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|000002d0| 0a 44 61 74 65 3a 20 36 | 20 4a 61 6e 20 38 38 20 |.Date: 6| Jan 88 |
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|00000420| 63 49 6c 72 6f 79 27 73 | 20 70 61 70 65 72 20 28 |cIlroy's| paper (|
|00000430| 22 42 65 73 74 20 41 70 | 70 72 6f 78 69 6d 61 74 |"Best Ap|proximat|
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|00000460| 64 20 46 6f 6c 65 79 20 | 26 20 56 61 6e 20 44 61 |d Foley |& Van Da|
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|00000480| 79 73 20 74 6f 20 64 72 | 61 77 20 74 68 65 20 63 |ys to dr|aw the c|
|00000490| 69 72 63 6c 65 3a 0a 0a | 3e 28 31 29 20 55 74 69 |ircle:..|>(1) Uti|
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|000004d0| 34 30 39 36 20 73 71 75 | 61 72 65 29 0a 20 20 20 |4096 squ|are).   |
|000004e0| 20 20 20 20 42 61 64 20 | 69 64 65 61 2e 0a 0a 3e |    Bad |idea...>|
|000004f0| 28 32 29 20 55 74 69 6c | 69 7a 65 20 22 64 65 76 |(2) Util|ize "dev|
|00000500| 69 63 65 20 63 6f 6f 72 | 64 69 6e 61 74 65 73 22 |ice coor|dinates"|
|00000510| 20 28 34 33 30 20 62 79 | 20 32 38 38 2c 20 69 6e | (430 by| 288, in|
|00000520| 20 74 68 69 73 20 63 61 | 73 65 29 2e 0a 20 20 20 | this ca|se)..   |
|00000530| 20 20 20 20 20 54 68 65 | 20 63 6f 72 72 65 63 74 |     The| correct|
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|00000550| 73 69 6e 67 20 73 6f 6d | 65 74 68 69 6e 67 20 73 |sing som|ething s|
|00000560| 69 6d 70 6c 65 20 74 68 | 61 74 20 77 6f 75 6c 64 |imple th|at would|
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|00000580| 20 64 72 61 77 20 6d 79 | 0a 3e 63 69 72 63 6c 65 | draw my|.>circle|
|00000590| 73 20 3f 3f 20 20 43 61 | 6e 20 61 6e 79 6f 6e 65 |s ??  Ca|n anyone|
|000005a0| 20 70 6f 69 6e 74 20 6d | 65 20 74 6f 20 61 6e 6f | point m|e to ano|
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|000005d0| 63 6f 76 65 72 73 20 74 | 68 65 20 64 72 61 77 69 |covers t|he drawi|
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|000005f0| 6e 20 61 20 73 63 72 65 | 65 6e 20 77 69 74 68 20 |n a scre|en with |
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|00000610| 63 74 0a 3e 72 61 74 69 | 6f 20 28 46 20 26 20 56 |ct.>rati|o (F & V|
|00000620| 44 20 6d 65 6e 74 69 6f | 6e 20 61 20 66 65 77 2c |D mentio|n a few,|
|00000630| 20 62 75 74 20 62 65 66 | 6f 72 65 20 49 20 67 6f | but bef|ore I go|
|00000640| 20 64 69 67 67 69 6e 67 | 20 75 70 20 74 68 65 20 | digging| up the |
|00000650| 61 72 74 69 63 6c 65 73 | 2c 0a 3e 64 6f 65 73 20 |articles|,.>does |
|00000660| 61 6e 79 6f 6e 65 20 6b | 6e 6f 77 20 69 66 20 74 |anyone k|now if t|
