346 lines
9.4 KiB
JavaScript
346 lines
9.4 KiB
JavaScript
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import { create as v2Create, distSquare as v2DistSquare } from './vector.js';
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var mathPow = Math.pow;
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var mathSqrt = Math.sqrt;
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var EPSILON = 1e-8;
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var EPSILON_NUMERIC = 1e-4;
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var THREE_SQRT = mathSqrt(3);
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var ONE_THIRD = 1 / 3;
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var _v0 = v2Create();
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var _v1 = v2Create();
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var _v2 = v2Create();
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function isAroundZero(val) {
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return val > -EPSILON && val < EPSILON;
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}
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function isNotAroundZero(val) {
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return val > EPSILON || val < -EPSILON;
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}
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export function cubicAt(p0, p1, p2, p3, t) {
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var onet = 1 - t;
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return onet * onet * (onet * p0 + 3 * t * p1)
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+ t * t * (t * p3 + 3 * onet * p2);
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}
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export function cubicDerivativeAt(p0, p1, p2, p3, t) {
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var onet = 1 - t;
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return 3 * (((p1 - p0) * onet + 2 * (p2 - p1) * t) * onet
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+ (p3 - p2) * t * t);
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}
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export function cubicRootAt(p0, p1, p2, p3, val, roots) {
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var a = p3 + 3 * (p1 - p2) - p0;
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var b = 3 * (p2 - p1 * 2 + p0);
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var c = 3 * (p1 - p0);
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var d = p0 - val;
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var A = b * b - 3 * a * c;
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var B = b * c - 9 * a * d;
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var C = c * c - 3 * b * d;
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var n = 0;
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if (isAroundZero(A) && isAroundZero(B)) {
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if (isAroundZero(b)) {
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roots[0] = 0;
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}
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else {
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var t1 = -c / b;
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if (t1 >= 0 && t1 <= 1) {
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roots[n++] = t1;
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}
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}
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}
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else {
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var disc = B * B - 4 * A * C;
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if (isAroundZero(disc)) {
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var K = B / A;
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var t1 = -b / a + K;
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var t2 = -K / 2;
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if (t1 >= 0 && t1 <= 1) {
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roots[n++] = t1;
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}
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if (t2 >= 0 && t2 <= 1) {
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roots[n++] = t2;
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}
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}
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else if (disc > 0) {
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var discSqrt = mathSqrt(disc);
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var Y1 = A * b + 1.5 * a * (-B + discSqrt);
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var Y2 = A * b + 1.5 * a * (-B - discSqrt);
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if (Y1 < 0) {
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Y1 = -mathPow(-Y1, ONE_THIRD);
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}
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else {
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Y1 = mathPow(Y1, ONE_THIRD);
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}
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if (Y2 < 0) {
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Y2 = -mathPow(-Y2, ONE_THIRD);
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}
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else {
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Y2 = mathPow(Y2, ONE_THIRD);
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}
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var t1 = (-b - (Y1 + Y2)) / (3 * a);
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if (t1 >= 0 && t1 <= 1) {
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roots[n++] = t1;
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}
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}
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else {
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var T = (2 * A * b - 3 * a * B) / (2 * mathSqrt(A * A * A));
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var theta = Math.acos(T) / 3;
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var ASqrt = mathSqrt(A);
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var tmp = Math.cos(theta);
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var t1 = (-b - 2 * ASqrt * tmp) / (3 * a);
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var t2 = (-b + ASqrt * (tmp + THREE_SQRT * Math.sin(theta))) / (3 * a);
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var t3 = (-b + ASqrt * (tmp - THREE_SQRT * Math.sin(theta))) / (3 * a);
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if (t1 >= 0 && t1 <= 1) {
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roots[n++] = t1;
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}
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if (t2 >= 0 && t2 <= 1) {
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roots[n++] = t2;
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}
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if (t3 >= 0 && t3 <= 1) {
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roots[n++] = t3;
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}
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}
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}
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return n;
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}
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export function cubicExtrema(p0, p1, p2, p3, extrema) {
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var b = 6 * p2 - 12 * p1 + 6 * p0;
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var a = 9 * p1 + 3 * p3 - 3 * p0 - 9 * p2;
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var c = 3 * p1 - 3 * p0;
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var n = 0;
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if (isAroundZero(a)) {
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if (isNotAroundZero(b)) {
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var t1 = -c / b;
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if (t1 >= 0 && t1 <= 1) {
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extrema[n++] = t1;
