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<div id="cubic3x5">
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{{20.8291142, 74.9221559}, {18.4755741, 65.0587801}, {21.1261573, 59.9182775}},
{{21.1261573, 59.9182775}, {24.474036, 53.4254499}, {36.6579558, 51.0041468}},
{{36.6579558, 51.0041468}, {50.2178533, 48.3093965}, {76.9233116, 50.0985771}},
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<div id="cubic3x5x">
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{{20.8291142, 74.9221559}, {18.3562971, 66.1376314}, {21.1261573, 59.9182775}},
{{21.1261573, 59.9182775}, {23.8960175, 53.6989236}, {36.6579558, 51.0041468}},
{{36.6579558, 51.0041468}, {49.4198942, 48.3093701}, {76.9233116, 50.0985771}},
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<div id="cubic3x6">
{{39.306348, 21.7912016}, {44.72463, 86.8568551}, {3.16400146, 77.3725818}, {0.981986477, 4.24671164}},
{{39.306348, 21.7912016}, {41.8751537, 52.6388057}, {32.26342, 62.4108917}},
{{32.26342, 62.4108917}, {23.2193358, 71.6058581}, {13.0917792, 55.754704}},
{{13.0917792, 55.754704}, {2.00097021, 38.3959145}, {0.981986477, 4.24671164}},
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<div id="cubic3x6x">
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{{39.306348, 21.7912016}, {41.2158823, 54.2230253}, {32.26342, 62.4108917}},
{{32.26342, 62.4108917}, {23.3109577, 70.5987581}, {13.0917792, 55.754704}},
{{13.0917792, 55.754704}, {2.87260067, 40.9106498}, {0.981986477, 4.24671164}},
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<div id="cubic3x7">
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{{85.4907277, 42.6604079}, {92.9820656, 39.0245896}, {81.4704732, 52.0202764}},
{{81.4704732, 52.0202764}, {71.0697229, 63.7619094}, {56.4037366, 66.489545}},
{{56.4037366, 66.489545}, {36.2148038, 70.2443591}, {14.7351715, 54.0271501}},
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<div id="cubic3x7x">
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{{85.4907277, 42.6604079}, {89.2978026, 42.0578592}, {81.4704732, 52.0202764}},
{{81.4704732, 52.0202764}, {73.6431437, 61.9826936}, {56.4037366, 66.489545}},
{{56.4037366, 66.489545}, {39.1643295, 70.9963964}, {14.7351715, 54.0271501}},
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<div id="cubic3x8">
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{{95.2957887, 36.3209844}, {73.0036621, 28.7988805}, {57.2191042, 37.0396513}},
{{57.2191042, 37.0396513}, {44.4309585, 43.7160611}, {36.8308235, 60.0949108}},
{{36.8308235, 60.0949108}, {30.9912846, 72.6795466}, {29.3620354, 87.7284659}},
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<div id="cubic3x8x">
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{{95.2957887, 36.3209844}, {71.2392316, 28.8763825}, {57.2191042, 37.0396513}},
{{57.2191042, 37.0396513}, {43.1989768, 45.20292}, {36.8308235, 60.0949108}},
{{36.8308235, 60.0949108}, {30.4626702, 74.9869017}, {29.3620354, 87.7284659}},
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<div id="cubic3x9">
{{11.6274826, 23.1005334}, {50.665531, 35.5788199}, {73.2259434, 8.43082047}, {96.7997166, 12.8374226}},
{{11.6274826, 23.1005334}, {26.8690196, 27.9724026}, {42.2684837, 25.6341105}},
{{42.2684837, 25.6341105}, {51.3514943, 24.254924}, {67.0182186, 18.4582098}},
{{67.0182186, 18.4582098}, {87.1065443, 11.0254957}, {96.7997166, 12.8374226}},
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<div id="cubic3x9x">
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{{11.6274826, 23.1005334}, {28.7555518, 28.1569895}, {42.2684837, 25.6341105}},
{{42.2684837, 25.6341105}, {55.7814156, 23.1112314}, {67.0182186, 18.4582098}},
{{67.0182186, 18.4582098}, {82.5639521, 11.3566582}, {96.7997166, 12.8374226}},
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<div id="cubic4x0">
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{{24.2578299, 1.34695745}, {27.9750096, 11.9564045}, {28.1705087, 26.7539994}},
{{28.1705087, 26.7539994}, {28.2848367, 35.4076429}, {26.8433323, 51.6959666}},
{{26.8433323, 51.6959666}, {24.9672902, 72.8943612}, {27.4957684, 77.9195086}},
{{27.4957684, 77.9195086}, {31.4664535, 85.8109263}, {48.4308047, 76.5337766}},
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<div id="cubic4x0x">
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{{24.2578299, 1.34695745}, {28.2364584, 13.5769276}, {28.1705087, 26.7539994}},
{{28.1705087, 26.7539994}, {28.104559, 39.9310711}, {26.8433323, 51.6959666}},
{{26.8433323, 51.6959666}, {24.5051265, 69.7176532}, {27.4957684, 77.9195086}},
{{27.4957684, 77.9195086}, {30.4864104, 86.121364}, {48.4308047, 76.5337766}},
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<div id="cubic4x1">
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{{3.18338154, 3.09354817}, {35.8260971, 34.1468066}, {48.9325859, 44.6922254}},
{{48.9325859, 44.6922254}, {62.4915199, 55.6016796}, {67.1257676, 54.3074276}},
{{67.1257676, 54.3074276}, {70.2512267, 53.4345498}, {72.6465479, 43.2128608}},
{{72.6465479, 43.2128608}, {76.4594277, 26.9419442}, {83.3354337, 18.6335197}},
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<div id="cubic4x1x">
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{{3.18338154, 3.09354817}, {34.807442, 33.2979688}, {48.9325859, 44.6922254}},
{{48.9325859, 44.6922254}, {63.0577297, 56.086482}, {67.1257676, 54.3074276}},
{{67.1257676, 54.3074276}, {71.1938054, 52.5283732}, {72.6465479, 43.2128608}},
{{72.6465479, 43.2128608}, {74.0679283, 31.8888383}, {83.3354337, 18.6335197}},
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<div id="cubic4x2">
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{{5.3607232, 97.6747591}, {7.15867444, 96.170374}, {9.99357731, 93.4972246}},
{{9.99357731, 93.4972246}, {15.4658237, 88.3372129}, {19.1058065, 87.2914549}},
{{19.1058065, 87.2914549}, {24.5745003, 85.7203128}, {35.9606711, 88.1040392}},
{{35.9606711, 88.1040392}, {47.3960315, 90.4980635}, {72.9397619, 98.5790647}},
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<div id="cubic4x2x">
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{{5.3607232, 97.6747591}, {8.01636596, 95.4093652}, {9.99357731, 93.4972246}},
{{9.99357731, 93.4972246}, {14.161732, 88.9702622}, {19.1058065, 87.2914549}},
{{19.1058065, 87.2914549}, {24.0498811, 85.6126476}, {35.9606711, 88.1040392}},
{{35.9606711, 88.1040392}, {47.871461, 90.5954307}, {72.9397619, 98.5790647}},
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<div id="cubic4x3">
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{{18.340571, 49.9760211}, {27.6759966, 65.333137}, {34.9254897, 64.1054159}},
{{34.9254897, 64.1054159}, {39.46946, 63.3358824}, {47.9840785, 52.4199142}},
{{47.9840785, 52.4199142}, {58.4594697, 38.9901831}, {66.2068641, 35.3036404}},
{{66.2068641, 35.3036404}, {79.5296469, 28.9640886}, {97.4081647, 39.0235061}},
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<div id="cubic4x3x">
{{18.340571, 49.9760211}, {46.9862021, 97.0991299}, {45.0770262, 9.57918773}, {97.4081647, 39.0235061}},
{{18.340571, 49.9760211}, {28.406995, 66.1423531}, {34.9254897, 64.1054159}},
{{34.9254897, 64.1054159}, {41.4439844, 62.0684788}, {47.9840785, 52.4199142}},
{{47.9840785, 52.4199142}, {54.9532374, 41.9238105}, {66.2068641, 35.3036404}},
{{66.2068641, 35.3036404}, {77.4604907, 28.6834703}, {97.4081647, 39.0235061}},
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<div id="cubic4x4">
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{{68.0670356, 2.66693188}, {56.7853646, 13.7638629}, {41.0137122, 27.3042275}},
{{41.0137122, 27.3042275}, {29.788878, 36.941033}, {31.0433353, 38.0354879}},
{{31.0433353, 38.0354879}, {32.2977925, 39.1299429}, {51.0493703, 36.059867}},
{{51.0493703, 36.059867}, {67.7999464, 33.3174024}, {79.6294187, 31.6402602}},
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<div id="cubic4x4x">
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{{68.0670356, 2.66693188}, {50.940695, 19.1344928}, {41.0137122, 27.3042275}},
{{41.0137122, 27.3042275}, {29.4752637, 36.6674193}, {31.0433353, 38.0354879}},
{{31.0433353, 38.0354879}, {32.6114068, 39.4035566}, {51.0493703, 36.059867}},
{{51.0493703, 36.059867}, {61.9478496, 34.2106234}, {79.6294187, 31.6402602}},
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<div id="cubic4x5">
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{{80.6109054, 27.4877124}, {82.5499811, 51.8990092}, {82.5259477, 65.0368853}},
{{82.5259477, 65.0368853}, {82.5124299, 72.4264589}, {81.7002161, 78.1564815}},
{{81.7002161, 78.1564815}, {81.2315331, 81.462956}, {81.4316783, 83.8990214}},
{{81.4316783, 83.8990214}, {81.7199102, 87.4072321}, {83.5185407, 96.1129614}},
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<div id="cubic4x5x">
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{{80.6109054, 27.4877124}, {82.6925268, 54.7439407}, {82.5259477, 65.0368853}},
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{{81.4316783, 83.8990214}, {81.6547145, 87.1356086}, {83.5185407, 96.1129614}},
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<div id="cubic4x6">
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{{70.5424749, 7.37512261}, {64.0240124, 41.5372735}, {57.0495799, 54.4661558}},