|00000670| 68 65 73 65 20 61 72 65 | 20 77 68 61 74 20 49 20 |hese are| what I |
|00000680| 73 68 6f 75 6c 64 20 62 | 65 20 6c 6f 6f 6b 69 6e |should b|e lookin|
|00000690| 67 20 61 74 29 20 3f 3f | 0a 0a 49 74 27 73 20 6e |g at) ??|..It's n|
|000006a0| 6f 74 20 72 65 61 6c 6c | 79 20 65 61 73 79 20 74 |ot reall|y easy t|
|000006b0| 6f 20 67 65 6e 65 72 61 | 74 65 20 67 6f 6f 64 20 |o genera|te good |
|000006c0| 6c 6f 6f 6b 69 6e 67 20 | 63 69 72 63 6c 65 73 20 |looking |circles |
|000006d0| 6f 6e 20 61 20 70 69 78 | 65 6c 20 67 72 69 64 2e |on a pix|el grid.|
|000006e0| 0a 41 66 74 65 72 20 74 | 72 79 69 6e 67 20 6c 6f |.After t|rying lo|
|000006f0| 74 73 20 6f 66 20 64 69 | 66 66 65 72 65 6e 74 20 |ts of di|fferent |
|00000700| 74 68 69 6e 67 73 2c 20 | 49 20 68 61 76 65 20 61 |things, |I have a|
|00000710| 64 6f 70 74 65 64 20 74 | 68 65 20 66 6f 6c 6c 6f |dopted t|he follo|
|00000720| 77 69 6e 67 0a 65 6c 6c | 69 70 73 65 20 64 72 61 |wing.ell|ipse dra|
|00000730| 77 65 72 2e 20 49 74 20 | 64 72 61 77 73 20 65 6c |wer. It |draws el|
|00000740| 6c 69 70 73 65 73 20 69 | 6e 20 70 69 78 65 6c 20 |lipses i|n pixel |
|00000750| 73 70 61 63 65 3b 20 74 | 6f 20 67 65 74 20 63 69 |space; t|o get ci|
|00000760| 72 63 6c 65 73 20 79 6f | 75 0a 66 65 65 64 20 69 |rcles yo|u.feed i|
|00000770| 74 20 74 68 65 20 70 72 | 6f 70 65 72 20 68 65 69 |t the pr|oper hei|
|00000780| 67 68 74 20 61 6e 64 20 | 77 69 64 74 68 20 69 6e |ght and |width in|
|00000790| 20 70 69 78 65 6c 73 2e | 20 54 68 69 73 20 74 68 | pixels.| This th|
|000007a0| 69 6e 65 20 77 6f 72 6b | 73 20 72 65 61 6c 6c 79 |ine work|s really|
|000007b0| 0a 77 65 6c 6c 20 66 6f | 72 20 63 69 72 63 6c 65 |.well fo|r circle|
|000007c0| 73 20 77 69 74 68 20 61 | 20 72 61 64 69 75 73 20 |s with a| radius |
|000007d0| 67 72 65 61 74 65 72 20 | 74 68 61 6e 20 34 2e 20 |greater |than 4. |
|000007e0| 46 6f 72 20 73 6d 61 6c | 6c 65 72 20 63 69 72 63 |For smal|ler circ|
|000007f0| 6c 65 73 2c 0a 69 74 20 | 70 61 79 73 20 69 6e 20 |les,.it |pays in |
|00000800| 74 65 72 6d 73 20 6f 66 | 20 6c 6f 6f 6b 69 6e 67 |terms of| looking|
|00000810| 20 6e 69 63 65 20 74 6f | 20 64 72 61 77 20 65 61 | nice to| draw ea|
|00000820| 63 68 20 73 69 7a 65 20 | 61 73 20 61 20 73 70 65 |ch size |as a spe|
|00000830| 63 69 61 6c 20 63 61 73 | 65 2e 0a 0a 54 68 65 20 |cial cas|e...The |
|00000840| 65 6e 63 6c 6f 73 65 64 | 20 70 72 6f 67 72 61 6d |enclosed| program|
|00000850| 20 75 73 65 73 20 74 68 | 65 20 73 74 61 6e 64 61 | uses th|e standa|
|00000860| 72 64 20 42 72 65 73 6e | 61 68 61 6e 20 61 6c 67 |rd Bresn|ahan alg|
|00000870| 6f 72 69 74 68 6d 20 66 | 6f 72 20 74 68 65 0a 62 |orithm f|or the.b|
