mirror of
https://github.com/scratchfoundation/paper.js.git
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126 lines
3.3 KiB
JavaScript
126 lines
3.3 KiB
JavaScript
/*
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* Paper.js
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*
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* This file is part of Paper.js, a JavaScript Vector Graphics Library,
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* based on Scriptographer.org and designed to be largely API compatible.
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* http://scriptographer.org/
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*
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* Copyright (c) 2011, Juerg Lehni & Jonathan Puckey
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* http://lehni.org/ & http://jonathanpuckey.com/
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*
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* All rights reserved. See LICENSE file for details.
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*/
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var Numerical = new function() {
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var abscissa = [
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-0.5773502692, 0.5773502692,
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-0.7745966692, 0.7745966692, 0,
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-0.8611363116, 0.8611363116, -0.3399810436, 0.3399810436,
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-0.9061798459, 0.9061798459, -0.5384693101, 0.5384693101, 0.0000000000,
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-0.9324695142, 0.9324695142, -0.6612093865, 0.6612093865, -0.2386191861, 0.2386191861,
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-0.9491079123, 0.9491079123, -0.7415311856, 0.7415311856, -0.4058451514, 0.4058451514, 0.0000000000,
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-0.9602898565, 0.9602898565, -0.7966664774, 0.7966664774, -0.5255324099, 0.5255324099, -0.1834346425, 0.1834346425
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];
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var weight = [
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1, 1,
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0.5555555556, 0.5555555556, 0.8888888888,
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0.3478548451, 0.3478548451, 0.6521451549, 0.6521451549,
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0.2369268851, 0.2369268851, 0.4786286705, 0.4786286705, 0.5688888888,
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0.1713244924, 0.1713244924, 0.3607615730, 0.3607615730, 0.4679139346, 0.4679139346,
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0.1294849662, 0.1294849662, 0.2797053915, 0.2797053915, 0.3818300505, 0.3818300505, 0.4179591837,
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0.1012285363, 0.1012285363, 0.2223810345, 0.2223810345, 0.3137066459, 0.3137066459, 0.3626837834, 0.3626837834
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];
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return {
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TOLERANCE: 10e-6,
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/**
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* Gauss-Legendre Numerical Integration, ported from Singularity:
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*
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* Copyright (c) 2006-2007, Jim Armstrong (www.algorithmist.net)
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* All Rights Reserved.
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*/
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gauss: function(f, a, b, n) {
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n = Math.min(Math.max(n, 2), 8);
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var l = n == 2 ? 0 : n * (n - 1) / 2 - 1,
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sum = 0,
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mul = 0.5 * (b - a),
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ab2 = mul + a;
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for(var i = 0; i < n; i++)
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sum += f(ab2 + mul * abscissa[l + i]) * weight[l + i];
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return mul * sum;
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},
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/**
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* Van Wijngaarden–Dekker–Brent method for root finding, implementation
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* based on Numerical Recipes in C
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*/
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brent: function(f, a, b, tol) {
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var c = b, d = 0, e = 0,
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fa = f(a),
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fb = f(b),
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fc = fb;
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for (var i = 1; i <= 64; i++) {
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if ((fb > 0.0 && fc > 0.0) || (fb < 0.0 && fc < 0.0)) {
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c = a;
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fc = fa;
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e = d = b - a;
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}
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if (Math.abs(fc) < Math.abs(fb)) {
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a = b;
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b = c;
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c = a;
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fa = fb;
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fb = fc;
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fc = fa;
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}
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var tol1 = 2 * Number.MIN_VALUE * Math.abs(b) + 0.5 * tol,
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xm = 0.5 * (c - b);
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if (Math.abs(xm) <= tol1 || fb == 0.0) {
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return b;
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}
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if (Math.abs(e) >= tol1 && Math.abs(fa) > Math.abs(fb)) {
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var p, q, r,
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s = fb / fa;
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if (a == c) {
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p = 2.0 * xm * s;
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q = 1.0 - s;
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} else {
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q = fa / fc;
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r = fb / fc;
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p = s * (2.0 * xm * q * (q - r) - (b - a) * (r - 1.0));
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q = (q - 1.0) * (r - 1.0) * (s - 1.0);
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}
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if (p > 0.0)
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q = -q;
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p = Math.abs(p);
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var min1 = 3.0 * xm * q - Math.abs(tol1 * q),
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min2 = Math.abs(e * q);
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if (2.0 * p < (min1 < min2 ? min1 : min2)) {
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e = d;
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d = p / q;
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} else {
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d = xm;
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e = d;
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}
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} else {
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d = xm;
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e = d;
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}
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a = b;
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fa = fb;
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if (Math.abs(d) > tol1)
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b += d;
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else
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b += xm >= 0.0 ? Math.abs(tol1) : -Math.abs(tol1);
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fb = f(b);
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}
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return b;
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}
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}
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};
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