# CurveScattering

## JavaScript performance comparison

Revision 4 of this test case created by Timo

## Info

Test for adaptive cubic curve flattening to line segments. Comparing the performance if the curve is first splitted into parts on local extremes (peak points). Splitting ensures that sharp turns are taken into account despite of the angle tolerance.

## Preparation code

``<script>    function rnd(intfloat, Amin, Amax) {    var num;    if (intfloat == "float") num = Number((Amin + (Amax - Amin) * Math.random()).toFixed(2));    else if (intfloat == "int") num = Math.floor(Amin + (1 + Amax - Amin) * Math.random());    return num;}var randomdata=[], randomitem=[];for(var i = 0;i<20;i++){  var randomitem=[]; for(var j=0;j<8;j++) {   if (j%2) randomitem.push(rnd("float", 0, 300));   else randomitem.push(rnd("float", 0, 500)); }  randomdata.push(randomitem);}</script><script>  Benchmark.prototype.setup = function() {    var data1 = "[[442.5, 471.058, 941.5, 473.058, 439.5, 382.058, 938.5, 387.058], [462.465, 218.772, 709.4649999999999, 221.772, 207.46499999999997, 130.772, 706.4649999999999, 135.772], [225.962, 203.705, 472.962, 206.705, -20.03800000000001, 217.705, 469.962, 120.70500000000001], [550.723, 231.138, 797.723, 162.138, 304.72299999999996, 245.138, 794.723, 148.138], [181.5, 92.42, 454.5, 47.42, -38.5, 130.42000000000002, 380.5, 55.42], [370.463, 156.546, 585.463, 252.546, 150.46300000000002, 194.546, 569.463, 119.54599999999999], [43, 54.789, 447, 200.789, 12, 142.789, 431, 67.789], [47.024, 99.077, 133.024, 249.077, 16.024, 187.077, 435.024, 112.077], [47.024, 314.795, 308.024, 463.795, 16.024, 402.795, 435.024, 327.795], [35.524, 287.078, 417.524, 428.078, 4.524000000000001, 375.078, 423.524, 300.078], [490.46, 594.825, 895.461, 669.825, 482.46, 616.825, 901.461, 541.825], [31.5, 418.753, 480.5, 414.753, 23.5, 440.753, 442.5, 365.753], [164.963, 545.474, 613.963, 541.474, 164.963, 545.474, 575.963, 492.47400000000005], [53.428, 250.78, 502.428, 246.78, 53.428, 250.78, 274.428, 242.78], [43, 278, 572, 252, 43, 278, 210, 272], [370.5, 105.862, 722.5, 25.861999999999995, 370.5, 105.862, 537.5, 99.862], [971.224, 324.661, 442.22400000000005, 331.661, 448.22400000000005, 182.661, 959.224, 285.661], [427.432, 631.102, -123.56799999999998, 615.102, -95.56799999999998, 489.102, 426.432, 491.102], [925.238, 346.82, 383.23800000000006, 378.82, 402.23800000000006, 204.82, 924.238, 206.82], [670.44, 701.422, 290.4390000000001, 553.422, 147.43900000000008, 559.422, 669.44, 561.422], [387, 16, 8, 8, -135, 14, 387, 16], [971.225, 84.38, 454.225, 93.38, 449.225, 82.38, 971.225, 84.38], [934.433, 61.266, 469.433, 60.266, 412.433, 59.266, 934.433, 61.266], [596.926, 36.044, 1101.926, 19.043999999999997, 579.926, 18.043999999999997, 1101.926, 20.043999999999997], [43.001, 43.413, 564.001, 43.413, 42.001, 42.413, 564.001, 44.413], [176.562, 441.572, 621.562, 441.572, 99.56200000000001, 440.572, 621.562, 442.572], [473.461, 518.474, 845.461, 519.474, 396.461, 517.474, 918.461, 519.474], [120, 218.565, 492, 219.565, 43, 217.565, 43, 217.565], [540.374, 361.514, 737.373, 452.514, 463.374, 360.514, 463.374, 360.514], [295.096, 787.451, -255.904, 771.451, 220.63400000000001, 808.451, 294.096, 647.451], [575.963, 738.356, 24.962999999999965, 733.578, 501.5, 744.627, 574.963, 696.545], [984.133, 816.737, -1011.9099999999999, 814.358, 714.386, 819.858, 980.5110000000001, 795.9259999999999], [72.339, 997.32, 14.350000000000001, 532.965, 74.588, 1312.153, 71.339, 857.32], [134.01, 1080.529, 85.448, 635.0799999999999, 134.01, 1080.529, 134.01, 834.113], [209.03, 1080.529, 217.801, 677.5, 209.03, 1080.529, 209.03, 834.113], [253.381, 929.973, 511.852, 801.944, 127.381, 861.971, 469.381, 873.973], [228.475, 1031.471, 460.746, 901.328, 333.746, 864.395, 351.706, 1030.992], [380.937, 1013.3, 594.5, 881.5, 486.208, 846.2239999999999, 504.169, 1012.8209999999999], [527.277, 1018.205, 696.763, 889.674, 632.547, 851.129, 650.508, 1017.726], [65.748, 1131.666, 2202.867, 907.671, -276.252, 1119.664, 65.748, 1131.666], [65.748, 1152.166, 2202.867, 1088.051, -276.252, 1148.73, 65.748, 1152.166], [77.365, 1180.648, 2214.483, 1144.843, -264.635, 1178.729, 77.365, 1180.648], [25.539, 1245.147, 2162.657, 1209.341, 107.539, 1286.147, 15.403000000000002, 1204.442], [32.761, 1398.949, 322.954, 1416.346, 31.836, 1076.346, 32.761, 1398.949], [189.198, 1379.448, 1876.433, 1373.595, 163.256, 1138.817, 189.198, 1379.448], [59.681, 1442.1, 991.914, 1409.892, 1489.914, 1318.871, 59.681, 1442.1]]";    var data2 = "[[10, 15, 10, 15, 10, 15, 10, 15], [10, 20, 10, 20, 10, 20, 110, 20], [10, 25, 10, 25, 10, 25, 210, 25], [10, 30, 10, 30, 10, 30, 310, 30], [10, 35, 10, 35, 110, 35, 10, 35], [10, 40, 10, 40, 110, 40, 110, 40], [10, 45, 10, 45, 110, 45, 210, 45], [10, 