|00000880| 65 73 74 20 61 70 70 72 | 6f 78 69 6d 61 74 69 6f |est appr|oximatio|
|00000890| 6e 20 6f 66 20 61 20 63 | 75 72 76 65 2e 20 49 74 |n of a c|urve. It|
|000008a0| 20 69 73 20 6f 70 74 69 | 6d 69 7a 65 64 20 66 6f | is opti|mized fo|
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|000008c0| 77 61 73 20 61 20 67 6f | 6f 64 20 72 65 66 65 72 |was a go|od refer|
|000008d0| 65 6e 63 65 20 74 6f 20 | 74 68 69 73 20 61 6e 20 |ence to |this an |
|000008e0| 61 72 74 69 63 6c 65 20 | 69 6e 20 44 72 2e 20 44 |article |in Dr. D|
|000008f0| 6f 62 62 73 20 4a 6f 75 | 72 6e 61 6c 20 69 6e 20 |obbs Jou|rnal in |
|00000900| 31 39 38 37 2c 0a 62 75 | 74 20 66 6f 72 20 63 69 |1987,.bu|t for ci|
|00000910| 72 63 6c 65 73 20 6f 6e | 6c 79 2c 20 6e 6f 74 20 |rcles on|ly, not |
|00000920| 65 6c 6c 69 70 73 65 73 | 2e 0a 0a 49 20 68 6f 70 |ellipses|...I hop|
|00000930| 65 20 74 68 61 74 20 74 | 68 69 73 20 63 61 6e 20 |e that t|his can |
|00000940| 68 65 6c 70 20 79 6f 75 | 2e 0a 0a 44 6f 75 67 20 |help you|...Doug |
|00000950| 4d 63 44 6f 6e 61 6c 64 | 0a 44 65 70 61 72 74 6d |McDonald|.Departm|
|00000960| 65 6e 74 20 6f 66 20 43 | 68 65 6d 69 73 74 72 79 |ent of C|hemistry|
|00000970| 0a 55 6e 69 76 65 72 73 | 69 74 79 20 6f 66 20 49 |.Univers|ity of I|
|00000980| 6c 6c 69 6e 6f 69 73 0a | 0a 0a 2f 2a 20 44 72 61 |llinois.|../* Dra|
|00000990| 77 20 61 6e 20 65 6c 6c | 69 70 73 65 20 77 69 74 |w an ell|ipse wit|
|000009a0| 68 20 77 69 64 74 68 20 | 69 72 78 20 61 6e 64 20 |h width |irx and |
|000009b0| 68 65 69 67 68 74 20 69 | 72 79 20 20 20 20 20 20 |height i|ry      |
|000009c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000009d0| 20 20 20 2a 2f 0a 2f 2a | 20 66 72 6f 6d 20 61 20 |   */./*| from a |
|000009e0| 72 6f 75 74 69 6e 65 20 | 62 79 20 54 69 6d 20 48 |routine |by Tim H|
|000009f0| 6f 67 61 6e 20 69 6e 20 | 44 72 2e 20 44 6f 62 62 |ogan in |Dr. Dobb|
|00000a00| 27 73 20 4a 6f 75 72 6e | 61 6c 20 4d 61 79 20 27 |'s Journ|al May '|
|00000a10| 38 35 20 70 2e 34 30 20 | 20 20 20 20 20 20 20 2a |85 p.40 |       *|
|00000a20| 2f 0a 2f 2a 20 49 6d 70 | 72 6f 76 65 64 20 62 79 |/./* Imp|roved by|
|00000a30| 20 63 61 6c 63 75 6c 61 | 74 69 6e 67 20 69 6e 63 | calcula|ting inc|
|00000a40| 72 65 6d 65 6e 74 73 20 | 69 6e 63 72 65 6d 65 6e |rements |incremen|
|00000a50| 74 61 6c 6c 79 2c 20 74 | 68 75 73 20 72 65 6d 6f |tally, t|hus remo|
|00000a60| 76 69 6e 67 20 61 6c 6c | 20 20 20 2a 2f 0a 2f 2a |ving all|   */./*|
|00000a70| 20 6d 75 6c 74 69 70 6c | 69 65 73 20 66 72 6f 6d | multipl|ies from|
|00000a80| 20 74 68 65 20 6c 6f 6f | 70 73 2e 20 54 68 65 73 | the loo|ps. Thes|