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}
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}
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}
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else {
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var disc = b * b - 4 * a * c;
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if (isAroundZero(disc)) {
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extrema[0] = -b / (2 * a);
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}
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else if (disc > 0) {
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var discSqrt = mathSqrt(disc);
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var t1 = (-b + discSqrt) / (2 * a);
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var t2 = (-b - discSqrt) / (2 * a);
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if (t1 >= 0 && t1 <= 1) {
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extrema[n++] = t1;
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}
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if (t2 >= 0 && t2 <= 1) {
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extrema[n++] = t2;
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}
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}
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}
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return n;
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}
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export function cubicSubdivide(p0, p1, p2, p3, t, out) {
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var p01 = (p1 - p0) * t + p0;
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var p12 = (p2 - p1) * t + p1;
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var p23 = (p3 - p2) * t + p2;
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var p012 = (p12 - p01) * t + p01;
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var p123 = (p23 - p12) * t + p12;
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var p0123 = (p123 - p012) * t + p012;
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out[0] = p0;
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out[1] = p01;
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out[2] = p012;
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out[3] = p0123;
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out[4] = p0123;
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out[5] = p123;
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out[6] = p23;
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out[7] = p3;
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}
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export function cubicProjectPoint(x0, y0, x1, y1, x2, y2, x3, y3, x, y, out) {
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var t;
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var interval = 0.005;
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var d = Infinity;
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var prev;
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var next;
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var d1;
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var d2;
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_v0[0] = x;
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_v0[1] = y;
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for (var _t = 0; _t < 1; _t += 0.05) {
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_v1[0] = cubicAt(x0, x1, x2, x3, _t);
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_v1[1] = cubicAt(y0, y1, y2, y3, _t);
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d1 = v2DistSquare(_v0, _v1);
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if (d1 < d) {
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t = _t;
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d = d1;
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}
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}
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d = Infinity;
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for (var i = 0; i < 32; i++) {
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if (interval < EPSILON_NUMERIC) {
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break;
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}
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prev = t - interval;
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next = t + interval;
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_v1[0] = cubicAt(x0, x1, x2, x3, prev);
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_v1[1] = cubicAt(y0, y1, y2, y3, prev);
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d1 = v2DistSquare(_v1, _v0);
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if (prev >= 0 && d1 < d) {
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t = prev;
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d = d1;
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}
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else {
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_v2[0] = cubicAt(x0, x1, x2, x3, next);
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_v2[1] = cubicAt(y0, y1, y2, y3, next);
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d2 = v2DistSquare(_v2, _v0);
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if (next <= 1 && d2 < d) {
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t = next;
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d = d2;
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}
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else {
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interval *= 0.5;
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}
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}
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}
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if (out) {
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out[0] = cubicAt(x0, x1, x2, x3, t);
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out[1] = cubicAt(y0, y1, y2, y3, t);
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}
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return mathSqrt(d);
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}
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export function cubicLength(x0, y0, x1, y1, x2, y2, x3, y3, iteration) {
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var px = x0;
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var py = y0;
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var d = 0;
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var step = 1 / iteration;
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for (var i = 1; i <= iteration; i++) {
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var t = i * step;
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var x = cubicAt(x0, x1, x2, x3, t);
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var y = cubicAt(y0, y1, y2, y3, t);
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var dx = x - px;
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var dy = y - py;
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d += Math.sqrt(dx * dx + dy * dy);
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px = x;
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py = y;
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}
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return d;
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}
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export function quadraticAt(p0, p1, p2, t) {
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var onet = 1 - t;
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return onet * (onet * p0 + 2 * t * p1) + t * t * p2;
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}
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export function quadraticDerivativeAt(p0, p1, p2, t) {
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return 2 * ((1 - t) * (p1 - p0) + t * (p2 - p1));
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}
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export function quadraticRootAt(p0, p1, p2, val, roots) {
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var a = p0 - 2 * p1 + p2;