50, 10, 50, 110, 50, 310, 50], [10, 55, 10, 55, 210, 55, 10, 55], [10, 60, 10, 60, 210, 60, 110, 60], [10, 65, 10, 65, 210, 65, 210, 65], [10, 70, 10, 70, 210, 70, 310, 70], [10, 75, 10, 75, 310, 75, 10, 75], [10, 80, 10, 80, 310, 80, 110, 80], [10, 85, 10, 85, 310, 85, 210, 85], [10, 90, 10, 90, 310, 90, 310, 90], [10, 95, 110, 95, 10, 95, 10, 95], [10, 100, 110, 100, 10, 100, 110, 100], [10, 105, 110, 105, 10, 105, 210, 105], [10, 110, 110, 110, 10, 110, 310, 110], [10, 115, 110, 115, 110, 115, 10, 115], [10, 120, 110, 120, 110, 120, 110, 120], [10, 125, 110, 125, 110, 125, 210, 125], [10, 130, 110, 130, 110, 130, 310, 130], [10, 135, 110, 135, 210, 135, 10, 135], [10, 140, 110, 140, 210, 140, 110, 140], [10, 145, 110, 145, 210, 145, 210, 145], [10, 150, 110, 150, 210, 150, 310, 150], [10, 155, 110, 155, 310, 155, 10, 155], [10, 160, 110, 160, 310, 160, 110, 160], [10, 165, 110, 165, 310, 165, 210, 165], [10, 170, 110, 170, 310, 170, 310, 170], [10, 175, 210, 175, 10, 175, 10, 175], [10, 180, 210, 180, 10, 180, 110, 180], [10, 185, 210, 185, 10, 185, 210, 185], [10, 190, 210, 190, 10, 190, 310, 190], [10, 195, 210, 195, 110, 195, 10, 195], [10, 200, 210, 200, 110, 200, 110, 200], [10, 205, 210, 205, 110, 205, 210, 205], [10, 210, 210, 210, 110, 210, 310, 210], [10, 215, 210, 215, 210, 215, 10, 215], [10, 220, 210, 220, 210, 220, 110, 220], [10, 225, 210, 225, 210, 225, 210, 225], [10, 230, 210, 230, 210, 230, 310, 230], [10, 235, 210, 235, 310, 235, 10, 235], [10, 240, 210, 240, 310, 240, 110, 240], [10, 245, 210, 245, 310, 245, 210, 245], [10, 250, 210, 250, 310, 250, 310, 250], [10, 255, 310, 255, 10, 255, 10, 255], [10, 260, 310, 260, 10, 260, 110, 260], [10, 265, 310, 265, 10, 265, 210, 265], [10, 270, 310, 270, 10, 270, 310, 270], [10, 275, 310, 275, 110, 275, 10, 275], [10, 280, 310, 280, 110, 280, 110, 280], [10, 285, 310, 285, 110, 285, 210, 285], [10, 290, 310, 290, 110, 290, 310, 290], [10, 295, 310, 295, 210, 295, 10, 295], [10, 300, 310, 300, 210, 300, 110, 300], [10, 305, 310, 305, 210, 305, 210, 305], [10, 310, 310, 310, 210, 310, 310, 310], [10, 315, 310, 315, 310, 315, 10, 315], [10, 320, 310, 320, 310, 320, 110, 320], [10, 325, 310, 325, 310, 325, 210, 325], [10, 330, 310, 330, 310, 330, 310, 330], [110, 335, 10, 335, 10, 335, 10, 335], [110, 340, 10, 340, 10, 340, 110, 340], [110, 345, 10, 345, 10, 345, 210, 345], [110, 350, 10, 350, 10, 350, 310, 350], [110, 355, 10, 355, 110, 355, 10, 355], [110, 360, 10, 360, 110, 360, 110, 360], [110, 365, 10, 365, 110, 365, 210, 365], [110, 370, 10, 370, 110, 370, 310, 370], [110, 375, 10, 375, 210, 375, 10, 375], [110, 380, 10, 380, 210, 380, 110, 380], [110, 385, 10, 385, 210, 385, 210, 385], [110, 390, 10, 390, 210, 390, 310, 390], [110, 395, 10, 395, 310, 395, 10, 395], [110, 400, 10, 400, 310, 400, 110, 400], [110, 405, 10, 405, 310, 405, 210, 405], [110, 410, 10, 410, 310, 410, 310, 410], [110, 415, 110, 415, 10, 415, 10, 415], [110, 420, 110, 420, 10, 420, 110, 420], [110, 425, 110, 425, 10, 425, 210, 425], [110, 430, 110, 430, 10, 430, 310, 430], [110, 435, 110, 435, 110, 435, 10, 435], [110, 440, 110, 440, 110, 440, 110, 440], [110, 445, 110, 445, 110, 445, 210, 445], [110, 450, 110, 450, 110, 450, 310, 450], [110, 455, 110, 455, 210, 455, 10, 455], [110, 460, 110, 460, 210, 460, 110, 460], [110, 465, 110, 465, 210, 465, 210, 465], [110, 470, 110, 470, 210, 470, 310, 470], [110, 475, 110, 475, 310, 475, 10, 475], [110, 480, 110, 480, 310, 480, 110, 480], [110, 485, 110, 485, 310, 485, 210, 485], [110, 490, 110, 490, 310, 490, 310, 490], [110, 495, 210, 495, 10, 495, 10, 495], [110, 500, 210, 500, 10, 500, 110, 500], [110, 505, 210, 505, 10, 505, 210, 505], [110, 510, 210, 510, 10, 510, 310, 510], [110, 515, 210, 515, 110, 515, 10, 515], [110, 520, 210, 520, 110, 520, 110, 520], [110, 525, 210, 525, 110, 525, 210, 525], [110, 530, 210, 530, 110, 530, 310, 530], [110, 535, 210, 535, 210, 535, 10, 535], [110, 540, 210, 540, 210, 540, 110, 540], [110, 545, 210, 545, 210, 545, 210, 545], [110, 550, 210, 550, 210, 550, 310, 550], [110, 555, 210, 555, 310, 555, 10, 555], [110, 560, 210, 560, 310, 560, 110, 560], [110, 565, 210, 565, 310, 565, 210, 565], [110, 570, 210, 570, 310, 570, 310, 570], [110, 575, 310, 575, 10, 575, 10, 575], [110, 580, 310, 580, 10, 580, 110, 580], [110, 585, 310, 585, 10, 585, 210, 585], [110, 590, 310, 590, 10, 590, 310, 590], [110, 595, 310, 595, 110, 595, 10, 595], [110, 600, 310, 600, 110, 600, 110, 600], [110, 605, 310, 605, 110, 605, 210, 605], [110, 610, 310, 610, 110, 610, 310, 610], [110, 615, 310, 615, 210, 615, 10, 615], [110, 620, 310, 620, 210, 620, 110, 620], [110, 625, 310, 625, 210, 625, 210, 625], [110, 630, 310, 630, 210, 630, 310, 630], [110, 635, 310, 635, 310, 635, 10, 635], [110, 640, 310, 640, 310, 640, 110, 640], [110, 