{{57.0495799, 54.4661558}, {53.0372544, 61.9040203}, {46.633996, 64.0865108}},
{{46.633996, 64.0865108}, {42.8562175, 65.3741311}, {41.4346736, 67.9484678}},
{{41.4346736, 67.9484678}, {39.1777978, 72.0355437}, {38.1617001, 83.6927474}},
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<div id="cubic4x6x">
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{{70.5424749, 7.37512261}, {63.0887524, 44.8198844}, {57.0495799, 54.4661558}},
{{57.0495799, 54.4661558}, {51.0104074, 64.1124273}, {46.633996, 64.0865108}},
{{46.633996, 64.0865108}, {43.5741104, 64.6069899}, {41.4346736, 67.9484678}},
{{41.4346736, 67.9484678}, {39.2952367, 71.2899457}, {38.1617001, 83.6927474}},
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<div id="cubic4x7">
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{{24.0062249, 72.6211198}, {30.5430063, 51.8208637}, {31.8675739, 40.5026282}},
{{31.8675739, 40.5026282}, {32.9179067, 31.5276894}, {30.6430223, 29.7760199}},
{{30.6430223, 29.7760199}, {28.7741669, 28.3369942}, {26.2185506, 31.7425273}},
{{26.2185506, 31.7425273}, {23.6812077, 35.1237098}, {24.4801394, 37.7033828}},
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<div id="cubic4x7x">
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{{24.0062249, 72.6211198}, {30.9441221, 50.1265572}, {31.8675739, 40.5026282}},
{{31.8675739, 40.5026282}, {32.7910257, 30.8786991}, {30.6430223, 29.7760199}},
{{30.6430223, 29.7760199}, {28.4950189, 28.6733406}, {26.2185506, 31.7425273}},
{{26.2185506, 31.7425273}, {23.9420823, 34.811714}, {24.4801394, 37.7033828}},
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<div id="cubic4x8">
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{{83.4128604, 19.944285}, {56.4409479, 37.8736494}, {40.6945347, 43.6697281}},
{{40.6945347, 43.6697281}, {27.6832174, 48.4590486}, {28.8268904, 43.5475174}},
{{28.8268904, 43.5475174}, {29.9619906, 38.6728026}, {42.6576802, 32.0063781}},
{{42.6576802, 32.0063781}, {57.6563877, 24.1306537}, {77.0346567, 21.4750355}},
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<div id="cubic4x8x">
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{{83.4128604, 19.944285}, {53.6969963, 39.3225107}, {40.6945347, 43.6697281}},
{{40.6945347, 43.6697281}, {27.6920731, 48.0169456}, {28.8268904, 43.5475174}},
{{28.8268904, 43.5475174}, {29.9617077, 39.0780892}, {42.6576802, 32.0063781}},
{{42.6576802, 32.0063781}, {55.3536527, 24.9346669}, {77.0346567, 21.4750355}},
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<div id="cubic4x9">
{{13.6133623, 99.7800201}, {2.79733483, 14.8064674}, {52.2975031, 64.1339272}, {98.9146078, 57.8132952}},
{{13.6133623, 99.7800201}, {10.1036384, 72.2067072}, {14.9007617, 60.2808941}},
{{14.9007617, 60.2808941}, {19.0431228, 49.9828423}, {30.5807774, 49.2954321}},
{{30.5807774, 49.2954321}, {37.7022355, 48.8711377}, {56.117561, 53.190874}},
{{56.117561, 53.190874}, {84.2814202, 59.7973522}, {98.9146078, 57.8132952}},
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<div id="cubic4x9x">
{{13.6133623, 99.7800201}, {2.79733483, 14.8064674}, {52.2975031, 64.1339272}, {98.9146078, 57.8132952}},
{{13.6133623, 99.7800201}, {10.0919269, 71.197946}, {14.9007617, 60.2808941}},
{{14.9007617, 60.2808941}, {19.7095965, 49.3638421}, {30.5807774, 49.2954321}},
{{30.5807774, 49.2954321}, {41.4519583, 49.2270222}, {56.117561, 53.190874}},
{{56.117561, 53.190874}, {76.476137, 59.3205959}, {98.9146078, 57.8132952}},
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<div id="cubic5x0">
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{{73.0163837, 15.1491032}, {70.9175181, 29.2180034}, {69.2121151, 36.2586021}},
{{69.2121151, 36.2586021}, {66.2435432, 48.5140774}, {62.0808557, 53.3239452}},
{{62.0808557, 53.3239452}, {56.8541433, 59.3632637}, {49.5132747, 54.1388813}},
{{49.5132747, 54.1388813}, {40.9233022, 48.0255311}, {29.4000415, 26.4971589}},
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<div id="cubic5x0x">
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{{73.5652707, 11.5053172}, {73.3009509, 13.2327574}, {73.0163837, 15.1491032}},
{{73.0163837, 15.1491032}, {71.6823308, 25.1891102}, {69.2121151, 36.2586021}},
{{69.2121151, 36.2586021}, {66.7418995, 47.328094}, {62.0808557, 53.3239452}},
{{62.0808557, 53.3239452}, {57.4198119, 59.3197964}, {49.5132747, 54.1388813}},
{{49.5132747, 54.1388813}, {41.6067374, 48.9579661}, {29.4000415, 26.4971589}},
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<div id="cubic5x1">
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{{80.7539402, 31.4736433}, {80.1293736, 30.8666193}, {81.0927918, 33.3061348}},
{{81.0927918, 33.3061348}, {82.7770389, 37.5708941}, {83.4256875, 40.319949}},
{{83.4256875, 40.319949}, {84.5951485, 45.2762733}, {83.5574674, 48.3997103}},
{{83.5574674, 48.3997103}, {82.2131806, 52.4460356}, {77.2064841, 53.3431558}},
{{77.2064841, 53.3431558}, {71.2104332, 54.4175525}, {60.0910899, 50.9480224}},
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<div id="cubic5x1x">
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{{80.7539402, 31.4736433}, {79.9741932, 30.7172975}, {81.0927918, 33.3061348}},
{{81.0927918, 33.3061348}, {82.2743126, 36.0212723}, {83.4256875, 40.319949}},
{{83.4256875, 40.319949}, {84.5770623, 44.6186258}, {83.5574674, 48.3997103}},
{{83.5574674, 48.3997103}, {82.5378725, 52.1807949}, {77.2064841, 53.3431558}},
{{77.2064841, 53.3431558}, {71.8750956, 54.5055166}, {60.0910899, 50.9480224}},
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<div id="cubic5x2">
{{30.9220007, 6.06626757}, {55.7590106, 41.691652}, {11.5944877, 68.5545306}, {95.99508, 89.3088364}},
{{30.9220007, 6.06626757}, {36.6680413, 14.3081978}, {38.6632502, 23.8943374}},
{{38.6632502, 23.8943374}, {39.8467707, 29.5806556}, {40.109652, 40.2122054}},
{{40.109652, 40.2122054}, {40.4211241, 52.8088852}, {42.588681, 58.5795625}},
{{42.588681, 58.5795625}, {46.141784, 68.0389732}, {57.1660752, 74.8906876}},
{{57.1660752, 74.8906876}, {70.1317224, 82.9489754}, {95.99508, 89.3088364}},
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<div id="cubic5x2x">
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{{50.528201, 27.4745214}, {53.3761101, 36.6040713}, {54.38742, 39.6099548}},
{{54.38742, 39.6099548}, {55.5064406, 42.9359834}, {55.7720854, 42.9677817}},
{{55.7720854, 42.9677817}, {55.9546136, 42.9896307}, {55.8827854, 40.8375726}},
{{55.8827854, 40.8375726}, {55.7725733, 37.5354848}, {55.9802468, 35.9707481}},
{{55.9802468, 35.9707481}, {56.3474228, 33.2042239}, {57.7009449, 33.0167369}},
{{57.7009449, 33.0167369}, {59.424989, 32.7779259}, {62.7612346, 36.6782932}},
{{62.7612346, 36.6782932}, {66.7088662, 41.293425}, {72.8774712, 51.6581711}},
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<div id="cubic7x8x">
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{{50.528201, 27.4745214}, {53.2265224, 36.1478361}, {54.38742, 39.6099548}},
{{54.38742, 39.6099548}, {55.5483175, 43.0720735}, {55.7720854, 42.9677817}},
{{55.7720854, 42.9677817}, {55.9958532, 42.8634898}, {55.8827854, 40.8375726}},
{{55.8827854, 40.8375726}, {55.7402514, 38.5138013}, {55.9802468, 35.9707481}},
{{55.9802468, 35.9707481}, {56.2202423, 33.4276949}, {57.7009449, 33.0167369}},
{{57.7009449, 33.0167369}, {59.1816474, 32.6057789}, {62.7612346, 36.6782932}},
{{62.7612346, 36.6782932}, {66.3408218, 40.7508075}, {72.8774712, 51.6581711}},
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<div id="cubic7x9">
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{{30.3413925, 47.7835835}, {46.0782555, 45.8095694}, {52.5540659, 48.2453346}},
{{52.5540659, 48.2453346}, {57.9511897, 50.2753703}, {56.8130484, 55.3244869}},
{{56.8130484, 55.3244869}, {55.9369414, 59.2111449}, {51.1961195, 64.811489}},
{{51.1961195, 64.811489}, {48.5753558, 67.9074035}, {43.7810591, 72.4967897}},
{{43.7810591, 72.4967897}, {41.2648644, 74.905441}, {42.230691, 74.4021224}},
{{42.230691, 74.4021224}, {43.1965176, 73.8988039}, {51.5076718, 68.470241}},
{{51.5076718, 68.470241}, {54.9756852, 66.2050527}, {57.0872154, 64.8290379}},
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<div id="cubic7x9x">
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{{30.3413925, 47.7835835}, {46.9458744, 45.8339148}, {52.5540659, 48.2453346}},
{{52.5540659, 48.2453346}, {58.1622574, 50.6567543}, {56.8130484, 55.3244869}},
{{56.8130484, 55.3244869}, {55.4638393, 59.9922194}, {51.1961195, 64.811489}},
{{51.1961195, 64.811489}, {46.9283998, 69.6307587}, {43.7810591, 72.4967897}},
{{43.7810591, 72.4967897}, {41.0234077, 75.0312707}, {42.230691, 74.4021224}},
{{42.230691, 74.4021224}, {43.4379742, 73.7729742}, {51.5076718, 68.470241}},
{{51.5076718, 68.470241}, {53.9259122, 66.8899375}, {57.0872154, 64.8290379}},
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<div id="cubic8x0">
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{{42.5967063, 22.8420382}, {34.7914244, 21.2139034}, {32.6593413, 19.878761}},
{{32.6593413, 19.878761}, {30.8695713, 18.7579803}, {33.1023831, 17.8591237}},
{{33.1023831, 17.8591237}, {34.8391625, 17.1599535}, {39.0195021, 16.5984277}},
{{39.0195021, 16.5984277}, {41.3590736, 16.2841638}, {45.5043686, 15.9119743}},
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{{47.8024311, 15.6545014}, {47.8704535, 15.5767993}, {44.9932779, 15.5487509}},
