109 lines
2.7 KiB
JavaScript
109 lines
2.7 KiB
JavaScript
const EPS = 0.001;
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const EPS_SQUARE = EPS * EPS;
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function side(x1, y1, x2, y2, x, y) {
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return (y2 - y1) * (x - x1) + (-x2 + x1) * (y - y1);
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}
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function naivePointInTriangle(x1, y1, x2, y2, x3, y3, x, y) {
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const checkSide1 = side(x1, y1, x2, y2, x, y) >= 0;
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const checkSide2 = side(x2, y2, x3, y3, x, y) >= 0;
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const checkSide3 = side(x3, y3, x1, y1, x, y) >= 0;
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return checkSide1 && checkSide2 && checkSide3;
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}
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function pointInTriangleBoundingBox(x1, y1, x2, y2, x3, y3, x, y) {
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const xMin = Math.min(x1, Math.min(x2, x3)) - EPS;
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const xMax = Math.max(x1, Math.max(x2, x3)) + EPS;
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const yMin = Math.min(y1, Math.min(y2, y3)) - EPS;
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const yMax = Math.max(y1, Math.max(y2, y3)) + EPS;
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return !(x < xMin || xMax < x || y < yMin || yMax < y);
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}
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function distanceSquarePointToSegment(x1, y1, x2, y2, x, y) {
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const p1_p2_squareLength = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
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const dotProduct =
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((x - x1) * (x2 - x1) + (y - y1) * (y2 - y1)) / p1_p2_squareLength;
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if (dotProduct < 0) {
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return (x - x1) * (x - x1) + (y - y1) * (y - y1);
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} else if (dotProduct <= 1) {
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const p_p1_squareLength = (x1 - x) * (x1 - x) + (y1 - y) * (y1 - y);
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return p_p1_squareLength - dotProduct * dotProduct * p1_p2_squareLength;
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} else {
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return (x - x2) * (x - x2) + (y - y2) * (y - y2);
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}
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}
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function accuratePointInTriangle(x1, y1, x2, y2, x3, y3, x, y) {
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if (!pointInTriangleBoundingBox(x1, y1, x2, y2, x3, y3, x, y)) {
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return false;
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}
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if (naivePointInTriangle(x1, y1, x2, y2, x3, y3, x, y)) {
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return true;
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}
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if (distanceSquarePointToSegment(x1, y1, x2, y2, x, y) <= EPS_SQUARE) {
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return true;
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}
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if (distanceSquarePointToSegment(x2, y2, x3, y3, x, y) <= EPS_SQUARE) {
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return true;
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}
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if (distanceSquarePointToSegment(x3, y3, x1, y1, x, y) <= EPS_SQUARE) {
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return true;
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}
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return false;
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}
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function printPoint(x, y) {
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return "(" + x + ", " + y + ")";
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}
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function printTriangle(x1, y1, x2, y2, x3, y3) {
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return (
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"Triangle is [" +
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printPoint(x1, y1) +
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", " +
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printPoint(x2, y2) +
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", " +
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printPoint(x3, y3) +
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"]"
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);
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}
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function test(x1, y1, x2, y2, x3, y3, x, y) {
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console.log(
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printTriangle(x1, y1, x2, y2, x3, y3) +
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"Point " +
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printPoint(x, y) +
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" is within triangle? " +
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(accuratePointInTriangle(x1, y1, x2, y2, x3, y3, x, y) ? "true" : "false")
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);
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}
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test(1.5, 2.4, 5.1, -3.1, -3.8, 1.2, 0, 0);
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test(1.5, 2.4, 5.1, -3.1, -3.8, 1.2, 0, 1);
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test(1.5, 2.4, 5.1, -3.1, -3.8, 1.2, 3, 1);
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console.log();
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test(
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0.1,
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0.1111111111111111,
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12.5,
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33.333333333333336,
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25,
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11.11111111111111,
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5.414285714285714,
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14.349206349206348
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);
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console.log();
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test(
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0.1,
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0.1111111111111111,
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12.5,
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33.333333333333336,
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-12.5,
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16.666666666666668,
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5.414285714285714,
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14.349206349206348
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);
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console.log();
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