645, 310, 645, 310, 645, 210, 645], [110, 650, 310, 650, 310, 650, 310, 650], [210, 655, 10, 655, 10, 655, 10, 655], [210, 660, 10, 660, 10, 660, 110, 660], [210, 665, 10, 665, 10, 665, 210, 665], [210, 670, 10, 670, 10, 670, 310, 670], [210, 675, 10, 675, 110, 675, 10, 675], [210, 680, 10, 680, 110, 680, 110, 680], [210, 685, 10, 685, 110, 685, 210, 685], [210, 690, 10, 690, 110, 690, 310, 690], [210, 695, 10, 695, 210, 695, 10, 695], [210, 700, 10, 700, 210, 700, 110, 700], [210, 705, 10, 705, 210, 705, 210, 705], [210, 710, 10, 710, 210, 710, 310, 710], [210, 715, 10, 715, 310, 715, 10, 715], [210, 720, 10, 720, 310, 720, 110, 720], [210, 725, 10, 725, 310, 725, 210, 725], [210, 730, 10, 730, 310, 730, 310, 730], [210, 735, 110, 735, 10, 735, 10, 735], [210, 740, 110, 740, 10, 740, 110, 740], [210, 745, 110, 745, 10, 745, 210, 745], [210, 750, 110, 750, 10, 750, 310, 750], [210, 755, 110, 755, 110, 755, 10, 755], [210, 760, 110, 760, 110, 760, 110, 760], [210, 765, 110, 765, 110, 765, 210, 765], [210, 770, 110, 770, 110, 770, 310, 770], [210, 775, 110, 775, 210, 775, 10, 775], [210, 780, 110, 780, 210, 780, 110, 780], [210, 785, 110, 785, 210, 785, 210, 785], [210, 790, 110, 790, 210, 790, 310, 790], [210, 795, 110, 795, 310, 795, 10, 795], [210, 800, 110, 800, 310, 800, 110, 800], [210, 805, 110, 805, 310, 805, 210, 805], [210, 810, 110, 810, 310, 810, 310, 810], [210, 815, 210, 815, 10, 815, 10, 815], [210, 820, 210, 820, 10, 820, 110, 820], [210, 825, 210, 825, 10, 825, 210, 825], [210, 830, 210, 830, 10, 830, 310, 830], [210, 835, 210, 835, 110, 835, 10, 835], [210, 840, 210, 840, 110, 840, 110, 840], [210, 845, 210, 845, 110, 845, 210, 845], [210, 850, 210, 850, 110, 850, 310, 850], [210, 855, 210, 855, 210, 855, 10, 855], [210, 860, 210, 860, 210, 860, 110, 860], [210, 865, 210, 865, 210, 865, 210, 865], [210, 870, 210, 870, 210, 870, 310, 870], [210, 875, 210, 875, 310, 875, 10, 875], [210, 880, 210, 880, 310, 880, 110, 880], [210, 885, 210, 885, 310, 885, 210, 885], [210, 890, 210, 890, 310, 890, 310, 890], [210, 895, 310, 895, 10, 895, 10, 895], [210, 900, 310, 900, 10, 900, 110, 900], [210, 905, 310, 905, 10, 905, 210, 905], [210, 910, 310, 910, 10, 910, 310, 910], [210, 915, 310, 915, 110, 915, 10, 915], [210, 920, 310, 920, 110, 920, 110, 920], [210, 925, 310, 925, 110, 925, 210, 925], [210, 930, 310, 930, 110, 930, 310, 930], [210, 935, 310, 935, 210, 935, 10, 935], [210, 940, 310, 940, 210, 940, 110, 940], [210, 945, 310, 945, 210, 945, 210, 945], [210, 950, 310, 950, 210, 950, 310, 950], [210, 955, 310, 955, 310, 955, 10, 955], [210, 960, 310, 960, 310, 960, 110, 960], [210, 965, 310, 965, 310, 965, 210, 965], [210, 970, 310, 970, 310, 970, 310, 970], [310, 975, 10, 975, 10, 975, 10, 975], [310, 980, 10, 980, 10, 980, 110, 980], [310, 985, 10, 985, 10, 985, 210, 985], [310, 990, 10, 990, 10, 990, 310, 990], [310, 995, 10, 995, 110, 995, 10, 995], [310, 1000, 10, 1000, 110, 1000, 110, 1000], [310, 1005, 10, 1005, 110, 1005, 210, 1005], [310, 1010, 10, 1010, 110, 1010, 310, 1010], [310, 1015, 10, 1015, 210, 1015, 10, 1015], [310, 1020, 10, 1020, 210, 1020, 110, 1020], [310, 1025, 10, 1025, 210, 1025, 210, 1025], [310, 1030, 10, 1030, 210, 1030, 310, 1030], [310, 1035, 10, 1035, 310, 1035, 10, 1035], [310, 1040, 10, 1040, 310, 1040, 110, 1040], [310, 1045, 10, 1045, 310, 1045, 210, 1045], [310, 1050, 10, 1050, 310, 1050, 310, 1050], [310, 1055, 110, 1055, 10, 1055, 10, 1055], [310, 1060, 110, 1060, 10, 1060, 110, 1060], [310, 1065, 110, 1065, 10, 1065, 210, 1065], [310, 1070, 110, 1070, 10, 1070, 310, 1070], [310, 1075, 110, 1075, 110, 1075, 10, 1075], [310, 1080, 110, 1080, 110, 1080, 110, 1080], [310, 1085, 110, 1085, 110, 1085, 210, 1085], [310, 1090, 110, 1090, 110, 1090, 310, 1090], [310, 1095, 110, 1095, 210, 1095, 10, 1095], [310, 1100, 110, 1100, 210, 1100, 110, 1100], [310, 1105, 110, 1105, 210, 1105, 210, 1105], [310, 1110, 110, 1110, 210, 1110, 310, 1110], [310, 1115, 110, 1115, 310, 1115, 10, 1115], [310, 1120, 110, 1120, 310, 1120, 110, 1120], [310, 1125, 110, 1125, 310, 1125, 210, 1125], [310, 1130, 110, 1130, 310, 1130, 310, 1130], [310, 1135, 210, 1135, 10, 1135, 10, 1135], [310, 1140, 210, 1140, 10, 1140, 110, 1140], [310, 1145, 210, 1145, 10, 1145, 210, 1145], [310, 1150, 210, 1150, 10, 1150, 310, 1150], [310, 1155, 210, 1155, 110, 1155, 10, 1155], [310, 1160, 210, 1160, 110, 1160, 110, 1160], [310, 1165, 210, 1165, 110, 1165, 210, 1165], [310, 1170, 210, 1170, 110, 1170, 310, 1170], [310, 1175, 210, 1175, 210, 1175, 10, 1175], [310, 1180, 210, 1180, 210, 1180, 110, 1180], [310, 1185, 210, 1185, 210, 1185, 210, 1185], [310, 1190, 210, 1190, 210, 1190, 310, 1190], [310, 1195, 210, 1195, 310, 1195, 10, 1195], [310, 1200, 210, 1200, 310, 1200, 110, 1200], [310, 1205, 210, 1205, 310, 1205, 210, 