|00000a90| 65 20 6d 75 6c 74 69 70 | 6c 69 65 73 20 77 65 72 |e multip|lies wer|
|00000aa0| 65 20 76 65 72 79 20 62 | 61 64 20 73 69 6e 63 65 |e very b|ad since|
|00000ab0| 20 74 68 65 79 20 20 2a | 2f 0a 2f 2a 20 77 65 72 | they  *|/./* wer|
|00000ac0| 65 20 28 6c 6f 6e 67 29 | 2a 28 6c 6f 6e 67 29 2e |e (long)|*(long).|
|00000ad0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000ae0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000af0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000b00| 20 20 20 2a 2f 0a 2f 2a | 20 57 72 69 74 74 65 6e |   */./*| Written|
|00000b10| 20 53 65 70 74 2e 20 37 | 2c 20 31 39 38 37 20 62 | Sept. 7|, 1987 b|
|00000b20| 79 20 4a 2e 44 2e 20 4d | 63 44 6f 6e 61 6c 64 20 |y J.D. M|cDonald |
|00000b30| 28 70 75 62 6c 69 63 20 | 64 6f 6d 61 69 6e 29 20 |(public |domain) |
|00000b40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 2a |        |       *|
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|00000b60| 20 20 20 61 6c 70 68 61 | 2c 20 62 65 74 61 2c 20 |   alpha|, beta, |
|00000b70| 61 6c 70 68 61 32 2c 20 | 61 6c 70 68 61 34 2c 20 |alpha2, |alpha4, |
|00000b80| 62 65 74 61 32 2c 20 62 | 65 74 61 34 2c 20 64 3b |beta2, b|eta4, d;|
|00000b90| 0a 73 74 61 74 69 63 20 | 6c 6f 6e 67 20 20 20 20 |.static |long    |
|00000ba0| 20 64 64 78 2c 20 64 64 | 79 2c 20 61 6c 70 68 61 | ddx, dd|y, alpha|
|00000bb0| 64 78 2c 20 62 65 74 61 | 64 79 3b 0a 73 74 61 74 |dx, beta|dy;.stat|
|00000bc0| 69 63 20 69 6e 74 20 20 | 20 20 20 20 64 79 2c 20 |ic int  |    dy, |
|00000bd0| 64 78 3b 0a 0a 65 78 74 | 65 72 6e 20 76 6f 69 64 |dx;..ext|ern void|
|00000be0| 20 20 20 20 20 65 5f 73 | 74 61 72 74 28 69 6e 74 |     e_s|tart(int|
|00000bf0| 2c 20 69 6e 74 2c 20 69 | 6e 74 20 2c 69 6e 74 29 |, int, i|nt ,int)|
|00000c00| 3b 0a 65 78 74 65 72 6e | 20 76 6f 69 64 20 20 20 |;.extern| void   |
|00000c10| 20 20 65 5f 78 64 28 29 | 3b 09 0a 65 78 74 65 72 |  e_xd()|;..exter|
|00000c20| 6e 20 76 6f 69 64 20 20 | 20 20 20 65 5f 78 64 79 |n void  |   e_xdy|
|00000c30| 75 28 29 3b 0a 65 78 74 | 65 72 6e 20 76 6f 69 64 |u();.ext|ern void|
|00000c40| 20 20 20 20 20 65 5f 79 | 75 28 29 3b 20 0a 0a 65 |     e_y|u(); ..e|
|00000c50| 6c 6c 69 70 73 65 28 78 | 2c 20 79 2c 20 69 72 78 |llipse(x|, y, irx|
|00000c60| 2c 20 69 72 79 2c 20 63 | 29 0a 20 20 20 20 69 6e |, iry, c|).    in|
|00000c70| 74 20 20 20 20 20 20 20 | 20 20 20 20 20 20 78 2c |t       |      x,|
|00000c80| 20 79 2c 20 69 72 78 2c | 20 69 72 79 3b 0a 20 20 | y, irx,| iry;.  |
|00000c90| 20 20 75 6e 73 69 67 6e | 65 64 20 20 20 20 20 20 |  unsign|ed      |
|00000ca0| 20 20 63 3b 0a 7b 0a 0a | 20 20 20 20 62 65 74 61 |  c;.{..|    beta|