{{44.9932779, 15.5487509}, {42.9381525, 15.5287163}, {34.6690635, 15.5040796}},
{{34.6690635, 15.5040796}, {32.6017407, 15.4979203}, {31.4640028, 15.4944166}},
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<div id="cubic8x0x">
{{42.5967063, 22.8420382}, {6.13525533, 15.2363991}, {78.1588409, 15.6382141}, {31.4640028, 15.4944166}},
{{42.5967063, 22.8420382}, {34.4196308, 21.1014023}, {32.6593413, 19.878761}},
{{32.6593413, 19.878761}, {30.8990517, 18.6561197}, {33.1023831, 17.8591237}},
{{33.1023831, 17.8591237}, {35.3057145, 17.0621277}, {39.0195021, 16.5984277}},
{{39.0195021, 16.5984277}, {42.7332897, 16.1347277}, {45.5043686, 15.9119743}},
{{45.5043686, 15.9119743}, {47.6292231, 15.7339768}, {47.8024311, 15.6545014}},
{{47.8024311, 15.6545014}, {47.9756391, 15.575026}, {44.9932779, 15.5487509}},
{{44.9932779, 15.5487509}, {42.0109167, 15.5224759}, {34.6690635, 15.5040796}},
{{34.6690635, 15.5040796}, {33.169788, 15.4996412}, {31.4640028, 15.4944166}},
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<div id="cubic8x1">
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{{29.0323957, 47.4745379}, {23.6693619, 37.6716337}, {20.3221199, 34.4936205}},
{{20.3221199, 34.4936205}, {17.5126817, 31.826221}, {16.162445, 33.8631071}},
{{16.162445, 33.8631071}, {15.1123784, 35.4471745}, {14.9546458, 39.8886357}},
{{14.9546458, 39.8886357}, {14.8663892, 42.3737787}, {15.0999972, 46.8758445}},
{{15.0999972, 46.8758445}, {15.2259779, 49.3037298}, {15.1224749, 49.3309043}},
{{15.1224749, 49.3309043}, {14.9775707, 49.3689487}, {14.2215808, 46.1220869}},
{{14.2215808, 46.1220869}, {13.6815881, 43.8028999}, {11.62512, 34.4989774}},
{{11.62512, 34.4989774}, {11.559983, 34.2042829}, {11.5269861, 34.0549996}},
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<div id="cubic8x1x">
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{{29.0323957, 47.4745379}, {23.339767, 37.184683}, {20.3221199, 34.4936205}},
{{20.3221199, 34.4936205}, {17.3044729, 31.802558}, {16.162445, 33.8631071}},
{{16.162445, 33.8631071}, {15.0204171, 35.9236561}, {14.9546458, 39.8886357}},
{{14.9546458, 39.8886357}, {14.8888745, 43.8536153}, {15.0999972, 46.8758445}},
{{15.0999972, 46.8758445}, {15.2455546, 49.1755419}, {15.1224749, 49.3309043}},
{{15.1224749, 49.3309043}, {14.9993952, 49.4862668}, {14.2215808, 46.1220869}},
{{14.2215808, 46.1220869}, {13.4437665, 42.757907}, {11.62512, 34.4989774}},
{{11.62512, 34.4989774}, {11.5764809, 34.2789225}, {11.5269861, 34.0549996}},
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<div id="cubic8x2">
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{{30.5187597, 28.7944151}, {30.823715, 29.4945431}, {31.3959629, 30.8080078}},
{{31.3959629, 30.8080078}, {34.9281707, 38.9153861}, {35.7821411, 40.9504208}},
{{35.7821411, 40.9504208}, {36.9776996, 43.7994693}, {36.8148424, 43.845334}},
{{36.8148424, 43.845334}, {36.6985159, 43.8780945}, {35.3792396, 41.9741019}},
{{35.3792396, 41.9741019}, {33.3589087, 39.0583404}, {32.0725075, 37.4554574}},
{{32.0725075, 37.4554574}, {29.7893226, 34.6105606}, {28.0338583, 33.4024856}},
{{28.0338583, 33.4024856}, {25.7901854, 31.8584352}, {24.3823693, 32.9522328}},
{{24.3823693, 32.9522328}, {22.7123482, 34.2497498}, {22.237118, 39.2417454}},
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<div id="cubic8x2x">
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{{31.3959629, 30.8080078}, {34.5380678, 38.0012585}, {35.7821411, 40.9504208}},
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{{35.3792396, 41.9741019}, {34.0487375, 39.9904922}, {32.0725075, 37.4554574}},
{{32.0725075, 37.4554574}, {30.0962775, 34.9204225}, {28.0338583, 33.4024856}},
{{28.0338583, 33.4024856}, {25.9714391, 31.8845487}, {24.3823693, 32.9522328}},
{{24.3823693, 32.9522328}, {22.7932996, 34.019917}, {22.237118, 39.2417454}},
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<div id="cubic8x3">
{{44.0194731, 35.2849254}, {33.7413378, 90.6639866}, {89.6236054, 3.93610117}, {54.0523993, 58.6752083}},
{{44.0194731, 35.2849254}, {41.8034025, 47.2252151}, {43.4093427, 51.8147312}},
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{{56.6514498, 48.9586591}, {59.3060696, 46.5778416}, {63.5477208, 42.0877376}},
{{63.5477208, 42.0877376}, {65.8388976, 39.6623562}, {66.0159848, 39.6831127}},
{{66.0159848, 39.6831127}, {66.2639069, 39.7121719}, {64.0479481, 43.2239426}},
{{64.0479481, 43.2239426}, {62.4651204, 45.7323502}, {55.9567221, 55.7452241}},
{{55.9567221, 55.7452241}, {54.718939, 57.649497}, {54.0523993, 58.6752083}},
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<div id="cubic8x3x">
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{{44.0194731, 35.2849254}, {41.7846308, 47.8464432}, {43.4093427, 51.8147312}},
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{{48.7793294, 54.2868164}, {52.524604, 52.7906136}, {56.6514498, 48.9586591}},
{{56.6514498, 48.9586591}, {60.7782955, 45.1267046}, {63.5477208, 42.0877376}},
{{63.5477208, 42.0877376}, {65.6800669, 39.7784361}, {66.0159848, 39.6831127}},
{{66.0159848, 39.6831127}, {66.3519027, 39.5877893}, {64.0479481, 43.2239426}},
{{64.0479481, 43.2239426}, {61.7439935, 46.8600958}, {55.9567221, 55.7452241}},
{{55.9567221, 55.7452241}, {55.0519496, 57.1371078}, {54.0523993, 58.6752083}},
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<div id="cubic8x4">
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{{34.4823321, 44.5556425}, {36.9549821, 36.1181121}, {37.4421857, 33.458373}},
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{{32.1835801, 43.5816708}, {33.1767952, 40.7989388}, {37.1569859, 29.7171487}},
{{37.1569859, 29.7171487}, {38.5382511, 25.8713805}, {39.3243103, 23.6824388}},
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<div id="cubic8x4x">
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{{32.1835801, 43.5816708}, {33.6241085, 39.5491663}, {37.1569859, 29.7171487}},
{{37.1569859, 29.7171487}, {38.146263, 26.9628595}, {39.3243103, 23.6824388}},
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<div id="cubic8x5">
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{{52.2780952, 52.3607383}, {56.0052548, 50.2542034}, {70.9344915, 42.0642523}},
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<div id="cubic8x5x">
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{{59.401457, 52.3770387}, {54.5679971, 53.5399363}, {50.919062, 54.7149606}},
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{{70.9344915, 42.0642523}, {71.9455119, 41.5096286}, {73.0077305, 40.9268787}},
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<div id="cubic8x6">
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<div id="cubic8x6x">
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<div id="cubic8x7">
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<div id="cubic8x7x">
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{{37.7133917, 69.1313755}, {35.340896, 71.3195506}, {32.4492169, 73.9888241}},
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<div id="cubic8x8">
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{{52.2592609, 33.6639071}, {47.5369986, 38.2126941}, {44.5524326, 41.278553}},
{{44.5524326, 41.278553}, {40.6568202, 45.2802731}, {39.8604011, 46.6125979}},
{{39.8604011, 46.6125979}, {38.901811, 48.2162178}, {42.4657645, 45.9031378}},
{{42.4657645, 45.9031378}, {46.5800498, 43.232881}, {56.6511208, 35.3872682}},
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<div id="cubic8x8x">
{{53.9853472, 31.729689}, {80.8833995, 7.2950833}, {8.46509939, 72.9253675}, {56.6511208, 35.3872682}},
{{53.9853472, 31.729689}, {55.0401587, 30.7714526}, {55.8968586, 29.9930402}},
{{55.8968586, 29.9930402}, {59.6366873, 26.5924749}, {60.0744106, 26.2078693}},
{{60.0744106, 26.2078693}, {60.5121339, 25.8232638}, {58.6982878, 27.5315648}},
{{58.6982878, 27.5315648}, {56.3310494, 29.756797}, {52.2592609, 33.6639071}},
{{52.2592609, 33.6639071}, {48.1874723, 37.5710172}, {44.5524326, 41.278553}},
{{44.5524326, 41.278553}, {40.9173929, 44.9860887}, {39.8604011, 46.6125979}},
{{39.8604011, 46.6125979}, {38.8034093, 48.2391072}, {42.4657645, 45.9031378}},
{{42.4657645, 45.9031378}, {46.1281196, 43.5671684}, {56.6511208, 35.3872682}},
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<div id="cubic8x9">
{{73.1810322, 53.6088109}, {3.28446082, 1.93300047}, {87.9389074, 89.2160727}, {54.5340817, 54.3107021}},
{{73.1810322, 53.6088109}, {58.5574459, 42.7973267}, {51.3867695, 38.9320081}},
{{51.3867695, 38.9320081}, {45.1924119, 35.5929695}, {44.6615376, 37.4897176}},
{{44.6615376, 37.4897176}, {44.2222697, 39.0591673}, {47.6643015, 44.1654891}},
{{47.6643015, 44.1654891}, {50.2846557, 48.0528359}, {55.0540263, 53.8428721}},
{{55.0540263, 53.8428721}, {57.6549797, 57.0004406}, {61.4896769, 61.4054165}},
{{61.4896769, 61.4054165}, {62.8763033, 62.9982556}, {62.6160157, 62.7489128}},
{{62.6160157, 62.7489128}, {62.3557281, 62.49957}, {59.4073763, 59.4106743}},
{{59.4073763, 59.4106743}, {56.5808171, 56.449377}, {54.5340817, 54.3107021}},
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<div id="cubic8x9x">
{{73.1810322, 53.6088109}, {3.28446082, 1.93300047}, {87.9389074, 89.2160727}, {54.5340817, 54.3107021}},