1205], [310, 1210, 210, 1210, 310, 1210, 310, 1210], [310, 1215, 310, 1215, 10, 1215, 10, 1215], [310, 1220, 310, 1220, 10, 1220, 110, 1220], [310, 1225, 310, 1225, 10, 1225, 210, 1225], [310, 1230, 310, 1230, 10, 1230, 310, 1230], [310, 1235, 310, 1235, 110, 1235, 10, 1235], [310, 1240, 310, 1240, 110, 1240, 110, 1240], [310, 1245, 310, 1245, 110, 1245, 210, 1245], [310, 1250, 310, 1250, 110, 1250, 310, 1250], [310, 1255, 310, 1255, 210, 1255, 10, 1255], [310, 1260, 310, 1260, 210, 1260, 110, 1260], [310, 1265, 310, 1265, 210, 1265, 210, 1265], [310, 1270, 310, 1270, 210, 1270, 310, 1270], [310, 1275, 310, 1275, 310, 1275, 10, 1275], [310, 1280, 310, 1280, 310, 1280, 110, 1280], [310, 1285, 310, 1285, 310, 1285, 210, 1285], [310, 1290, 310, 1290, 310, 1290, 310, 1290]]";    var data3 = "[[495.415283203125, 81.71070098877, 495.415283203125, 81.71070098877, 495.415283203125, 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1182.602783203125, 409.011291503906, 1147.882690429688, 409.011291503906, 1147.882690429688, 409.011291503906, 1147.882690429688], [605.103271484375, 1187.526733398438, 408.143280029297, 1152.806762695313, 408.143280029297, 1152.806762695313, 506.623291015625, 1170.166748046875], [604.235290527344, 1192.450805664063, 407.275268554688, 1157.730712890625, 407.275268554688, 1157.730712890625, 604.235290527344, 1192.450805664063], [603.367309570313, 1197.374755859375, 406.407287597656, 1162.65478515625, 504.887298583984, 1180.014770507813, 307.927276611328, 1145.294799804688], [602.499267578125, 1202.298706054688, 405.539276123047, 1167.578735351563, 504.019287109375, 1184.938720703125, 405.539276123047, 1167.578735351563], [601.631286621094, 1207.222778320313, 404.671264648438, 1172.502685546875, 503.151275634766, 1189.86279296875, 503.151275634766, 1189.86279296875], [600.763305664063, 1212.146728515625, 403.803283691406, 1177.4267578125, 502.283294677734, 1194.786743164063, 600.763305664063, 1212.146728515625], [599.895263671875, 1217.07080078125, 402.935272216797, 1182.350708007813, 599.895263671875, 1217.07080078125, 304.455261230469, 1164.99072265625], [599.027282714844, 1221.994750976563, 402.067291259766, 1187.274780273438, 599.027282714844, 1221.994750976563, 402.067291259766, 1187.274780273438], [598.159301757813, 1226.918701171875, 401.199279785156, 1192.19873046875, 598.159301757813, 1226.918701171875, 499.679290771484, 1209.558715820313], [597.291259765625, 1231.8427734375, 400.331268310547, 1197.122802734375, 597.291259765625, 1231.8427734375, 597.291259765625, 1231.8427734375], [596.423278808594, 1236.766723632813, 497.943298339844, 1219.40673828125, 300.983276367188, 1184.686767578125, 300.983276367188, 1184.686767578125], [595.555297851563, 1241.690795898438, 497.075286865234, 1224.330688476563, 300.115264892578, 1189.610717773438, 398.595275878906, 1206.970703125], [594.687316894531, 1246.61474609375, 496.207275390625, 1229.254760742188, 299.247283935547, 1194.534790039063, 496.207275390625, 1229.254760742188], [593.819274902344, 1251.538696289063, 495.339294433594, 1234.1787109375, 298.379272460938, 1199.458740234375, 593.819274902344, 1251.538696289063], [592.951293945313, 1256.462768554688, 494.471282958984, 1239.102783203125, 395.991271972656, 1221.742797851563, 297.511260986328, 1204.382690429688], [592.083312988281, 1261.38671875, 493.603271484375, 1244.026733398438, 395.123291015625, 1226.666748046875, 395.123291015625, 1226.666748046875], [591.215270996094, 1266.310791015625, 492.735290527344, 1248.950805664063, 394.255279541016, 1231.590698242188, 492.735290527344, 1248.950805664063], [590.347290039063, 1271.234741210938, 491.867279052734, 1253.874755859375, 393.387268066406, 1236.514770507813, 590.347290039063, 1271.234741210938], [589.479309082031, 1276.15869140625, 490.999267578125, 1258.798706054688, 490.999267578125, 1258.798706054688, 294.039276123047, 1224.078735351563], [588.611267089844, 1281.082763671875, 490.131286621094, 1263.722778320313, 490.131286621094, 1263.722778320313, 391.651275634766, 1246.36279296875], [587.743286132813, 1286.006713867188, 489.263275146484, 1268.646728515625, 489.263275146484, 1268.646728515625, 489.263275146484, 1268.646728515625], [586.875305175781, 1290.930786132813, 488.395294189453, 1273.57080078125, 488.395294189453, 1273.57080078125, 586.875305175781, 1290.930786132813], [586.007263183594, 1295.854736328125, 487.527282714844, 1278.494750976563, 586.007263183594, 1295.854736328125, 290.567260742188, 1243.774780273438], [585.139282226563, 1300.77880859375, 486.659271240234, 1283.418701171875, 585.139282226563, 1300.77880859375, 388.179290771484, 1266.058715820313], [584.271301269531, 1305.702758789063, 485.791290283203, 1288.3427734375, 584.271301269531, 1305.702758789063, 485.791290283203, 1288.3427734375], [583.403259277344, 1310.626708984375, 