|00000cb0| 20 3d 20 28 6c 6f 6e 67 | 29 20 69 72 78 20 2a 28 | = (long|) irx *(|
|00000cc0| 6c 6f 6e 67 29 20 69 72 | 78 3b 0a 20 20 20 20 61 |long) ir|x;.    a|
|00000cd0| 6c 70 68 61 20 3d 20 28 | 6c 6f 6e 67 29 20 69 72 |lpha = (|long) ir|
|00000ce0| 79 20 2a 28 6c 6f 6e 67 | 29 20 69 72 79 3b 0a 0a |y *(long|) iry;..|
|00000cf0| 20 20 20 20 69 66 20 28 | 61 6c 70 68 61 20 3d 3d |    if (|alpha ==|
|00000d00| 20 30 4c 29 0a 09 61 6c | 70 68 61 20 3d 20 31 4c | 0L)..al|pha = 1L|
|00000d10| 3b 0a 20 20 20 20 69 66 | 20 28 62 65 74 61 20 3d |;.    if| (beta =|
|00000d20| 3d 20 30 4c 29 0a 09 62 | 65 74 61 20 3d 20 31 4c |= 0L)..b|eta = 1L|
|00000d30| 3b 0a 0a 20 20 20 20 64 | 79 20 3d 20 30 3b 0a 20 |;..    d|y = 0;. |
|00000d40| 20 20 20 64 78 20 3d 20 | 69 72 78 3b 0a 20 20 20 |   dx = |irx;.   |
|00000d50| 20 61 6c 70 68 61 32 20 | 3d 20 61 6c 70 68 61 20 | alpha2 |= alpha |
|00000d60| 3c 3c 20 31 3b 0a 20 20 | 20 20 61 6c 70 68 61 34 |<< 1;.  |  alpha4|
|00000d70| 20 3d 20 61 6c 70 68 61 | 32 20 3c 3c 20 31 3b 0a | = alpha|2 << 1;.|
|00000d80| 20 20 20 20 62 65 74 61 | 32 20 3d 20 62 65 74 61 |    beta|2 = beta|
|00000d90| 20 3c 3c 20 31 3b 0a 20 | 20 20 20 62 65 74 61 34 | << 1;. |   beta4|
|00000da0| 20 3d 20 62 65 74 61 32 | 20 3c 3c 20 31 3b 0a 20 | = beta2| << 1;. |
|00000db0| 20 20 20 61 6c 70 68 61 | 64 78 20 3d 20 61 6c 70 |   alpha|dx = alp|
|00000dc0| 68 61 20 2a 20 64 78 3b | 0a 20 20 20 20 62 65 74 |ha * dx;|.    bet|
|00000dd0| 61 64 79 20 3d 20 30 3b | 0a 20 20 20 20 64 64 78 |ady = 0;|.    ddx|
|00000de0| 20 3d 20 61 6c 70 68 61 | 34 20 2a 20 28 31 20 2d | = alpha|4 * (1 -|
|00000df0| 20 64 78 29 3b 0a 20 20 | 20 20 64 64 79 20 3d 20 | dx);.  |  ddy = |
|00000e00| 62 65 74 61 32 20 2a 20 | 33 3b 0a 0a 20 20 20 20 |beta2 * |3;..    |
|00000e10| 64 20 3d 20 61 6c 70 68 | 61 32 20 2a 20 28 28 6c |d = alph|a2 * ((l|
|00000e20| 6f 6e 67 29 20 28 64 78 | 20 2d 20 31 29 20 2a 20 |ong) (dx| - 1) * |
|00000e30| 64 78 29 20 2b 20 61 6c | 70 68 61 20 2b 20 62 65 |dx) + al|pha + be|
|00000e40| 74 61 32 20 2a 20 28 31 | 20 2d 20 61 6c 70 68 61 |ta2 * (1| - alpha|
|00000e50| 29 3b 0a 20 20 20 20 65 | 5f 73 74 61 72 74 28 78 |);.    e|_start(x|
|00000e60| 20 2d 20 64 78 2c 20 78 | 20 2b 20 64 78 2c 20 79 | - dx, x| + dx, y|
|00000e70| 2c 20 63 29 3b 0a 20 20 | 20 20 20 20 20 20 20 20 |, c);.  |        |
|00000e80| 2f 2a 20 65 5f 73 74 61 | 72 74 20 64 72 61 77 73 |/* e_sta|rt draws|
|00000e90| 20 6c 65 66 74 20 61 6e | 64 20 72 69 67 68 74 6d | left an|d rightm|
|00000ea0| 6f 73 74 20 70 69 78 65 | 6c 73 20 6f 6e 20 76 65 |ost pixe|ls on ve|
