 2c 20 69 74 20 69 73 | 20 74 69 6d 65 20 66 6f |t, it is| time fo|
|00006070| 72 20 74 68 65 20 64 72 | 61 77 69 6e 67 20 61 6c |r the dr|awing al|
|00006080| 67 6f 72 69 74 68 6d 2e | 20 20 54 68 69 73 20 69 |gorithm.|  This i|
|00006090| 73 20 66 61 69 72 6c 79 | 0a 73 74 72 61 69 67 68 |s fairly|.straigh|
|000060a0| 74 2d 20 66 6f 72 77 61 | 72 64 2e 0a 20 20 20 20 |t- forwa|rd..    |
|000060b0| 31 29 20 43 6f 6d 70 61 | 72 65 20 74 68 65 20 72 |1) Compa|re the r|
|000060c0| 6f 6f 74 20 6e 6f 64 65 | 20 77 69 74 68 20 79 6f |oot node| with yo|
|000060d0| 75 2e 0a 20 20 20 20 32 | 29 20 49 66 20 79 6f 75 |u..    2|) If you|
|000060e0| 20 61 72 65 20 49 6e 2d | 46 72 6f 6e 74 2d 4f 66 | are In-|Front-Of|
|000060f0| 20 74 68 65 20 72 6f 6f | 74 20 6e 6f 64 65 2c 0a | the roo|t node,.|
|00006100| 20 20 20 20 20 20 20 20 | 64 72 61 77 20 27 52 6f |        |draw 'Ro|
|00006110| 6f 74 2d 3e 42 61 63 6b | 27 2c 20 74 68 65 6e 20 |ot->Back|', then |
|00006120| 74 68 65 20 52 6f 6f 74 | 20 73 75 72 66 61 63 65 |the Root| surface|
|00006130| 2c 20 74 68 65 6e 20 27 | 52 6f 6f 74 2d 3e 46 72 |, then '|Root->Fr|
|00006140| 6f 6e 74 27 2e 0a 20 20 | 20 20 20 20 20 49 66 20 |ont'..  |     If |
|00006150| 79 6f 75 20 61 72 65 20 | 42 65 68 69 6e 64 20 74 |you are |Behind t|
|00006160| 68 65 20 72 6f 6f 74 20 | 6e 6f 64 65 2c 0a 20 20 |he root |node,.  |
|00006170| 20 20 20 20 20 20 64 72 | 61 77 20 27 52 6f 6f 74 |      dr|aw 'Root|
|00006180| 2d 3e 46 72 6f 6e 74 27 | 2c 20 74 68 65 6e 20 74 |->Front'|, then t|
|00006190| 68 65 20 52 6f 6f 74 20 | 73 75 72 66 61 63 65 20 |he Root |surface |
|000061a0| 28 75 6e 6c 65 73 73 20 | 79 6f 75 27 72 65 0a 20 |(unless |you're. |
|000061b0| 20 20 20 20 20 20 20 62 | 61 63 6b 66 61 63 65 20 |       b|ackface |
|000061c0| 63 75 6c 6c 69 6e 67 29 | 2c 20 74 68 65 6e 20 27 |culling)|, then '|
|000061d0| 52 6f 6f 74 2d 3e 42 61 | 63 6b 27 2e 0a 0a 20 20 |Root->Ba|ck'...  |
|000061e0| 20 20 20 49 20 66 75 6c | 6c 79 20 61 64 6d 69 74 |   I ful|ly admit|
|000061f0| 20 74 68 61 74 20 49 20 | 64 69 64 6e 27 74 20 62 | that I |didn't b|
|00006200| 65 6c 69 65 76 65 20 42 | 53 50 2d 74 72 65 65 73 |elieve B|SP-trees|
|00006210| 20 77 6f 75 6c 64 20 77 | 6f 72 6b 20 77 68 65 6e | would w|ork when|
|00006220| 20 49 0a 66 69 72 73 74 | 20 72 65 61 64 20 61 62 | I.first| read ab|
|00006230| 6f 75 74 20 74 68 65 6d | 20 69 6e 20 46 6f 6c 65 |out them| in Fole|