{{73.1810322, 53.6088109}, {57.8490138, 42.3222252}, {51.3867695, 38.9320081}},
{{51.3867695, 38.9320081}, {44.9245252, 35.5417911}, {44.6615376, 37.4897176}},
{{44.6615376, 37.4897176}, {44.3985499, 39.4376442}, {47.6643015, 44.1654891}},
{{47.6643015, 44.1654891}, {50.9300531, 48.893334}, {55.0540263, 53.8428721}},
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{{61.4896769, 61.4054165}, {62.9413752, 63.0605913}, {62.6160157, 62.7489128}},
{{62.6160157, 62.7489128}, {62.2906562, 62.4372343}, {59.4073763, 59.4106743}},
{{59.4073763, 59.4106743}, {57.5885087, 57.5036974}, {54.5340817, 54.3107021}},
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<div id="cubic4">
{{24.2578299, 1.34695745}, {6.77689729, 99.312693}, {3.18338154, 3.09354817}, {59.132973, 47.8778685}},
{{38.313885, 41.465269}, {48.4308047, 76.5337766}, {93.264044, 88.7879534}, {83.3354337, 18.6335197}}
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<div id="cubic5">
{{24.0062249, 72.6211198}, {22.3913226, 30.9587957}, {80.7539402, 31.4736433}, {99.6348716, 63.2867312}},
{{43.1612821, 11.6690897}, {24.4801394, 37.7033828}, {77.5229567, 28.3334108}, {60.0910899, 50.9480224}}
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(gdb) p q2
$7 = {{x = 24.006224853920855, y = 72.621119847810419}, {x = 29.758671200376888, y = 31.764642512385173}, {x = 71.277052443896736, y = 42.309313461363033}}
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{{x = 34.879150914024962, y = 83.862726601601125}, {x = 35.095810134304429, y = 83.693473210169543}, {x = 35.359284111931586, y = 83.488069234177502}}
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{{x = 54.080923997834752, y = 38.089631608729078}, {x = 10.447347774378651, y = 88.574043981998258}, {x = 33.294667831293616, y = 83.482240551841556}, {x = 25.649263209500006, y = 87.166762066617025}}
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{{x = 25.367434474345036, y = 50.4712103169743}, {x = 17.865013304933097, y = 37.356741010559439}, {x = 16.818988838905465, y = 37.682915484123129}}
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{{x = 25.367434474345036, y = 50.4712103169743}, {x = 5.2367042308844178, y = 13.28800847441331}, {x = 21.031375239152169, y = 74.32364443052731}, {x = 60.821163496384933, y = 21.294883741668837}}
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{{x = 36.148792695174222, y = 70.336952793070424}, {x = 36.141613037691357, y = 70.711654739870085}, {x = 36.154708826402597, y = 71.088492662905836}}
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{{x = 369.84860200000003, y = 145.68026699999999}, {x = 382.36041299999999, y = 121.298294}, {x = 406.20770299999998, y = 121.298294}}
{{x = 369.850525, y = 145.67596399999999}, {x = 382.36291499999999, y = 121.29286999999999}, {x = 406.21127300000001, y = 121.29286999999999}}
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{{x = 67.25299631583178, y = 21.109080184767524}, {x = 43.617595267398613, y = 33.658034168577529}, {x = 33.38371819435676, y = 44.214192553988745}}
{{x = 40.476838859398541, y = 39.543209911285999}, {x = 36.701186108431131, y = 34.8817994016458}, {x = 30.102144288878023, y = 26.739063172945315}}
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{{x = 59.981867574297752, y = 19.243986850744687}, {x = 59.992798861020468, y = 19.257454808070786}, {x = 60.003741189575571, y = 19.270930807443623}}
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{{x = 53.674595921148828, y = 8.9336467482771944}, {x = 48.248201817389678, y = 7.5279448682106773}, {x = 89.942031162763953, y = 55.717752573880254}, {x = 81.402728418541486, y = 35.656530426655216}}
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{{353.2948,194.351074}, {353.2948,173.767563}, {364.167572,160.819855}},
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<div id="quad10">
{{8, 8}, {10, 10}, {8, -10}},
{{8, 8}, {12, 12}, {14, 4}},
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<div id="quad11">
{{x = 50.934805397717923, y = 51.52391952648901}, {x = 56.803308902971423, y = 44.246234610627596}, {x = 69.776888596721406, y = 40.166645096692555}}
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{{18.1312339, 31.6473732}, {95.5711034, 63.5350219}, {92.3283165, 62.0158945}, {18.5656052, 32.1268808}},
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{{98.3415562, 26.5353662}, {15.3721551, 59.8107939}, {77.1895742, 25.1742572}, {11.7326863, 91.2589209}},
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{{95.6513419, 12.1029701}, {63.4801516, 10.9081754}, {41.0209588, 39.2537121}, {65.9441362, 23.0970739}},
{{14.6179238, 83.4452002}, {33.7032426, 50.3981092}, {37.1399002, 10.3032037}, {92.5218685, 15.0431467}},
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<div id="cubic14">
{{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}},
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{{67.4265481,37.9937726}, {51.1295132,57.5422812}, {44.5947482,65.6442673}},
{{44.5947482,65.6442673}, {35.2387481,77.3910511}, {43.2346162,66.2224493}},
{{43.2346162,66.2224493}, {51.8234203,54.2750917}, {75.3863417,18.24489}},
{{61.3365082,82.6931328}, {54.8250789,71.6639328}, {47.7274442,61.4049645}},
{{47.7274442,61.4049645}, {40.6298095,51.1459962}, {35.9460478,45.2252785}},
{{35.9460478,45.2252785}, {31.2622861,39.3045608}, {31.9924758,41.2901124}},
{{31.9924758,41.2901124}, {32.7226655,43.275664}, {41.866885,56.7355037}},
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<div id="quad12">
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{{x = 53.774852327053594, y = 53.318060789841951}, {x = 45.787877803416805, y = 51.393492026284981}, {x = 46.703936967162392, y = 53.06860709822206}}
{{x = 46.703936967162392, y = 53.06860709822206}, {x = 47.619996130907957, y = 54.74372217015916}, {x = 53.020051653535361, y = 48.633140968832024}}
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{{40.3684631, 72.7588382}, {85.2198593, 90.174892}, {31.9101421, 13.7580149}, {72.0483425, 16.4930846}},
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{{98.3415562, 26.5353662}, {15.3721551, 59.8107939}, {77.1895742, 25.1742572}, {11.7326863, 91.2589209}},
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{{95.6513419, 12.1029701}, {63.4801516, 10.9081754}, {41.0209588, 39.2537121}, {65.9441362, 23.0970739}},
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{{95.6513419,12.1029701}, {79.216947,12.1911515}, {68.1126831,18.0126375}},
{{68.1126831,18.0126375}, {57.0084192,23.8341235}, {55.4198832,27.1619689}},
{{55.4198832,27.1619689}, {53.8313472,30.4898143}, {65.9441362,23.0970739}},
{{14.6179238,83.4452002}, {20.3825754,73.0912112}, {25.0377248,62.5209893}},
{{25.0377248,62.5209893}, {33.2090045,41.6303758}, {46.9147771,27.3313746}},
{{46.9147771,27.3313746}, {60.6205496,13.0323735}, {92.5218685,15.0431467}},
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{{55.7513494,12.929877}, {52.399261,23.0070161}, {46.4958203,27.5595279}},
{{46.4958203,27.5595279}, {40.5923795,32.1120397}, {33.5495747,34.9548738}},
{{33.5495747,34.9548738}, {25.3214643,38.1279717}, {17.6150117,44.5570525}},
{{17.6150117,44.5570525}, {9.90855921,50.9861334}, {4.93643419,66.6494508}},
{{12.4426199,23.1121812}, {17.0040168,19.5021098}, {18.7553606,21.0894159}},
{{18.7553606,21.0894159}, {20.5067044,22.676722}, {21.4650431,26.4450934}},
{{21.4650431,26.4450934}, {22.5692754,31.7464864}, {26.4671516,34.648351}},
{{26.4671516,34.648351}, {30.3650278,37.5502156}, {41.873704,30.8489321}},
{{41.873704,30.8489321}, {53.3823801,24.1476487}, {77.3190123,0.63959742}},
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{{67.4265481,37.9937726}, {51.1295132,57.5422812}, {44.5947482,65.6442674}},
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<div id="cubic20">
{{x = 42.449716172390481, y = 52.379709366885805}, {x = 27.896043159019225, y = 48.797373636065686}, {x = 92.770268299044233, y = 89.899302036454571}, {x = 12.102066544863426, y = 99.43241951960718}}
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{{7.53748091,82.4417029}, {15.5677076,52.942994}, {29.9404074,49.1672596}},
{{29.9404074,49.1672596}, {44.3131071,45.3915253}, {58.1067559,59.5061814}},
{{58.1067559,59.5061814}, {71.9004047,73.6208375}, {78.1934785,97.7932998}},
{{97.7005731,53.5326022}, {91.6030843,68.4083459}, {72.6510251,64.2972928}},
{{72.6510251,64.2972928}, {53.6989659,60.1862397}, {35.2053722,44.8391126}},
{{35.2053722,44.8391126}, {16.7117786,29.4919856}, {11.9896864,10.6595075}},
</div>
<div id="quad20">
{{29.9404074,49.1672596}, {44.3131071,45.3915253}, {58.1067559,59.5061814}},
{{72.6510251,64.2972928}, {53.6989659,60.1862397}, {35.2053722,44.8391126}},
</div>
<div id="cubic23">
{{x = 32.484981432782945, y = 75.082940782924624}, {x = 42.467313093350882, y = 48.131159948246157}, {x = 3.5963115764764657, y = 43.208665839959245}, {x = 79.442476890721579, y = 89.709102357602262}}
{{x = 18.98573861410177, y = 93.308887208490106}, {x = 40.405250173250792, y = 91.039661826118675}, {x = 8.0467721950480584, y = 42.100282172719147}, {x = 40.883324221187891, y = 26.030185504830527}}
{{32.4849814,75.0829408}, {35.4553509,65.5763004}, {33.5767697,60.2097835}},
{{33.5767697,60.2097835}, {31.6981886,54.8432666}, {31.1663962,54.7302484}},
{{31.1663962,54.7302484}, {31.1662882,54.7301074}, {31.1663969,54.7302485}},