|00000eb0| 72 74 69 63 61 6c 20 63 | 65 6e 74 65 72 6c 69 6e |rtical c|enterlin|
|00000ec0| 65 20 2a 2f 0a 20 20 20 | 20 20 20 20 20 20 20 2f |e */.   |       /|
|00000ed0| 2a 20 65 5f 79 75 20 64 | 72 61 77 73 20 61 20 70 |* e_yu d|raws a p|
|00000ee0| 69 78 65 6c 20 69 6e 20 | 72 69 67 68 74 20 74 6f |ixel in |right to|
|00000ef0| 70 20 71 75 61 64 72 61 | 6e 74 20 6f 6e 65 20 75 |p quadra|nt one u|
|00000f00| 70 20 66 72 6f 6d 20 70 | 72 65 76 69 6f 75 73 20 |p from p|revious |
|00000f10| 20 2a 2f 0a 20 20 20 20 | 20 20 20 20 20 20 2f 2a | */.    |      /*|
|00000f20| 20 65 5f 78 64 20 64 72 | 61 77 73 20 61 20 70 69 | e_xd dr|aws a pi|
|00000f30| 78 65 6c 20 69 6e 20 72 | 69 67 68 74 20 74 6f 70 |xel in r|ight top|
|00000f40| 20 71 75 61 64 72 61 6e | 74 20 6f 6e 65 20 6c 65 | quadran|t one le|
|00000f50| 66 74 20 66 72 6f 6d 20 | 70 72 65 76 69 6f 75 73 |ft from |previous|
|00000f60| 2a 2f 0a 20 20 20 20 20 | 20 20 20 20 20 2f 2a 20 |*/.     |     /* |
|00000f70| 65 5f 78 64 79 75 20 64 | 72 61 77 73 20 61 20 70 |e_xdyu d|raws a p|
|00000f80| 69 78 65 6c 20 69 6e 20 | 72 69 67 68 74 20 74 6f |ixel in |right to|
|00000f90| 70 20 71 75 61 64 72 61 | 6e 74 20 75 70 20 61 6e |p quadra|nt up an|
|00000fa0| 64 20 6c 65 66 74 20 66 | 72 6f 6d 20 20 20 20 2a |d left f|rom    *|
|00000fb0| 2f 0a 20 20 20 20 20 20 | 20 20 20 20 2f 2a 20 70 |/.      |    /* p|
|00000fc0| 72 65 76 69 6f 75 73 2e | 20 65 5f 79 75 2c 20 65 |revious.| e_yu, e|
|00000fd0| 5f 78 64 2c 20 61 6e 64 | 20 65 5f 78 64 79 75 20 |_xd, and| e_xdyu |
|00000fe0| 61 6c 73 6f 20 64 72 61 | 77 20 74 68 65 20 63 6f |also dra|w the co|
|00000ff0| 72 72 65 73 70 6f 6e 64 | 69 6e 67 20 20 20 2a 2f |rrespond|ing   */|
|00001000| 0a 20 20 20 20 20 20 20 | 20 20 20 2f 2a 20 70 69 |.       |   /* pi|
|00001010| 78 65 6c 73 20 69 6e 20 | 74 68 65 20 6f 74 68 65 |xels in |the othe|
|00001020| 72 20 74 68 72 65 65 20 | 71 75 61 64 72 61 6e 74 |r three |quadrant|
|00001030| 73 2e 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |s.      |        |
|00001040| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 2a 2f 0a |        |     */.|
|00001050| 20 20 20 20 20 20 20 20 | 20 20 2f 2a 20 63 20 69 |        |  /* c i|
|00001060| 73 20 74 68 65 20 63 6f | 6c 6f 72 20 20 20 20 20 |s the co|lor     |
|00001070| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001080| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001090| 20 20 20 20 20 20 20 20 | 20 20 20 20 2a 2f 0a 20 |        |    */. |
|000010a0| 20 20 20 64 6f 20 7b 0a | 09 69 66 20 28 64 20 3e |   do {.|.if (d >|
|000010b0| 3d 20 30 29 20 7b 0a 09 | 20 20 20 20 64 20 2b 3d |= 0) {..|    d +=|