|00006240| 79 2d 76 61 6e 20 44 61 | 6d 2c 20 6e 6f 72 20 64 |y-van Da|m, nor d|
|00006250| 69 64 20 49 20 62 65 6c | 69 65 76 65 20 74 68 65 |id I bel|ieve the|
|00006260| 79 20 77 6f 75 6c 64 0a | 77 6f 72 6b 20 61 66 74 |y would.|work aft|
|00006270| 65 72 20 73 65 65 69 6e | 67 20 74 68 65 6d 20 77 |er seein|g them w|
|00006280| 6f 72 6b 20 66 6f 72 20 | 6d 65 2e 20 20 4e 6f 77 |ork for |me.  Now|
|00006290| 2c 20 74 68 72 65 65 20 | 6d 6f 6e 74 68 73 20 6c |, three |months l|
|000062a0| 61 74 65 72 2c 20 49 20 | 66 75 6c 6c 79 0a 62 65 |ater, I |fully.be|
|000062b0| 6c 69 65 76 65 20 74 68 | 65 79 20 77 6f 72 6b 2c |lieve th|ey work,|
|000062c0| 20 61 6e 64 20 49 20 63 | 61 6e 20 65 76 65 6e 20 | and I c|an even |
|000062d0| 73 61 79 20 49 20 75 6e | 64 65 72 73 74 61 6e 64 |say I un|derstand|
|000062e0| 20 77 68 79 2e 20 20 49 | 20 6d 61 79 20 73 6f 6f | why.  I| may soo|
|000062f0| 6e 0a 61 74 74 65 6d 70 | 74 20 61 6e 20 65 78 70 |n.attemp|t an exp|
|00006300| 6c 61 6e 61 74 69 6f 6e | 20 68 65 72 65 2c 20 62 |lanation| here, b|
|00006310| 75 74 20 73 75 66 66 69 | 63 65 20 69 74 20 66 6f |ut suffi|ce it fo|
|00006320| 72 20 6e 6f 77 20 74 6f | 20 73 61 79 2c 20 27 74 |r now to| say, 't|
|00006330| 68 65 79 20 63 61 6e 20 | 62 65 0a 67 72 6f 6b 6b |hey can |be.grokk|
|00006340| 65 64 27 2e 0a 0a 31 33 | 29 20 53 68 61 64 69 6e |ed'...13|) Shadin|
|00006350| 67 2e 0a 0a 20 20 20 20 | 20 53 6f 72 72 79 2e 2e |g...    | Sorry..|
|00006360| 2e 20 54 68 69 73 20 69 | 73 20 61 20 46 41 51 20 |. This i|s a FAQ |
|00006370| 69 6e 2d 70 72 6f 67 72 | 65 73 73 2e 20 20 57 69 |in-progr|ess.  Wi|
|00006380| 6c 6c 20 64 6f 20 6d 6f | 72 65 20 6c 61 74 65 72 |ll do mo|re later|
|00006390| 2e 20 20 50 6c 65 61 73 | 65 0a 66 65 65 6c 20 66 |.  Pleas|e.feel f|
|000063a0| 72 65 65 20 74 6f 20 73 | 65 6e 64 20 6d 65 20 61 |ree to s|end me a|
|000063b0| 20 70 61 72 61 67 72 61 | 70 68 20 66 6f 72 20 74 | paragra|ph for t|
|000063c0| 68 69 73 20 73 65 63 74 | 69 6f 6e 2e 0a 0a 31 34 |his sect|ion...14|
|000063d0| 29 20 33 2d 73 70 61 63 | 65 20 63 6c 69 70 70 69 |) 3-spac|e clippi|
|000063e0| 6e 67 2e 0a 0a 20 20 20 | 20 20 53 6f 72 72 79 2e |ng...   |  Sorry.|
|000063f0| 2e 2e 20 54 68 69 73 20 | 69 73 20 61 20 46 41 51 |.. This |is a FAQ|
+--------+-------------------------+-------------------------+--------+--------+