{{31.1663969,54.7302485}, {30.4117445,54.6146017}, {40.1631726,62.9428436}},
{{40.1631726,62.9428436}, {49.9146008,71.2710854}, {79.4424769,89.7091024}},
{{18.9857386,93.3088872}, {25.7662938,92.3417699}, {26.5917262,85.8225583}},
{{26.5917262,85.8225583}, {27.4171586,79.3033467}, {26.141946,69.8089528}},
{{26.141946,69.8089528}, {24.2922348,57.665767}, {26.0404936,45.4260361}},
{{26.0404936,45.4260361}, {27.7887523,33.1863051}, {40.8833242,26.0301855}},
</div>
<div id="quad21">
{{31.1663962,54.7302484}, {31.1662882,54.7301074}, {31.1663969,54.7302485}},
{{26.0404936,45.4260361}, {27.7887523,33.1863051}, {40.8833242,26.0301855}},
</div>
<div id="cubic24">
{{x = 65.454505973241524, y = 93.881892270353575}, {x = 45.867360264932437, y = 92.723972719499827}, {x = 2.1464054482739447, y = 74.636369140183717}, {x = 33.774068594804994, y = 40.770872887582925}}
{{x = 72.963387832494163, y = 95.659300729473728}, {x = 11.809496633619768, y = 82.209921247423594}, {x = 13.456139067865974, y = 57.329313623406605}, {x = 36.060621606214262, y = 70.867335643091849}}
{{65.454506,93.8818923}, {54.7397995,93.2922678}, {41.5072916,87.1234036}},
{{41.5072916,87.1234036}, {28.2747836,80.9545395}, {23.5780771,69.3344126}},
{{23.5780771,69.3344126}, {18.8813706,57.7142857}, {33.7740686,40.7708729}},
{{72.9633878,95.6593007}, {42.7738746,88.4730382}, {31.1932785,80.2458029}},
{{31.1932785,80.2458029}, {19.6126823,72.0185676}, {21.9918152,68.2892325}},
{{21.9918152,68.2892325}, {24.370948,64.5598974}, {36.0606216,70.8673356}},
</div>
<div id="quad22">
{{41.5072916,87.1234036}, {28.2747836,80.9545395}, {23.5780771,69.3344126}},
{{72.9633878,95.6593007}, {42.7738746,88.4730382}, {31.1932785,80.2458029}},
</div>
<div id="cubic25">
{{x = 39.765160968417838, y = 33.060396198677083}, {x = 5.1922921581157908, y = 66.854301452103215}, {x = 31.619281802149157, y = 25.269248720849514}, {x = 81.541621071073038, y = 70.025341524754353}}
{{x = 46.078911165743556, y = 48.259962651999651}, {x = 20.24450549867214, y = 49.403916182650214}, {x = 0.26325131778756683, y = 24.46489805563581}, {x = 15.915006546264051, y = 83.515023059917155}}
{{39.765161,33.0603962}, {30.6426004,41.804305}, {26.9359756,44.8138368}},
{{26.9359756,44.8138368}, {21.5667569,48.8605535}, {26.2727712,47.6735862}},
{{26.2727712,47.6735862}, {31.3832959,46.2642047}, {45.8264929,49.1528875}},
{{45.8264929,49.1528875}, {60.2696898,52.0415702}, {81.5416211,70.0253415}},
{{46.0789112,48.2599627}, {35.5887068,48.1941457}, {27.2014026,45.6924463}},
{{27.2014026,45.6924463}, {19.5490336,43.4817863}, {15.020365,44.2719744}},
{{15.020365,44.2719744}, {10.4916964,45.0621625}, {10.3896311,53.6689795}},
{{10.3896311,53.6689795}, {10.2875658,62.2757965}, {15.9150065,83.5150231}},
</div>
<div id="cubic26">
{{x = 95.837747722788592, y = 45.025976907939643}, {x = 16.564570095652982, y = 0.72959763963222402}, {x = 63.209855865319199, y = 68.047528419665767}, {x = 57.640240647662544, y = 59.524565264361243}}
{{x = 51.593891741518817, y = 38.53849970667553}, {x = 62.34752929878772, y = 74.924924725166022}, {x = 74.810149322641152, y = 34.17966562983564}, {x = 29.368398119401373, y = 94.66719277886078}}
{{95.8377477,45.0259769}, {72.4120612,32.1119735}, {61.9589898,30.3422249}},
{{61.9589898,30.3422249}, {51.5059185,28.5724763}, {49.7502617,33.4480576}},
{{49.7502617,33.4480576}, {47.9946048,38.3236388}, {50.6611618,45.345625}},
{{50.6611618,45.345625}, {53.3277187,52.3676112}, {56.1412886,57.0370775}},
{{56.1412886,57.0370775}, {58.9548585,61.7065438}, {57.6402406,59.5245653}},
{{51.5938917,38.5384997}, {54.39659,47.5609728}, {56.9124968,51.2509862}},
{{56.9124968,51.2509862}, {59.4284036,54.9409997}, {60.7901347,55.8937858}},
{{60.7901347,55.8937858}, {63.1940269,56.8659601}, {59.551481,59.5998651}},
{{59.551481,59.5998651}, {56.8806183,61.8512737}, {49.6576236,69.6523525}},
{{49.6576236,69.6523525}, {42.434629,77.4534313}, {29.3683981,94.6671928}},
</div>
<div id="quad23">
{{x = 56.14128857485079, y = 57.037077517172825}, {x = 58.954858484191291, y = 61.706543802985237}, {x = 57.640240647662544, y = 59.524565264361243}}
{{x = 59.551480981235549, y = 59.599865066889976}, {x = 56.880618274428095, y = 61.851273706132794}, {x = 49.657623623535379, y = 69.652352522894546}}
</div>
<div id="cubic27">
{{x = 56.14128857485079, y = 57.037077517172825}, {x = 57.779490695232283, y = 59.900114769069532}, {x = 58.754163691193881, y = 61.229157895422141}, {x = 57.640240647662544, y = 59.524565264361243}}
{{x = 56.14128857485079, y = 57.037077517172825}, {x = 58.954858484191291, y = 61.706543802985237}, {x = 57.640240647662544, y = 59.524565264361243}}
</div>
<div id="testCubic1">
{{0, 0}, {0, 1}, {1, 1}, {1, 0}},
{{1, 0}, {0, 0}, {0, 1}, {1, 1}},
{{0,0}, {0.0185185185,0.5}, {0.259259259,0.666666667}},
{{0.259259259,0.666666667}, {0.5,0.833333333}, {0.740740741,0.666666667}},
{{0.740740741,0.666666667}, {0.981481481,0.5}, {1,0}},
{{1,0}, {0.5,0.0185185185}, {0.333333333,0.259259259}},
{{0.333333333,0.259259259}, {0.166666667,0.5}, {0.333333333,0.740740741}},
{{0.333333333,0.740740741}, {0.5,0.981481481}, {1,1}},
</div>
<div id="testCubic1a">
{{x = 0.30075438676757493, y = 0.69070348972827045}, {x = 0.30339450221247349, y = 0.69543451478800855}, {x = 0.30613761677734441, y = 0.7001387457168422}, {x = 0.30898373046218741, y = 0.70481409186990207}}
{{x = 0.29518590813009821, y = 0.69101626953781281}, {x = 0.29986125428315819, y = 0.69386238322265548}, {x = 0.30456548521199123, y = 0.69660549778752689}, {x = 0.30929651027172955, y = 0.69924561323242507}}
</div>
<div id="testCubic1b">
{{x = 0.3039751936710845, y = 0.69622610811401087}, {x = 0.3037698832307662, y = 0.69610758676672113}}
{{x = 0.3037698832307662, y = 0.69610758676672113}, {x = 0.30387252963474076, y = 0.69616688005807803}}
{{x = 0.30387252963474076, y = 0.69616688005807803}, {x = 0.3039751936710845, y = 0.69622610811401087}}
</div>
<div id="cubicOp1d">
{{0, 1}, {0, 2}, {1, 0}, {1, 0}},
{{0, 1}, {0, 1}, {1, 0}, {2, 0}},
{{0,1}, {0.0078125,1.35546875}, {0.15625,1.265625}},
{{0.15625,1.265625}, {0.3046875,1.17578125}, {0.5,0.875}},
{{0.5,0.875}, {0.6953125,0.57421875}, {0.84375,0.296875}},
{{0.84375,0.296875}, {0.9921875,0.01953125}, {1,0}},
{{0,1}, {0.00925925926,0.981481481}, {0.296296296,0.740740741}},
{{0.296296296,0.740740741}, {0.583333333,0.5}, {1.03703704,0.259259259}},
{{1.03703704,0.259259259}, {1.49074074,0.0185185185}, {2,0}},
</div>
<div id="cubicTest1">
{{0, 1}, {5, 6}, {1, 0}, {1, 0}},
{{0, 1}, {0, 1}, {1, 0}, {6, 5}},
{{0,1}, {1.474,2.466}, {2.024,2.816}},
{{2.024,2.816}, {2.574,3.166}, {2.512,2.808}},
{{2.512,2.808}, {2.45,2.45}, {2.088,1.792}},
{{2.088,1.792}, {1.726,1.134}, {1.376,0.584}},
{{1.376,0.584}, {1.026,0.034}, {1,0}},
{{0,1}, {-0.0277777778,0.935185185}, {0.444444444,0.925925926}},
{{0.444444444,0.925925926}, {0.916666667,0.916666667}, {2.22222222,1.74074074}},
{{2.22222222,1.74074074}, {3.52777778,2.56481481}, {6,5}},
</div>
<div id="cubicTest2">
{{fX = 0, fY = 1}, {fX = 0, fY = 2}, {fX = 1, fY = 0}, {fX = 5, fY = 0}}
{{fX = 0, fY = 1}, {fX = 0, fY = 5}, {fX = 1, fY = 0}, {fX = 2, fY = 0}}
</div>
<div id="cubicTest3">
{{x = 0, y = 1}, {x = 1, y = 6}, {x = 1, y = 0}, {x = 2, y = 0}}
{{x = 0, y = 1}, {x = 0, y = 2}, {x = 1, y = 0}, {x = 6, y = 1}}
{{0,1}, {0.296,2.466}, {0.496,2.816}},
{{0.496,2.816}, {0.696,3.166}, {0.848,2.808}},
{{0.848,2.808}, {1,2.45}, {1.152,1.792}},
{{1.152,1.792}, {1.304,1.134}, {1.504,0.584}},
{{1.504,0.584}, {1.704,0.034}, {2,0}},
{{0,1}, {-0.040150997,1.4850292}, {0.586736465,1.17347293}},
{{0.586736465,1.17347293}, {1.11546634,0.936942311}, {2.40073788,0.7574854}},
{{2.40073788,0.7574854}, {3.68600943,0.578028489}, {6,1}},
</div>
<div id="lineTest1">
{{x = 1.3834888994942065, y = 0.93137912059586503}, {x = 1.3835184247369658, y = 0.93128386633972826}}
{{x = 1.3834889487833637, y = 0.93138119876148517}, {x = 1.3835243637966514, y = 0.93137251518247632}}
</div>
<div id="lineQuad1">
{{x = 0.5, y = 0.875}, {x = 0.65728065326954233, y = 0.63483143515742313}, {x = 0.78907579690950191, y = 0.3959256577144401}}
{{x = 0.78906720197447666, y = 0.39595053259806418}, {x = 0.78966023971986588, y = 0.39559384654294}}}
</div>
<div id="lineQuad2">
{{x = 0.78907579690950191, y = 0.3959256577144401}, {x = 0.78953800250469452, y = 0.39509830801181633}}
{{x = 0.29629629629629628, y = 0.74074074074074081}, {x = 0.49667506598603178, y = 0.57646999653254238}, {x = 0.78906720197447666, y = 0.39595053259806418}}
</div>
<div id="x1">
{{0.5,0.875}, {0.657581172,0.634357518}, {0.789538003,0.395098308}},
{{0.296296296,0.740740741}, {0.496887363,0.576287939}, {0.78966024,0.395593847}},
</div>
<div id="x2">
{{0.5,0.875}, {0.657280653,0.634831435}, {0.789075797,0.395925658}},
{{0.296296296,0.740740741}, {0.496675066,0.576469997}, {0.789067202,0.395950533}},
</div>
<div id="x3">
{{0.789075797,0.395925658}, {0.789538003,0.395098308}},
{{0.296296296,0.740740741}, {0.496675066,0.576469997}, {0.789067202,0.395950533}},
</div>
<div id="x4">
{{0.789538003,0.395098308}, {0.818060471,0.344004048}, {0.84375,0.296875}},
{{0.296296296,0.740740741}, {0.496887363,0.576287939}, {0.78966024,0.395593847}},
</div>
<div id="x5">
{{0.789538003,0.395098308}, {0.818060471,0.344004048}, {0.84375,0.296875}},
