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123 lines
3.9 KiB
123 lines
3.9 KiB
// distance between 2 points
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function distance(p1, p2) {
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return Math.sqrt(distanceSq(p1, p2));
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}
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// distance between 2 points squared
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function distanceSq(p1, p2) {
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return Math.pow(p1[0] - p2[0], 2) + Math.pow(p1[1] - p2[1], 2);
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}
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// Sistance squared from a point p to the line segment vw
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function distanceToSegmentSq(p, v, w) {
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const l2 = distanceSq(v, w);
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if (l2 === 0) {
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return distanceSq(p, v);
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}
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let t = ((p[0] - v[0]) * (w[0] - v[0]) + (p[1] - v[1]) * (w[1] - v[1])) / l2;
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t = Math.max(0, Math.min(1, t));
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return distanceSq(p, lerp(v, w, t));
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}
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function lerp(a, b, t) {
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return [
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a[0] + (b[0] - a[0]) * t,
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a[1] + (b[1] - a[1]) * t,
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];
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}
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// Adapted from https://seant23.wordpress.com/2010/11/12/offset-bezier-curves/
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function flatness(points, offset) {
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const p1 = points[offset + 0];
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const p2 = points[offset + 1];
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const p3 = points[offset + 2];
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const p4 = points[offset + 3];
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let ux = 3 * p2[0] - 2 * p1[0] - p4[0];
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ux *= ux;
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let uy = 3 * p2[1] - 2 * p1[1] - p4[1];
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uy *= uy;
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let vx = 3 * p3[0] - 2 * p4[0] - p1[0];
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vx *= vx;
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let vy = 3 * p3[1] - 2 * p4[1] - p1[1];
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vy *= vy;
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if (ux < vx) {
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ux = vx;
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}
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if (uy < vy) {
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uy = vy;
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}
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return ux + uy;
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}
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function getPointsOnBezierCurveWithSplitting(points, offset, tolerance, newPoints) {
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const outPoints = newPoints || [];
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if (flatness(points, offset) < tolerance) {
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const p0 = points[offset + 0];
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if (outPoints.length) {
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const d = distance(outPoints[outPoints.length - 1], p0);
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if (d > 1) {
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outPoints.push(p0);
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}
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}
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else {
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outPoints.push(p0);
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}
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outPoints.push(points[offset + 3]);
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}
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else {
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// subdivide
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const t = .5;
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const p1 = points[offset + 0];
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const p2 = points[offset + 1];
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const p3 = points[offset + 2];
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const p4 = points[offset + 3];
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const q1 = lerp(p1, p2, t);
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const q2 = lerp(p2, p3, t);
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const q3 = lerp(p3, p4, t);
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const r1 = lerp(q1, q2, t);
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const r2 = lerp(q2, q3, t);
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const red = lerp(r1, r2, t);
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getPointsOnBezierCurveWithSplitting([p1, q1, r1, red], 0, tolerance, outPoints);
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getPointsOnBezierCurveWithSplitting([red, r2, q3, p4], 0, tolerance, outPoints);
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}
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return outPoints;
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}
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export function simplify(points, distance) {
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return simplifyPoints(points, 0, points.length, distance);
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}
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// Ramer–Douglas–Peucker algorithm
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// https://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm
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function simplifyPoints(points, start, end, epsilon, newPoints) {
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const outPoints = newPoints || [];
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// find the most distance point from the endpoints
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const s = points[start];
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const e = points[end - 1];
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let maxDistSq = 0;
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let maxNdx = 1;
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for (let i = start + 1; i < end - 1; ++i) {
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const distSq = distanceToSegmentSq(points[i], s, e);
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if (distSq > maxDistSq) {
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maxDistSq = distSq;
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maxNdx = i;
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}
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}
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// if that point is too far, split
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if (Math.sqrt(maxDistSq) > epsilon) {
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simplifyPoints(points, start, maxNdx + 1, epsilon, outPoints);
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simplifyPoints(points, maxNdx, end, epsilon, outPoints);
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}
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else {
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if (!outPoints.length) {
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outPoints.push(s);
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}
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outPoints.push(e);
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}
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return outPoints;
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}
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export function pointsOnBezierCurves(points, tolerance = 0.15, distance) {
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const newPoints = [];
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const numSegments = (points.length - 1) / 3;
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for (let i = 0; i < numSegments; i++) {
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const offset = i * 3;
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getPointsOnBezierCurveWithSplitting(points, offset, tolerance, newPoints);
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}
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if (distance && distance > 0) {
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return simplifyPoints(newPoints, 0, newPoints.length, distance);
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}
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return newPoints;
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}
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