484.923278808594, 1293.266723632813, 583.403259277344, 1310.626708984375, 583.403259277344, 1310.626708984375], [582.535278320313, 1315.55078125, 582.535278320313, 1315.55078125, 287.095275878906, 1263.470703125, 287.095275878906, 1263.470703125], [581.667297363281, 1320.474731445313, 581.667297363281, 1320.474731445313, 286.227264404297, 1268.394775390625, 384.707275390625, 1285.754760742188], [580.799255371094, 1325.398803710938, 580.799255371094, 1325.398803710938, 285.359283447266, 1273.318725585938, 482.319274902344, 1308.038696289063], [579.931274414063, 1330.32275390625, 579.931274414063, 1330.32275390625, 284.491271972656, 1278.242797851563, 579.931274414063, 1330.32275390625], [579.063293457031, 1335.246704101563, 579.063293457031, 1335.246704101563, 382.103271484375, 1300.526733398438, 283.623260498047, 1283.166748046875], [578.1953125, 1340.170776367188, 578.1953125, 1340.170776367188, 381.235290527344, 1305.450805664063, 381.235290527344, 1305.450805664063], [577.327270507813, 1345.0947265625, 577.327270507813, 1345.0947265625, 380.367279052734, 1310.374755859375, 478.847290039063, 1327.734741210938], [576.459289550781, 1350.018798828125, 576.459289550781, 1350.018798828125, 379.499267578125, 1315.298706054688, 576.459289550781, 1350.018798828125], [575.59130859375, 1354.942749023438, 575.59130859375, 1354.942749023438, 477.111267089844, 1337.582763671875, 280.151275634766, 1302.86279296875], [574.723266601563, 1359.86669921875, 574.723266601563, 1359.86669921875, 476.243286132813, 1342.506713867188, 377.763275146484, 1325.146728515625], [573.855285644531, 1364.790771484375, 573.855285644531, 1364.790771484375, 475.375274658203, 1347.430786132813, 475.375274658203, 1347.430786132813], [572.9873046875, 1369.714721679688, 572.9873046875, 1369.714721679688, 474.507293701172, 1352.354736328125, 572.9873046875, 1369.714721679688], [572.119262695313, 1374.638793945313, 572.119262695313, 1374.638793945313, 572.119262695313, 1374.638793945313, 276.679260253906, 1322.558715820313], [571.251281738281, 1379.562744140625, 571.251281738281, 1379.562744140625, 571.251281738281, 1379.562744140625, 374.291290283203, 1344.8427734375], [570.38330078125, 1384.48681640625, 570.38330078125, 1384.48681640625, 570.38330078125, 1384.48681640625, 471.903289794922, 1367.126708984375], [569.515258789063, 1389.410766601563, 569.515258789063, 1389.410766601563, 569.515258789063, 1389.410766601563, 569.515258789063, 1389.410766601563]]";         data1=JSON.parse(data1);    data2=JSON.parse(data2);    data3=JSON.parse(data3);    if (typeof(randomdata)!="undefined" && typeof(randomdata[0])!="undefined") data4=randomdata;    else alert("randomdata not exists");        var CPoint = function() {      var arg = arguments;      if(arg.length == 1) {        this.X = arg[0].X;        this.Y = arg[0].Y      }else {        if(arg.length == 2) {          this.X = arg[0];          this.Y = arg[1]        }      }    };        function Subdivide(x1, y1, x2, y2, x3, y3, x4, y4, t)    {      var p1pX = x1 + (x2 - x1) * t;          p1pY = y1 + (y2 - y1) * t,          p2pX = x2 + (x3 - x2) * t,          p2pY = y2 + (y3 - y2) * t,          p3pX = x3 + (x4 - x3) * t,          p3pY = y3 + (y4 - y3) * t,          p1dX = p1pX + (p2pX - p1pX) * t,          p1dY = p1pY + (p2pY - p1pY) * t,          p2dX = p2pX + (p3pX - p2pX) * t,          p2dY = p2pY + (p3pY - p2pY) * t,          p1tX = p1dX + (p2dX - p1dX) * t,          p1tY = p1dY + (p2dY - p1dY) * t;      return [[x1, y1, p1pX, p1pY, p1dX, p1dY, p1tX, p1tY],              [p1tX, p1tY, p2dX, p2dY, p3pX, p3pY, x4, y4]];    }        function find_Inflection_Points(p1x,p1y,p2x,p2y,p3x,p3y,p4x,p4y)    {      var ax = -p1x + 3*p2x - 3*p3x + p4x;      var bx = 3*p1x - 6*p2x + 3*p3x;      var cx = -3*p1x + 3*p2x;          var ay = -p1y + 3*p2y - 3*p3y + p4y;      var by = 3*p1y - 6*p2y + 3*p3y;      var cy = -3*p1y + 3*p2y;      var a = 3*(ay*bx-ax*by);      var b = 3*(ay*cx-ax*cy);      var c = by*cx-bx*cy;      var r2 = b*b - 4*a*c;      var firstIfp = 0;      var secondIfp = 0;      if (r2>=0 && a!==0)      {        var r = Math.sqrt(r2);        firstIfp = (-b + r) / (2*a);        secondIfp = (-b - r) / (2*a);        if ((firstIfp>0 && firstIfp<1) && (secondIfp>0 && secondIfp<1))        {          if (firstIfp>secondIfp)          {            var tmp = firstIfp;            firstIfp = secondIfp;            secondIfp = tmp;          }          if (secondIfp-firstIfp >0.00001)            return [firstIfp, secondIfp];          else return [firstIfp];        }        else if (firstIfp>0 && firstIfp<1)          return [firstIfp];        else if (secondIfp>0 && secondIfp<1)        {          firstIfp = secondIfp;          return [firstIfp];        }        return [];      }      else return [];    };        var CPoint2 = function(x, y)    {        this.X = x;        this.Y = y;    };          function compare_num(a,b) {      return a < b ? -1 : a > b ? 