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var b = 2 * (p1 - p0);
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var c = p0 - val;
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var n = 0;
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if (isAroundZero(a)) {
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if (isNotAroundZero(b)) {
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var t1 = -c / b;
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if (t1 >= 0 && t1 <= 1) {
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roots[n++] = t1;
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}
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}
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}
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else {
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var disc = b * b - 4 * a * c;
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if (isAroundZero(disc)) {
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var t1 = -b / (2 * a);
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if (t1 >= 0 && t1 <= 1) {
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roots[n++] = t1;
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}
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}
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else if (disc > 0) {
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var discSqrt = mathSqrt(disc);
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var t1 = (-b + discSqrt) / (2 * a);
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var t2 = (-b - discSqrt) / (2 * a);
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if (t1 >= 0 && t1 <= 1) {
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roots[n++] = t1;
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}
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if (t2 >= 0 && t2 <= 1) {
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roots[n++] = t2;
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}
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}
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}
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return n;
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}
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export function quadraticExtremum(p0, p1, p2) {
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var divider = p0 + p2 - 2 * p1;
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if (divider === 0) {
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return 0.5;
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}
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else {
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return (p0 - p1) / divider;
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}
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}
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export function quadraticSubdivide(p0, p1, p2, t, out) {
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var p01 = (p1 - p0) * t + p0;
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var p12 = (p2 - p1) * t + p1;
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var p012 = (p12 - p01) * t + p01;
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out[0] = p0;
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out[1] = p01;
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out[2] = p012;
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out[3] = p012;
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out[4] = p12;
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out[5] = p2;
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}
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export function quadraticProjectPoint(x0, y0, x1, y1, x2, y2, x, y, out) {
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var t;
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var interval = 0.005;
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var d = Infinity;
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_v0[0] = x;
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_v0[1] = y;
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for (var _t = 0; _t < 1; _t += 0.05) {
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_v1[0] = quadraticAt(x0, x1, x2, _t);
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_v1[1] = quadraticAt(y0, y1, y2, _t);
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var d1 = v2DistSquare(_v0, _v1);
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if (d1 < d) {
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t = _t;
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d = d1;
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}
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}
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d = Infinity;
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for (var i = 0; i < 32; i++) {
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if (interval < EPSILON_NUMERIC) {
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break;
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}
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var prev = t - interval;
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var next = t + interval;
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_v1[0] = quadraticAt(x0, x1, x2, prev);
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_v1[1] = quadraticAt(y0, y1, y2, prev);
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var d1 = v2DistSquare(_v1, _v0);
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if (prev >= 0 && d1 < d) {
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t = prev;
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d = d1;
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}
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else {
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_v2[0] = quadraticAt(x0, x1, x2, next);
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_v2[1] = quadraticAt(y0, y1, y2, next);
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var d2 = v2DistSquare(_v2, _v0);
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if (next <= 1 && d2 < d) {
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t = next;
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d = d2;
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}
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else {
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interval *= 0.5;
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}
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}
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}
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if (out) {
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out[0] = quadraticAt(x0, x1, x2, t);
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out[1] = quadraticAt(y0, y1, y2, t);
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}
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return mathSqrt(d);
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}
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export function quadraticLength(x0, y0, x1, y1, x2, y2, iteration) {
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var px = x0;
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var py = y0;
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var d = 0;
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var step = 1 / iteration;
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for (var i = 1; i <= iteration; i++) {
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var t = i * step;
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var x = quadraticAt(x0, x1, x2, t);
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var y = quadraticAt(y0, y1, y2, t);
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var dx = x - px;
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var dy = y - py;
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d += Math.sqrt(dx * dx + dy * dy);
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px = x;
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py = y;
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}
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return d;
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}
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