{{0.78966024,0.395593847}, {0.908006316,0.324112697}, {1.03703704,0.259259259}},
</div>
<div id="cubicX">
{{x = 0, y = 1}, {x = 0, y = 2}, {x = 1, y = 0}, {x = 1, y = 0}}
{{x = 0, y = 1}, {x = 0, y = 2}, {x = 1, y = 0}, {x = 6, y = 1}}
</div>
<div id="cubicOp2d">
{{0,2}, {0,1}, {1,0}, {1,0}},
{{0,1}, {0,1}, {2,0}, {1,0}},
{{0,2}, {0.0185185185,1.49074074}, {0.259259259,1.03703704}},
{{0.259259259,1.03703704}, {0.5,0.583333333}, {0.740740741,0.296296296}},
{{0.740740741,0.296296296}, {0.981481481,0.00925925926}, {1,0}},
{{0,1}, {0.01953125,0.9921875}, {0.296875,0.84375}},
{{0.296875,0.84375}, {0.57421875,0.6953125}, {0.875,0.5}},
{{0.875,0.5}, {1.17578125,0.3046875}, {1.265625,0.15625}},
{{1.265625,0.15625}, {1.35546875,0.0078125}, {1,0}},
</div>
<div id="cubicOp2da">
{{0.395593847,0.78966024}, {0.576287939,0.496887363}, {0.740740741,0.296296296}},
{{0.395098308,0.789538003}, {0.634357518,0.657581172}, {0.875,0.5}},
</div>
<div id="cubicOp3d">
{{0,1}, {2,3}, {1,0}, {1,0}},
{{0,1}, {0,1}, {1,0}, {3,2}},
{{0,1}, {0.592,1.584}, {0.872,1.664}},
{{0.872,1.664}, {1.152,1.744}, {1.216,1.512}},
{{1.216,1.512}, {1.28,1.28}, {1.224,0.928}},
{{1.224,0.928}, {1.168,0.576}, {1.088,0.296}},
{{1.088,0.296}, {1.008,0.016}, {1,0}},
{{0,1}, {0,0.962962963}, {0.333333333,0.814814815}},
{{0.333333333,0.814814815}, {0.666666667,0.666666667}, {1.33333333,0.851851852}},
{{1.33333333,0.851851852}, {2,1.03703704}, {3,2}},
</div>
<div id="cubicOp3da">
{{1.224,0.928}, {1.17328164,0.604609714}, {1.09894996,0.336624845}},
{{1.09895195,0.33662897}, {1.22307655,0.2359436}, {1.265625,0.15625}},
</div>
<div id="cubicOp3db">
{{x = 1.2071879545809394, y = 0.82163474041730045}, {x = 1.1534203513372994, y = 0.52790870069930229}, {x = 1.0880000000000001, y = 0.29599999999999982}}
{{x = 1.205732763658403, y = 0.81345617746834109}, {x = 1.267928895828891, y = 0.83008534558465619}, {x = 1.3333333333333333, y = 0.85185185185185175}}
</div>
<div id="cubicOp3dc">
part=(1.20718795,0.82163474 1.17452925,0.632190117 1.1284272,0.444233064 1.088,0.296)
quad=(1.20718795,0.82163474 1.15342035,0.527908701 1.088,0.296)
part=(1.20573276,0.813456177 1.24719685,0.824565605 1.28973037,0.837317532 1.33333333,0.851851852)
quad=(1.20573276,0.813456177 1.2679289,0.830085346 1.33333333,0.851851852)
</div>
<div id="cubicOp3dd">
{{1.20718795,0.82163474 1.17452925,0.632190117 1.1284272,0.444233064 1.088,0.296)
{{1.20718795,0.82163474 1.15342035,0.527908701 1.088,0.296)
{{1.20568441,0.813443223 1.20570053,0.813447541 1.20571665,0.813451859 1.20573276,0.813456177)
{{1.20568441,0.813443223 1.20570859,0.8134497 1.20573276,0.813456177)
{{0.33333333333333326, y = 0.81481481481481488}, {x = 0.63396444791444551, y = 0.68743368362444768}, {x = 1.205732763658403, y = 0.81345617746834109}}
</div>
<div id="cubicOp3de">
{{1.2071879545809394,0.82163474041730045}, {1.2065040319428038,0.81766753259119995}, {1.2058123269101506,0.81370135061854221}},
{{1.205684411948591,0.81344322326274499}, {1.2057085875611198,0.81344969999329253}, {1.205732763658403,0.81345617746834109}},
</div>
<div id="cubicOp7">
{{0,1}, {3,4}, {1,0}, {3,0}},
{{0,1}, {0,3}, {1,0}, {4,3}},
{{0,1}, {0.837764189,1.83435757}, {1.22841861,2.02640973}},
{{1.22841861,2.02640973}, {1.61907304,2.21846188}, {1.74657491,1.9930452}},
{{1.74657491,1.9930452}, {1.87407679,1.76762853}, {1.92238332,1.34957962}},
{{1.92238332,1.34957962}, {1.97220681,0.867804601}, {2.17393047,0.447689071}},
{{2.17393047,0.447689071}, {2.37565413,0.0275735418}, {3,0}},
{{0,1}, {-0.00234073071,1.60655471}, {0.142631845,1.70125304}},
{{0.142631845,1.70125304}, {0.28760442,1.79595137}, {0.60797907,1.68776977}},
{{0.60797907,1.68776977}, {1.0447864,1.50810914}, {1.87464474,1.63655092}},
{{1.87464474,1.63655092}, {2.70450308,1.76499271}, {4,3}},
</div>
<div id="cubicOp7a">
{{x = 1.7465749139282332, y = 1.9930452039527999}, {x = 1.8417960084006277, y = 1.8552583419678612}, {x = 1.8799591210677749, y = 1.6157879692142081}, {x = 1.9223833226085514, y = 1.3495796165215643}}
{{x = 0.6079790696638232, y = 1.6877697663020552}, {x = 0.90321659591661663, y = 1.6123550739533821}, {x = 1.3173732025571312, y = 1.5065640064343382}, {x = 1.8746447406062119, y = 1.636550924974228}}
{{x = 1.7465749139282332, y = 1.9930452039527999}, {x = 1.8740767879671056, y = 1.7676285282679607}, {x = 1.9223833226085514, y = 1.3495796165215643}}
{{x = 0.6079790696638232, y = 1.6877697663020552}, {x = 1.0447863962878021, y = 1.5081091374717195}, {x = 1.8746447406062119, y = 1.636550924974228}}
</div>
<div id="cubicOp7b">
{{x = 1.7465749139282332, y = 1.9930452039527999}, {x = 1.8417960084006277, y = 1.8552583419678612}, {x = 1.8799591210677749, y = 1.6157879692142081}, {x = 1.9223833226085514, y = 1.3495796165215643}}
{{x = 1.8746447406062119, y = 1.636550924974228}, {x = 2.4319162786552919, y = 1.7665378435141166}, {x = 3.1323027481129411, y = 2.1323027481129406}, {x = 4, y = 3}}
{{x = 1.7465749139282332, y = 1.9930452039527999}, {x = 1.8740767879671056, y = 1.7676285282679607}, {x = 1.9223833226085514, y = 1.3495796165215643}}
{{x = 1.8746447406062119, y = 1.636550924974228}, {x = 2.7045030849246219, y = 1.7649927124767357}, {x = 4, y = 3}}
</div>
<div id="cubicOp8">
{{0,1}, {0,5}, {1,0}, {4,0}},
{{0,1}, {0,4}, {1,0}, {5,0}},
{{0,1}, {-0.00421781142,2.47981485}, {0.214213168,2.53784857}},
{{0.214213168,2.53784857}, {0.432644147,2.59588228}, {0.924337655,1.94072717}},
{{0.924337655,1.94072717}, {1.39158994,1.32418496}, {2.14967426,0.687365435}},
{{2.14967426,0.687365435}, {2.90775858,0.0505459108}, {4,0}},
{{0,1}, {-0.00720132722,2.05525633}, {0.206394399,2.10503282}},
{{0.206394399,2.10503282}, {0.419990125,2.15480931}, {0.940798831,1.67439357}},
{{0.940798831,1.67439357}, {1.48941875,1.16280321}, {2.47884711,0.60465921}},
{{2.47884711,0.60465921}, {3.46827548,0.0465152042}, {5,0}},
</div>
<div id="cubicOp8a">
{{x = 0.92433765471479945, y = 1.9407271660071879}, {x = 1.2518504275349398, y = 1.5283649441281617}, {x = 1.7179390069715588, y = 1.0614995059145118}}
{{x = 0.94079883097732186, y = 1.6743935703752681}, {x = 1.2598825072629554, y = 1.3977856697533602}, {x = 1.7179167190286528, y = 1.0665031295527474}}
</div>
<div id="cubicOp9d">
{{0,1}, {1,2}, {1,0}, {6,1}},
{{0,1}, {1,6}, {1,0}, {2,1}},
</div>
<div id="cubicOp11d">
Cubic cubic1 = {{0,1}, {3,4}, {1,0}, {5,1}};
Cubic cubic2 = {{0,1}, {1,5}, {1,0}, {4,3}};
{{0,1}, {1.10659493,2.10239153}, {1.50615334,2.12918252}},
{{1.50615334,2.12918252}, {1.90571174,2.15597351}, {2.1530827,1.71245386}},
{{2.1530827,1.71245386}, {2.39265628,1.2948736}, {2.98481198,0.986316183}},
{{2.98481198,0.986316183}, {3.57696768,0.677758769}, {5,1}},
{{0,1}, {0.351042317,2.40055211}, {0.610765407,2.56687524}},
{{0.610765407,2.56687524}, {0.870488497,2.73319838}, {1.21251591,2.40319262}},
{{1.21251591,2.40319262}, {1.57068059,2.04916077}, {2.21702741,1.98363478}},
{{2.21702741,1.98363478}, {2.86337424,1.91810879}, {4,3}},
</div>
<div id="cubicOp12d">
{{0, 1}, {1, 6}, {1, 0}, {1, 0}},
{{0, 1}, {0, 1}, {1, 0}, {6, 1}},
{{0,1}, {0.298,2.466}, {0.488,2.816}},
{{0.488,2.816}, {0.678,3.166}, {0.784,2.808}},
{{0.784,2.808}, {0.89,2.45}, {0.936,1.792}},
{{0.936,1.792}, {0.982,1.134}, {0.992,0.584}},
{{0.992,0.584}, {1.002,0.034}, {1,0}},
{{0,1}, {-0.0277777778,0.972222222}, {0.444444444,0.777777778}},
{{0.444444444,0.777777778}, {0.916666667,0.583333333}, {2.22222222,0.555555556}},
{{2.22222222,0.555555556}, {3.52777778,0.527777778}, {6,1}},
</div>
<div id="cubicOp13d">
{{0,1}, {4,5}, {1,0}, {5,3}},
{{0,1}, {3,5}, {1,0}, {5,4}},
{{0,1}, {1.48018645,2.46752265}, {1.93281168,2.58856757}},
{{1.93281168,2.58856757}, {2.38543691,2.7096125}, {2.51967352,2.34531784}},
{{2.51967352,2.34531784}, {2.65263731,2.00639194}, {3.1212119,1.98608967}},
{{3.1212119,1.98608967}, {3.5897865,1.96578739}, {5,3}},
{{0,1}, {1.05556321,2.39540407}, {1.46049052,2.58073968}},
{{1.46049052,2.58073968}, {1.86541784,2.76607529}, {2.09544533,2.51981963}},
{{2.09544533,2.51981963}, {2.33331524,2.25252128}, {2.92003302,2.39442311}},
{{2.92003302,2.39442311}, {3.5067508,2.53632493}, {5,4}},
</div>
<div id="cubicTest4">
{{x = 0, y = 1}, {x = 4, y = 5}, {x = 1, y = 0}, {x = 5, y = 3}}
{{x = 0, y = 1}, {x = 1, y = 6}, {x = 1, y = 0}, {x = 2, y = 0}}
</div>
<div id="cubicTest5">
{{x = 0, y = 1}, {x = 1, y = 6}, {x = 1, y = 0}, {x = 1, y = 0}}
{{x = 0, y = 1}, {x = 1, y = 6}, {x = 1, y = 0}, {x = 2, y = 1}}
</div>
<div id="cubicTest6">
{{x = 0, y = 1}, {x = 4, y = 5}, {x = 1, y = 0}, {x = 5, y = 3}}
{{x = 4, y = 4}, {x = 3, y = 4}, {x = 1, y = 2}, {x = 0, y = 0}}
</div>
<div id="cubicTest7">
{{x = 0, y = 1}, {x = 1.9274705288631189e-19, y = 1.0000000000000002}, {x = 0.0017190297609673323, y = 0.99828097023903239}, {x = 0.0053709083094631276, y = 0.99505672974365911}}
</div>
<div id="cubicOp16d">
{{0,2},{0,1},{3,0},{1,0}},
{{0,3},{0,1},{2,0},{1,0}},
{{0,2}, {0.0229970175,1.6585632}, {0.366509308,1.33437416}},
{{0.366509308,1.33437416}, {0.710021598,1.01018513}, {1.09808495,0.737739381}},
{{1.09808495,0.737739381}, {1.40607875,0.517813127}, {1.57937247,0.352342403}},
{{1.57937247,0.352342403}, {1.75266619,0.186871679}, {1.64451042,0.0942001592}},
{{1.64451042,0.0942001592}, {1.53635465,0.00152863961}, {1,0}},
{{0,3}, {0.0263932023,2.17082039}, {0.352786405,1.57082039}},
{{0.352786405,1.57082039}, {0.679179607,0.970820393}, {0.988854382,0.6}},