1 : 0;    }        var get_t_values_of_extremes = function (p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {      var tvalues=[],      a = (c2x - 2 * c1x + p1x) - (p2x - 2 * c2x + c1x),      b = 2 * (c1x - p1x) - 2 * (c2x - c1x),      sqrt1 = Math.sqrt(b * b - 4 * a * (p1x - c1x)),      t1 = (-b + sqrt1) / 2 / a,      t2 = (-b - sqrt1) / 2 / a;      Math.abs(t1) > "1e12" && (t1 = 0.5);      Math.abs(t2) > "1e12" && (t2 = 0.5);      if (t1 > 0 && t1 < 1) tvalues.push(t1);      if (t2 > 0 && t2 < 1 && t2!==t1) tvalues.push(t2);              a = (c2y - 2 * c1y + p1y) - (p2y - 2 * c2y + c1y);      b = 2 * (c1y - p1y) - 2 * (c2y - c1y);      sqrt1 = Math.sqrt(b * b - 4 * a * (p1y - c1y));      var t3 = (-b + sqrt1) / 2 / a;      var t4 = (-b - sqrt1) / 2 / a;      Math.abs(t3) > "1e12" && (t3 = 0.5);      Math.abs(t4) > "1e12" && (t4 = 0.5);      if (t3 > 0 && t3 < 1 && t3!==t1 && t3!==t2) tvalues.push(t3);      if (t4 > 0 && t4 < 1 && t4!==t1 && t4!==t2 && t4!==t3) tvalues.push(t4);      /*      var inflectionpoints = find_Inflection_Points(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);      if (inflectionpoints[0]) tvalues.push(inflectionpoints[0]);      if (inflectionpoints[1]) tvalues.push(inflectionpoints[1]);      console.log(inflectionpoints[0],inflectionpoints[1]);      */       tvalues.sort(compare_num);      return tvalues;    };            var approximate = function(x1, y1, x2, y2, x3, y3, x4, y4, m_approximation_scale, m_angle_tolerance, split, angle)    {      if (typeof(m_approximation_scale) == "undefined") m_approximation_scale = 1;      if (typeof(m_angle_tolerance) == "undefined") m_angle_tolerance = 179;            var m_cusp_limit = 0;            var pi =    3.141592653589793;      var pi2 =   6.283185307179586;      var pi180 = 0.017453292519943; // pi/180;            var m_points = [];            var m_angle_tolerance = m_angle_tolerance * pi180;      var m_cusp_limit = m_cusp_limit * pi180;            var m_distance_tolerance_square = 0.5 / m_approximation_scale;      m_distance_tolerance_square *= m_distance_tolerance_square;                  var curve_distance_epsilon                  = 1e-12; // 1e-30      var curve_collinearity_epsilon              = 1e-12; // 1e-30      var curve_angle_tolerance_epsilon           = 0.01;      var curve_recursion_limit = 32;          if (m_cusp_limit !== 0) m_cusp_limit = pi - m_cusp_limit;      var atan_calc=0;         if (split)     {       var args = [x1, y1, x2, y2, x3, y3, x4, y4];       var tvalues = get_t_values_of_extremes(x1, y1, x2, y2, x3, y3, x4, y4);       var parts = [], part2 = [], t, i, part = args, pl;       if (tvalues.length==0) parts.push(args);       else       {         pl = tvalues.length;         for(i = 0; i < pl; i++)         {           t = !i ? tvalues[i] : (tvalues[i]-tvalues[i-1])/(1-tvalues[i-1]);           part2 = Subdivide(part[0], part[1], part[2], part[3], part[4], part[5], part[6], part[7], t);           parts.push(part2[0]);           part = part2[1].slice(0);         }         parts.push(part2[1]);       }       pl = parts.length;       for(i = 0; i < pl; i++)       {         m_points.push(new CPoint2(parts[i][0], parts[i][1]));         recursive_bezier(parts[i][0], parts[i][1], parts[i][2], parts[i][3], parts[i][4], parts[i][5], parts[i][6], parts[i][7], 0);       }       pl--;       m_points.push(new CPoint2(parts[pl][6], parts[pl][7]));      }      else // original behaviour      {          m_points.push(new CPoint2(x1, y1));          recursive_bezier(x1, y1, x2, y2, x3, y3, x4, y4, 0);          m_points.push(new CPoint2(x4, y4));        }            if (typeof(parts)=="undefined") return [m_points, atan_calc, [], []];      else return [m_points, atan_calc, parts, tvalues];          function calc_sq_distance(x1, y1, x2, y2)      {        var dx = x2-x1;        var dy = y2-y1;        return dx * dx + dy * dy;      }          function recursive_bezier(x1, y1, x2, y2, x3, y3, x4, y4, level)      {            if(level > curve_recursion_limit)         {          return;        }            // Calculate all the mid-points of the line segments        //----------------------        var x12   = (x1 + x2) / 2;        var y12   = (y1 + y2) / 2;        var x23   = (x2 + x3) / 2;        var y23   = (y2 + y3) / 2;        var x34   = (x3 + x4) / 2;        var y34   = (y3 + y4) / 2;        var x123  = (x12 + x23) / 2;        var y123  = (y12 + y23) / 2;        var x234  = (x23 + x34) / 2;        var y234  = (y23 + y34) / 2;        var x1234 = (x123 + x234) / 2;        var y1234 = (y123 + y234) / 2;                // Try to approximate the full cubic curve by a single straight line            //------------------            var dx = x4-x1;            var dy = y4-y1;                var d2 = Math.abs(((x2 - x4) * dy - (y2 - y4) * dx));            var d3 = Math.abs(((x3 - x4) * dy - (y3 - y4) * dx));            var da1, da2, k;                        var d2d3 = ( ( d2 > curve_collinearity_epsilon?1:0) << 1 ) +                        (d3 > curve_collinearity_epsilon?1:0);                        switch( d2d3)            {            case 0:                // All collinear OR p1==p4                //----------------------                k = dx*dx + dy*dy;                if(k == 0)                {                    d2 = calc_sq_distance(x1, y1, x2, y2);                    d3 = calc_sq_distance(x4, y4, x3, y3);                }                else                {                    k   = 1 / k;                    da1 = x2 - x1;                    da2 = y2 - y1;                    d2  = k * (da1*dx + da2*dy);                    da1 = x3 - x1;                    da2 = y3 - y1;                    d3  = k * (da1*dx + da2*dy);                    if(d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1)                    {                        // Simple collinear case, 1---2---3---4                        // We can leave just two endpoints                        return;                    }                         if(d2 <= 0) d2 = calc_sq_distance(x2, y2, x1, y1);                    else if(d2 >= 1) d2 = calc_sq_distance(x2, y2, x4, y4);                    else             d2 = calc_sq_distance(x2, y2, x1 + d2*dx, y1 + d2*dy);                             if(d3 <= 0) d3 = calc_sq_distance(x3, y3, x1, y1);                    else if(d3 >= 1) d3 = calc_sq_distance(x3, y3, x4, y4);                    else             d3 = calc_sq_distance(x3, y3, x1 + d3*dx, y1 + d3*dy);                }                if(d2 > d3)                {                    if(d2 < m_distance_tolerance_square)                    {                        m_points.push(new CPoint2(x2, y2));                        return;                    }                }                else                {                    if(d3 < m_distance_tolerance_square)                    {                        m_points.push(new CPoint2(x3, y3));                        return;                    }                }                break;                case 1:                // p1,p2,p4 are collinear, p3 is significant                //----------------------                if(d3 * d3 <= m_distance_tolerance_square * (dx*dx + dy*dy))                {                    if(m_angle_tolerance < curve_angle_tolerance_epsilon)                    {                        m_points.push(new CPoint2(x23, y23));                        return;                    }                        // Angle Condition                    //----------------------                    da1 = Math.abs(Math.atan2(y4 - y3, x4 - x3) - Math.atan2(y3 - y2, x3 - x2));    atan_calc++;                    if(da1 >= pi) da1 = pi2 - da1;                        if(da1 < m_angle_tolerance)                    {                        m_points.push(new CPoint2(x2, y2));                        m_points.push(new CPoint2(x3, y3));                        return;                    }                        if(m_cusp_limit != 0.0)                    {                        if(da1 > m_cusp_limit)                        {                            m_points.push(new CPoint2(x3, y3));                            return;                        }                    }                }                break;                case 2:                // p1,p3,p4 are collinear, p2 is significant                //----------------------                if(d2 * d2 <= m_distance_tolerance_square * (dx*dx + dy*dy))                {                    if(m_angle_tolerance < curve_angle_tolerance_epsilon)                    {                        m_points.push(new CPoint2(x23, y23));                        return;                    }                        // Angle Condition                    //----------------------                    da1 = Math.abs(Math.atan2(y3 - y2, x3 - x2) - Math.atan2(y2 - y1, x2 - x1));    atan_calc++;                    if(da1 >= pi) da1 = pi2 - da1;                        if(da1 < m_angle_tolerance)                    {                        m_points.push(new CPoint2(x2, y2));                        m_points.push(new CPoint2(x3, y3));                        return;                    }                        if(m_cusp_limit != 0.0)                    {                        if(da1 > m_cusp_limit)                        {                            m_points.push(new CPoint2(x2, y2));                            return;                        }                    }                }                break;                case 3:                 // Regular case                //-----------------                    if (angle) {      var max_d = d2>d3? d2:d3;      var measure = max_d*max_d*0.75;    }    else measure = (d2 + d3)*(d2 + d3);                if(measure <= m_distance_tolerance_square * (dx*dx + dy*dy))                {                    // If the curvature doesn't exceed the distance_tolerance value                    // we tend to finish subdivisions.                    //----------------------                    if(m_angle_tolerance < curve_angle_tolerance_epsilon)                    {                        m_points.push(new CPoint2(x23, y23));                        return;                    }                        // Angle & Cusp Condition                    //----------------------                  if (!split)                  {                    if (!angle)    {                    k   = Math.atan2(y3 - y2, x3 - x2);                    da1 = Math.abs(k - Math.atan2(y2 - y1, x2 - x1));                    da2 = Math.abs(Math.atan2(y4 - y3, x4 - x3) - k);    atan_calc++;                    if(da1 >= pi) da1 = pi2 - da1;                    if(da2 >= pi) da2 = pi2 - da2;                                      if(da1 + da2 < m_angle_tolerance)                    {                        // Finally we can stop the recursion                        //----------------------                        m_points.push(new CPoint2(x23, y23));                        return;                    }    }    else // if angle    {    var anglecond = Math.pow(dx*dx + dy*dy, 2) / (180 / ( 1 / 180 ) );    if (anglecond < 0.000000001) anglecond = 0.000000001;    if (measure < anglecond)     {      m_points.push(new CPoint2(x23, y23));      return;    }        }                    }                else                {                da1 = Math.abs(Math.atan2(y2 - y1, x2 - x1) - Math.atan2(y4 - y3, x4 - x3));                if(da1 >= pi) da1 = pi2 - da1;                  if(da1 < m_angle_tolerance)                  {                        // Finally we can stop the recursion                        //----------------------                        m_points.push(new CPoint2(x23, y23));                        return;                  }                }                        if(m_cusp_limit != 0.0)                    {                        if(da1 > m_cusp_limit)                        {                            m_points.push(new CPoint2(x2, y2));                            return;                        }                      if (!split)                      {                        if(da2 > m_cusp_limit)                        {                            m_points.push(new CPoint2(x3, y3));                            return;                        }                      }                    }                }                break;            }                // Continue subdivision            //----------------------            recursive_bezier(x1, y1, x12, y12, x123, y123, x1234, y1234, level + 1);             recursive_bezier(x1234, y1234, x234, y234, x34, y34, x4, y4, level + 1);       }    }  };</script>``

## Test runner

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Testing in unknown unknown
Test Ops/sec
Pow
``var data = data4;var newdata = [], newdata_item, m_approximation_scale, m_angle_tolerance, split;m_approximation_scale = 1;m_angle_tolerance = 1;split = false;for(var i = 0;i < data.length;i++) {  x1 = data[i][0], y1 = data[i][1], x2 = data[i][2], y2 = data[i][3], x3 = data[i][4], y3 = data[i][5], x4 = data[i][6], y4 = data[i][7];  newdata_item = approximate(x1, y1, x2, y2, x3, y3, x4, y4, m_approximation_scale, m_angle_tolerance, split, true);  newdata.push(newdata_item)};``
pendingâ€¦
Atan
``var data = data4;var newdata = [], newdata_item, m_approximation_scale, m_angle_tolerance, split;m_approximation_scale = 1;m_angle_tolerance = 1;split = false;for(var i = 0;i < data.length;i++) {  x1 = data[i][0], y1 = data[i][1], x2 = data[i][2], y2 = data[i][3], x3 = data[i][4], y3 = data[i][5], x4 = data[i][6], y4 = data[i][7];  newdata_item = approximate(x1, y1, x2, y2, x3, y3, x4, y4, m_approximation_scale, m_angle_tolerance, split, false);  newdata.push(newdata_item)};``
pendingâ€¦
Angle 0
``var data = data4;var newdata = [], newdata_item, m_approximation_scale, m_angle_tolerance, split;m_approximation_scale = 1;m_angle_tolerance = 0;split = false;for(var i = 0;i < data.length;i++) {  x1 = data[i][0], y1 = data[i][1], x2 = data[i][2], y2 = data[i][3], x3 = data[i][4], y3 = data[i][5], x4 = data[i][6], y4 = data[i][7];  newdata_item = approximate(x1, y1, x2, y2, x3, y3, x4, y4, m_approximation_scale, m_angle_tolerance, split, false);  newdata.push(newdata_item)};``
pendingâ€¦

## Revisions

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