|000010c0| 20 64 64 78 3b 0a 09 20 | 20 20 20 64 78 2d 2d 3b | ddx;.. |   dx--;|
|000010d0| 0a 09 20 20 20 20 61 6c | 70 68 61 64 78 20 2d 3d |..    al|phadx -=|
|000010e0| 20 61 6c 70 68 61 3b 0a | 09 20 20 20 20 64 64 78 | alpha;.|.    ddx|
|000010f0| 20 2b 3d 20 61 6c 70 68 | 61 34 3b 0a 09 20 20 20 | += alph|a4;..   |
|00001100| 20 65 5f 78 64 79 75 28 | 29 3b 0a 09 7d 20 65 6c | e_xdyu(|);..} el|
|00001110| 73 65 0a 09 20 20 20 20 | 65 5f 79 75 28 29 3b 0a |se..    |e_yu();.|
|00001120| 09 64 20 2b 3d 20 64 64 | 79 3b 0a 09 64 79 2b 2b |.d += dd|y;..dy++|
|00001130| 3b 0a 09 62 65 74 61 64 | 79 20 2b 3d 20 62 65 74 |;..betad|y += bet|
|00001140| 61 3b 0a 09 64 64 79 20 | 2b 3d 20 62 65 74 61 34 |a;..ddy |+= beta4|
|00001150| 3b 0a 20 20 20 20 7d 20 | 77 68 69 6c 65 20 28 61 |;.    } |while (a|
|00001160| 6c 70 68 61 64 78 20 3e | 20 62 65 74 61 64 79 29 |lphadx >| betady)|
|00001170| 3b 0a 0a 20 20 20 20 64 | 20 3d 20 62 65 74 61 32 |;..    d| = beta2|
|00001180| 20 2a 20 28 28 6c 6f 6e | 67 29 20 64 79 20 2a 20 | * ((lon|g) dy * |
|00001190| 28 64 79 20 2b 20 31 29 | 29 20 2b 20 61 6c 70 68 |(dy + 1)|) + alph|
|000011a0| 61 32 20 2a 20 28 28 6c | 6f 6e 67 29 20 64 78 20 |a2 * ((l|ong) dx |
|000011b0| 2a 20 28 64 78 20 2d 20 | 32 29 20 2b 20 31 29 20 |* (dx - |2) + 1) |
|000011c0| 0a 09 2b 20 62 65 74 61 | 20 2a 20 28 31 20 2d 20 |..+ beta| * (1 - |
|000011d0| 61 6c 70 68 61 32 29 3b | 0a 20 20 20 20 64 64 78 |alpha2);|.    ddx|
|000011e0| 20 3d 20 61 6c 70 68 61 | 32 20 2a 20 28 33 20 2d | = alpha|2 * (3 -|
|000011f0| 20 28 64 78 20 3c 3c 20 | 31 29 29 3b 0a 20 20 20 | (dx << |1));.   |
|00001200| 20 64 64 79 20 3d 20 62 | 65 74 61 34 20 2a 20 28 | ddy = b|eta4 * (|
|00001210| 31 20 2b 20 64 79 29 3b | 0a 0a 20 20 20 20 64 6f |1 + dy);|..    do|
|00001220| 20 7b 0a 09 69 66 20 28 | 64 20 3c 3d 20 30 29 20 | {..if (|d <= 0) |
|00001230| 7b 0a 09 20 20 20 20 64 | 20 2b 3d 20 64 64 79 3b |{..    d| += ddy;|
|00001240| 0a 09 20 20 20 20 64 64 | 79 20 2b 3d 20 62 65 74 |..    dd|y += bet|
|00001250| 61 34 3b 0a 09 20 20 20 | 20 64 79 2b 2b 3b 0a 09 |a4;..   | dy++;..|
|00001260| 20 20 20 20 65 5f 78 64 | 79 75 28 29 3b 0a 09 7d |    e_xd|yu();..}|
|00001270| 20 65 6c 73 65 0a 09 20 | 20 20 20 65 5f 78 64 28 | else.. |   e_xd(|
|00001280| 29 3b 0a 09 64 20 2b 3d | 20 64 64 78 3b 0a 09 64 |);..d +=| ddx;..d|
|00001290| 64 78 20 2b 3d 20 61 6c | 70 68 61 34 3b 0a 09 64 |dx += al|pha4;..d|
|000012a0| 78 2d 2d 3b 0a 20 20 20 | 20 7d 20 77 68 69 6c 65 |x--;.   | } while|
|000012b0| 20 28 64 78 20 3e 20 30 | 29 3b 0a 7d 0a 0a 0a    | (dx > 0|);.}... |
+--------+-------------------------+-------------------------+--------+--------+