{{0.988854382,0.6}, {1.23200941,0.3}, {1.27672209,0.15}},
{{1.27672209,0.15}, {1.32143477,9.25185854e-17}, {1,0}},
</div>
<div id="quadOp16d">
{{1.64451042,0.0942001592}, {1.53635465,0.00152863961}, {1,0}},
{{1.27672209,0.15}, {1.32143477,9.25185854e-17}, {1,0}},
</div>
<div id="cubicOp20d">
{{0,6},{1,2},{1,0},{1,0}},
{{0,1},{0,1},{6,0},{2,1}},
{{0,6}, {0.71875,3}, {0.875,1.5}},
{{0.875,1.5}, {1.03125,1.11022302e-16}, {1,0}},
{{0,1}, {0.0625,0.98828125}, {0.875,0.859375}},
{{0.875,0.859375}, {1.6875,0.73046875}, {2.5,0.625}},
{{2.5,0.625}, {3.3125,0.51953125}, {3.375,0.578125}},
{{3.375,0.578125}, {3.4375,0.63671875}, {2,1}},
</div>
<div id="cubicOp21d">
{{1,2},{5,6},{1,0},{1,0}},
{{0,1},{0,1},{2,1},{6,5}},
{{1,2}, {2.176,3.168}, {2.536,3.328}},
{{2.536,3.328}, {2.896,3.488}, {2.728,3.024}},
{{2.728,3.024}, {2.56,2.56}, {2.152,1.856}},
{{2.152,1.856}, {1.744,1.152}, {1.384,0.592}},
{{1.384,0.592}, {1.024,0.032}, {1,0}},
{{0,1}, {7.40148683e-17,0.962962963}, {0.666666667,1.14814815}},
{{0.666666667,1.14814815}, {1.33333333,1.33333333}, {2.66666667,2.18518519}},
{{2.66666667,2.18518519}, {4,3.03703704}, {6,5}},
</div>
<div id="quadOp21d">
{{2.728,3.024}, {2.56,2.56}, {2.152,1.856}},
{{0.666666667,1.14814815}, {1.33333333,1.33333333}, {2.66666667,2.18518519}},
</div>
<div id="cubicSelf1">
{{3.34,8.98}, {1.95,10.27}, {3.76,7.65}, {4.96,10.64}},
{{3.34,8.98}, {2.83363281,9.4265625}, {2.83796875,9.363125}},
{{2.83796875,9.363125}, {2.84230469,9.2996875}, {3.17875,9.1725}},
{{3.17875,9.1725}, {3.51519531,9.0453125}, {4.00515625,9.300625}},
{{4.00515625,9.300625}, {4.49511719,9.5559375}, {4.96,10.64}},
</div>
<div id="quadSelf1">
{{3.34,8.98}, {2.83363281,9.4265625}, {2.83796875,9.363125}},
{{2.83796875,9.363125}, {2.84230469,9.2996875}, {3.17875,9.1725}},
</div>
<div id="cubicOp27d">
{{0,1}, {3,6}, {1,0}, {5,2}},
{{0,1}, {2,5}, {1,0}, {6,3}},
{{0,1}, {1.11687388,2.858568}, {1.5151589,3.0010603}},
{{1.5151589,3.0010603}, {1.91344391,3.14355261}, {2.16505631,2.55782454}},
{{2.16505631,2.55782454}, {2.40541285,2.02193091}, {2.99836023,1.68247638}},
{{2.99836023,1.68247638}, {3.5913076,1.34302184}, {5,2}},
{{0,1}, {0.691228423,2.3859516}, {1.0489054,2.56156367}},
{{1.0489054,2.56156367}, {1.40658238,2.73717574}, {1.80814127,2.41537795}},
{{1.80814127,2.41537795}, {2.23475077,2.05922313}, {3.16529668,1.98358763}},
{{3.16529668,1.98358763}, {4.0958426,1.90795214}, {6,3}},
</div>
<div id="quadOp27d">
{{1.80814127,2.41537795}, {2.23475077,2.05922313}, {3.16529668,1.98358763}},
{{2.16505631,2.55782454}, {2.40541285,2.02193091}, {2.99836023,1.68247638}},
</div>
<div id="cubicOp30d">
{{0,1}, {2,5}, {6,0}, {5,3}},
{{0,6}, {3,5}, {1,0}, {5,2}},
{{0,1}, {0.585028897,2.1161006}, {1.31572211,2.42528354}},
{{1.31572211,2.42528354}, {2.04641532,2.73446648}, {2.77656625,2.5918049}},
{{2.77656625,2.5918049}, {3.50671719,2.44914333}, {4.09011926,2.20971038}},
{{4.09011926,2.20971038}, {4.74608133,1.9335932}, {5.02469918,2.00694987}},
{{5.02469918,2.00694987}, {5.30331702,2.08030653}, {5,3}},
{{0,6}, {0.946962644,5.64705935}, {1.35765232,4.89865813}},
{{1.35765232,4.89865813}, {1.768342,4.1502569}, {1.97833659,3.34197296}},
{{1.97833659,3.34197296}, {2.2269947,2.25886123}, {2.79472921,1.73568666}},
{{2.79472921,1.73568666}, {3.36246373,1.21251209}, {5,2}},
</div>
<div id="quadOp30d">
{{4.09011926,2.20971038}, {4.74608133,1.9335932}, {5.02469918,2.00694987}},
{{2.79472921,1.73568666}, {3.36246373,1.21251209}, {5,2}},
</div>
<div id="cubicOp34d">
{{x = 1.0097960937999808, y = 2.2108396209439607}, {x = 1, y = 2.1969085233712229}, {x = 1, y = 2.1347920612232207}, {x = 1, y = 2}}
{{x = 1.0097960937999808, y = 2.2108396209439607}, {x = 1.0242251996917398, y = 2.2313593593386498}, {x = 1.0599075827658746, y = 2.1473377437648784}, {x = 1.1481481481481481, y = 2.0370370370370372}}
{{x = 1.0097960958786989, y = 2.2108396260650962}, {x = 0.73607693096853644, y = 1.9329854848088734}, {x = 0.40437628284615079, y = 1.5391683771282005}, {x = 0, y = 1}}
{{x = 1.0097960958786989, y = 2.2108396260650962}, {x = 1.8566294376993437, y = 3.0704657726520206}, {x = 2.1484860084122528, y = 2.8201383770234716}, {x = 2.320499529631658, y = 2.3301248824079162}}
</div>
<div id="cubicOp34da">
{{x = 1.0097960937999808, y = 2.2108396209439607}, {x = 1, y = 2.1969085233712229}, {x = 1, y = 2.1347920612232207}, {x = 1, y = 2}}
{{x = 1.0097960937999808, y = 2.2108396209439607}, {x = 1.0242251996917398, y = 2.2313593593386498}, {x = 1.0599075827658746, y = 2.1473377437648784}, {x = 1.1481481481481481, y = 2.0370370370370372}}
</div>
<div id="cubicOp34db">
{{1,2}, {1,3}, {1,0}, {5,3}},
{{0,1}, {3,5}, {2,1}, {3,1}},
{{1,2}, {0.984375,2.3359375}, {1.0625,2.15625}},
{{1.0625,2.15625}, {1.140625,1.9765625}, {1.5,1.75}},
{{1.5,1.75}, {1.859375,1.5234375}, {2.6875,1.71875}},
{{2.6875,1.71875}, {3.515625,1.9140625}, {5,3}},
{{0,1}, {0.983539095,2.30041152}, {1.47325103,2.61316872}},
{{1.47325103,2.61316872}, {1.96296296,2.92592593}, {2.1563786,2.64609053}},
{{2.1563786,2.64609053}, {2.34979424,2.36625514}, {2.44444444,1.88888889}},
{{2.44444444,1.88888889}, {2.52083333,1.54166667}, {2.63888889,1.27777778}},
{{2.63888889,1.27777778}, {2.75694444,1.01388889}, {3,1}},
</div>
<div id="quadOp34d">
{{1,2}, {0.984375,2.3359375}, {1.0625,2.15625}},
{{0,1}, {0.983539095,2.30041152}, {1.47325103,2.61316872}},
</div>
<div id="cubicOp35d">
{{0,1}, {1,5}, {2,1}, {4,0}},
{{1,2}, {0,4}, {1,0}, {5,1}},
{{0,1}, {0.324417544,2.27953848}, {0.664376547,2.58940267}},
{{0.664376547,2.58940267}, {1.00433555,2.89926686}, {1.39091893,2.58136885}},
{{1.39091893,2.58136885}, {1.7775023,2.26347084}, {2.24179297,1.65972271}},
{{2.24179297,1.65972271}, {2.61097963,1.18900727}, {3.04664862,0.731366192}},
{{3.04664862,0.731366192}, {3.48231762,0.273725118}, {4,0}},
{{1,2}, {0.62109375,2.70703125}, {0.640625,2.546875}},
{{0.640625,2.546875}, {0.66015625,2.38671875}, {1.125,1.875}},
{{1.125,1.875}, {1.58984375,1.36328125}, {2.546875,1.015625}},
{{2.546875,1.015625}, {3.50390625,0.66796875}, {5,1}},
</div>
<div id="cubicOp35da">
{{x = 0.44618727783085621, y = 2.2840286415243063}, {x = 0.51170845243761109, y = 2.4044088819954914}, {x = 0.57783675570457882, y = 2.4985733182515446}, {x = 0.64483584772311509, y = 2.5694222112973661}}
{{x = 0.64244110111854291, y = 2.5673840215265367}, {x = 0.63479413812245555, y = 2.5620057200094775}, {x = 0.64115438240274059, y = 2.533597555954064}, {x = 0.6620248993310307, y = 2.4876932484482714}}
</div>
<div id="line0">
{{2, 1}, {2, 1}},
</div>
<div id="line1">
{{2, 1}, {1, 1}},
</div>
<div id="line2">
{{2, 1}, {2, 2}}
</div>
<div id="line3">
{{1, 1}, {2, 2}},
</div>
<div id="line4">
{{3, 0}, {2, 1}},
</div>
<div id="line5">
{{3, 2}, {1, 1}},
</div>
<div id="tri0">
{{2, 0}, {3, 1}},
{{3, 1}, {2, 2}},
{{2, 2}, {2, 0}},
</div>
<div id="tri1">
{{3, 1}, {2, 2}},
{{2, 2}, {1, 1}},
{{1, 1}, {3, 1}},
</div>
<div id="tri2">
{{3, 0}, {2, 1}},
{{2, 1}, {3, 2}},
{{3, 2}, {3, 0}},
</div>
<div id="testQuad0">
{{1, 1}, {2, 1}, {0, 2}},
</div>
<div id="testQuad1">
{{0, 0}, {1, 1}, {3, 1}},
</div>
<div id="testQuad2">
{{2, 0}, {1, 1}, {2, 2}},
</div>
<div id="testQuad3">
{{4, 0}, {0, 1}, {4, 2}},
</div>
<div id="testQuad4">
{{0, 0}, {0, 1}, {1, 1}},
</div>
<div id="cubicOp65d">
{{0,1}, {1,5}, {1,0}, {1,0}},
{{0,1}, {0,1}, {1,0}, {5,1}},
</div>
</div>
<script type="text/javascript">
var testDivs = [
cubicOp65d,
testQuad0,
testQuad1,
testQuad2,
testQuad3,
testQuad4,
tri0,
tri1,
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cubicOp35da,
cubicOp35d,
quadOp34d,
cubicOp34db,
cubicOp34d,
cubicOp34da,
quadOp30d,
cubicOp30d,
quadOp27d,
cubicOp27d,
quadSelf1,
cubicSelf1,
quadOp21d,
cubicOp21d,
cubicOp20d,
quadOp16d,
cubicOp16d,
cubicTest7,
cubicTest6,
cubicTest5,
cubicTest4,
cubicOp13d,
cubicOp12d,
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cubicOp9d,
cubicOp8a,
cubicOp8,
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cubicOp7a,
cubicOp7,
cubicOp3de,
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cubicOp3d,
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cubic2x6x,
cubic2x7,
cubic2x7x,
cubic2x8,
cubic2x8x,
cubic2x9,
cubic2x9x,
cubic3x0,
cubic3x0x,
cubic3x1,
cubic3x1x,
cubic3x2,
cubic3x2x,
cubic3x3,
cubic3x3x,
cubic3x4,
cubic3x4x,
cubic3x5,
cubic3x5x,
cubic3x6,
cubic3x6x,
cubic3x7,
cubic3x7x,
cubic3x8,
cubic3x8x,
cubic3x9,
cubic3x9x,
cubic4x0,
cubic4x0x,
cubic4x1,
cubic4x1x,
cubic4x2,
cubic4x2x,
cubic4x3,
cubic4x3x,
cubic4x4,
cubic4x4x,
cubic4x5,
cubic4x5x,
cubic4x6,
cubic4x6x,
cubic4x7,
cubic4x7x,
cubic4x8,
cubic4x8x,
cubic4x9,
cubic4x9x,
cubic5x0,
cubic5x0x,
cubic5x1,
cubic5x1x,
cubic5x2,
cubic5x2x,
cubic5x3,
cubic5x3x,
cubic5x4,
cubic5x4x,
cubic5x5,
cubic5x5x,
cubic5x6,
cubic5x6x,
cubic5x7,
cubic5x7x,
cubic5x8,
cubic5x8x,
cubic5x9,
cubic5x9x,
cubic6x0,
cubic6x0x,
cubic6x1,
cubic6x1x,
cubic6x2,
cubic6x2x,
cubic6x3,
cubic6x3x,
cubic6x4,
cubic6x4x,
cubic6x5,
cubic6x5x,
cubic6x6,
cubic6x6x,
cubic6x7,
cubic6x7x,
cubic6x8,
cubic6x8x,
cubic6x9,
cubic6x9x,
cubic7x0,
cubic7x0x,
cubic7x1,
cubic7x1x,
cubic7x2,
cubic7x2x,
cubic7x3,
cubic7x3x,
cubic7x4,
cubic7x4x,
cubic7x5,
cubic7x5x,
cubic7x6,
cubic7x6x,
cubic7x7,
cubic7x7x,
cubic7x8,
cubic7x8x,
cubic7x9,
cubic7x9x,
cubic8x0,
cubic8x0x,
cubic8x1,
cubic8x1x,
cubic8x2,
cubic8x2x,
cubic8x3,
cubic8x3x,
cubic8x4,
cubic8x4x,
cubic8x5,
cubic8x5x,
cubic8x6,
cubic8x6x,
cubic8x7,
cubic8x7x,
cubic8x8,
cubic8x8x,
cubic8x9,
cubic8x9x,
cubic3,
cubic2,
cubic1,
];
var scale, columns, rows, xStart, yStart;
var ticks = 10;
var at_x = 13 + 0.5;
var at_y = 23 + 0.5;
var decimal_places = 3;
var tests = [];
var testTitles = [];
var testIndex = 0;
var ctx;
var minScale = 1;
var subscale = 1;
var curveT = -1;
var drawCubics = true;
var drawQuads = true;
var drawControlLines = true;
var drawTangents = false;
var drawGrid = true;
var xmin, xmax, ymin, ymax;
function parse(test, title) {
var curveStrs = test.split("{{");
if (curveStrs.length == 1)
curveStrs = test.split("=(");
var pattern = /[a-z$=]?-?\d+\.*\d*e?-?\d*/g;
var curves = [];
for (var c in curveStrs) {
var curveStr = curveStrs[c];
var points = curveStr.match(pattern);
var pts = [];
for (var wd in points) {
var num = parseFloat(points[wd]);
if (isNaN(num)) continue;
pts.push(num);
}
if (pts.length > 2)
curves.push(pts);
}
if (curves.length >= 1) {
tests.push(curves);
testTitles.push(title);
}
}
function init(test) {
var canvas = document.getElementById('canvas');
if (!canvas.getContext) return;
canvas.width = window.innerWidth - at_x;
canvas.height = window.innerHeight - at_y;
ctx = canvas.getContext('2d');
xmin = Infinity;
xmax = -Infinity;
ymin = Infinity;
ymax = -Infinity;
for (var curves in test) {
var curve = test[curves];
var last = curve.length;
for (var idx = 0; idx < last; idx += 2) {
xmin = Math.min(xmin, curve[idx]);
xmax = Math.max(xmax, curve[idx]);
ymin = Math.min(ymin, curve[idx + 1]);
ymax = Math.max(ymax, curve[idx + 1]);
}
}
var testW = xmax - xmin;
var testH = ymax - ymin;
subscale = 1;
while (testW * subscale < 0.1 && testH * subscale < 0.1) {
subscale *= 10;
}
while (testW * subscale > 10 && testH * subscale > 10) {
subscale /= 10;
}
calcFromScale();
}
function calcFromScale() {
xStart = Math.floor(xmin * subscale) / subscale;
yStart = Math.floor(ymin * subscale) / subscale;
var xEnd = Math.ceil(xmin * subscale) / subscale;
var yEnd = Math.ceil(ymin * subscale) / subscale;
var cCelsW = Math.floor(ctx.canvas.width / 10);
var cCelsH = Math.floor(ctx.canvas.height / 10);
var testW = xEnd - xStart;
var testH = yEnd - yStart;
var scaleWH = 1;
while (cCelsW > testW * scaleWH * 10 && cCelsH > testH * scaleWH * 10) {
scaleWH *= 10;
}
while (cCelsW * 10 < testW * scaleWH && cCelsH * 10 < testH * scaleWH) {
scaleWH /= 10;
}
columns = Math.ceil(xmax * subscale) - Math.floor(xmin * subscale) + 1;
rows = Math.ceil(ymax * subscale) - Math.floor(ymin * subscale) + 1;
var hscale = ctx.canvas.width / columns / ticks;
var vscale = ctx.canvas.height / rows / ticks;
minScale = Math.floor(Math.min(hscale, vscale));
scale = minScale * subscale;
}
function drawPoint(px, py, xoffset, yoffset, unit) {
var label = px.toFixed(decimal_places) + ", " + py.toFixed(decimal_places);
var _px = px * unit + xoffset;
var _py = py * unit + yoffset;
ctx.beginPath();
ctx.arc(_px, _py, 3, 0, Math.PI*2, true);
ctx.closePath();
ctx.fill();
ctx.fillText(label, _px + 5, _py);
}
function draw(test, title, scale) {
ctx.fillStyle = "rgba(0,0,0, 0.1)";
ctx.font = "normal 50px Arial";
ctx.fillText(title, 50, 50);
ctx.font = "normal 10px Arial";
var unit = scale * ticks;
ctx.lineWidth = 1;
if (drawGrid) {
var i;
for (i = 0; i <= rows * ticks; ++i) {
ctx.strokeStyle = (i % ticks) != 0 ? "rgb(200,200,200)" : "black";
ctx.beginPath();
ctx.moveTo(at_x + 0, at_y + i * minScale);
ctx.lineTo(at_x + ticks * columns * minScale, at_y + i * minScale);
ctx.stroke();
}
for (i = 0; i <= columns * ticks; ++i) {
ctx.strokeStyle = (i % ticks) != 0 ? "rgb(200,200,200)" : "black";
ctx.beginPath();
ctx.moveTo(at_x + i * minScale, at_y + 0);
ctx.lineTo(at_x + i * minScale, at_y + ticks * rows * minScale);
ctx.stroke();
}
}
var xoffset = xStart * -unit + at_x;
var yoffset = yStart * -unit + at_y;
ctx.fillStyle = "rgb(40,80,60)"
if (drawGrid) {
for (i = 0; i <= columns; i += 1)
{
num = xStart + i / subscale;
ctx.fillText(num.toFixed(decimal_places), xoffset + num * unit - 5, 10);
}
for (i = 0; i <= rows; i += 1)
{
num = yStart + i / subscale;
ctx.fillText(num.toFixed(decimal_places), 0, yoffset + num * unit + 0);
}
}
var curves, pts;
for (curves in test) {
var curve = test[curves];
if (curve.length == 6 && !drawQuads) {
continue;
}
if (curve.length == 8 && !drawCubics) {
continue;
}
ctx.beginPath();
ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit);
switch (curve.length) {
case 4:
ctx.lineTo(
xoffset + curve[2] * unit, yoffset + curve[3] * unit);
break;
case 6:
ctx.quadraticCurveTo(
xoffset + curve[2] * unit, yoffset + curve[3] * unit,
xoffset + curve[4] * unit, yoffset + curve[5] * unit);
break;
case 8:
ctx.bezierCurveTo(
xoffset + curve[2] * unit, yoffset + curve[3] * unit,
xoffset + curve[4] * unit, yoffset + curve[5] * unit,
xoffset + curve[6] * unit, yoffset + curve[7] * unit);
break;
}
ctx.strokeStyle = drawQuads && drawCubics && curve.length == 6 ? "red" : "black";
if (curve.length == 4) {
ctx.strokeStyle = "blue";
}
ctx.stroke();
if (drawControlLines && (curve.length == 6 || curve.length == 8)) {
ctx.strokeStyle = "rgba(0,0,0, 0.3)";
ctx.beginPath();
ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit);
ctx.lineTo(xoffset + curve[2] * unit, yoffset + curve[3] * unit);
ctx.lineTo(xoffset + curve[4] * unit, yoffset + curve[5] * unit);
if (curve.length == 8)
ctx.lineTo(xoffset + curve[6] * unit, yoffset + curve[7] * unit);
// ctx.lineTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit);
ctx.stroke();
}
if (curveT >= 0 && curveT <= 1) {
var x, y;
var t = curveT;
switch (curve.length) {
case 4:
var a = 1 - t;
var b = t;
x = a * curve[0] + b * curve[2];
y = a * curve[1] + b * curve[3];
break;
case 6:
var one_t = 1 - t;
var a = one_t * one_t;
var b = 2 * one_t * t;
var c = t * t;
x = a * curve[0] + b * curve[2] + c * curve[4];
y = a * curve[1] + b * curve[3] + c * curve[5];
break;
case 8:
var one_t = 1 - t;
var one_t2 = one_t * one_t;
var a = one_t2 * one_t;
var b = 3 * one_t2 * t;
var t2 = t * t;
var c = 3 * one_t * t2;
var d = t2 * t;
x = a * curve[0] + b * curve[2] + c * curve[4] + d * curve[6];
y = a * curve[1] + b * curve[3] + c * curve[5] + d * curve[7];
break;
}
drawPoint(x, y, xoffset, yoffset, unit);
var num = curveT.toFixed(decimal_places);
ctx.beginPath();
ctx.rect(200,10,200,10);
ctx.fillStyle="white";
ctx.fill();
ctx.fillStyle="black";
ctx.fillText(num, 230, 18);
if (drawTangents && curve.length == 8) {
var one_t = 1 - t;
var a = curve[0];
var b = curve[2];
var c = curve[4];
var d = curve[6];
var dx = (b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t;
a = curve[1];
b = curve[3];
c = curve[5];
d = curve[7];
var dy = (b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t;
ctx.beginPath();
ctx.moveTo(xoffset + (x - dx) * unit, yoffset + (y - dy) * unit);
ctx.lineTo(xoffset + (x + dx) * unit, yoffset + (y + dy) * unit);
ctx.stroke();
}
}
}
}
function drawTop() {
init(tests[testIndex]);
redraw();
}
function redraw() {
ctx.beginPath();
ctx.rect(0, 0, ctx.canvas.width, ctx.canvas.height);
ctx.fillStyle="white";
ctx.fill();
draw(tests[testIndex], testTitles[testIndex], scale);
}
function doKeyPress(evt) {
var char = String.fromCharCode(evt.charCode);
switch (char) {
case 'c':
drawCubics ^= true;
redraw();
break;
case 'd':
decimal_places++;
redraw();
break;
case 'D':
decimal_places--;
if (decimal_places < 1) {
decimal_places = 1;
}
redraw();
break;
case 'g':
drawGrid ^= true;
redraw();
break;
case 'l':
drawControlLines ^= true;
redraw();
break;
case 'N':
testIndex += 9;
case 'n':
if (++testIndex >= tests.length)
testIndex = 0;
mouseX = Infinity;
drawTop();
break;
case 'P':
testIndex -= 9;
case 'p':
if (--testIndex < 0)
testIndex = tests.length - 1;
mouseX = Infinity;
drawTop();
break;
case 'q':
drawQuads ^= true;
redraw();
break;
case 't':
drawTangents ^= true;
redraw();
break;
case 'x':
drawCubics ^= true;
drawQuads ^= true;
redraw();
break;
case '-':
case '_':
subscale /= 2;
calcFromScale();
redraw();
break;
case '+':
case '=':
subscale *= 2;
calcFromScale();
redraw();
break;
}
}
function handleMouseClick() {
var e = window.event;
var tgt = e.target || e.srcElement;
var min = tgt.offsetTop + Math.ceil(at_y);
var max = min + ticks * rows * minScale;
curveT = (e.clientY - min) / (max - min);
redraw();
}
function calcXY() {
var e = window.event;
var tgt = e.target || e.srcElement;
var left = tgt.offsetLeft;
var top = tgt.offsetTop;
var unit = scale * ticks;
mouseX = (e.clientX - left - Math.ceil(at_x) + 1) / unit + xStart;
mouseY = (e.clientY - top - Math.ceil(at_y)) / unit + yStart;
}
function handleMouseOver() {
calcXY();
var num = mouseX.toFixed(decimal_places) + ", " + mouseY.toFixed(decimal_places);
ctx.beginPath();
ctx.rect(30,10,200,10);
ctx.fillStyle="white";
ctx.fill();
ctx.fillStyle="black";
ctx.fillText(num, 30, 18);
}
function start() {
for (i = 0; i < testDivs.length; ++i) {
var title = testDivs[i].id.toString();
var str = testDivs[i].firstChild.data;
parse(str, title);
}
drawTop();
window.addEventListener('keypress', doKeyPress, true);
window.onresize = function() {
drawTop();
}
}
</script>
</head>
<body onLoad="start();">
<canvas id="canvas" width="750" height="500"
onmousemove="handleMouseOver()"
onclick="handleMouseClick()"
></canvas >
</body>
</html>