paper.js/src/util/MathUtils.js

var MathUtils = new function() {
	var maxDepth = 53; // MANT_DIGITS: 64 bit: 53 digits, 32 bit: 24 digits

	// Gauss-Legendre Numerical Integration, a Gauss.as port from Singularity:
	//
	// Copyright (c) 2006-2007, Jim Armstrong (www.algorithmist.net)
	// All Rights Reserved.
	//
	// Simplified and further optimised by Juerg Lehni.

	var abscissa = [
		-0.5773502692, 0.5773502692,
		-0.7745966692, 0.7745966692, 0,
		-0.8611363116, 0.8611363116, -0.3399810436, 0.3399810436,
		-0.9061798459, 0.9061798459, -0.5384693101, 0.5384693101, 0.0000000000,
		-0.9324695142, 0.9324695142, -0.6612093865, 0.6612093865, -0.2386191861, 0.2386191861,
		-0.9491079123, 0.9491079123, -0.7415311856, 0.7415311856, -0.4058451514, 0.4058451514, 0.0000000000,
		-0.9602898565, 0.9602898565, -0.7966664774, 0.7966664774, -0.5255324099, 0.5255324099, -0.1834346425, 0.1834346425
	];

	var weight = [
		1, 1,
		0.5555555556, 0.5555555556, 0.8888888888,
		0.3478548451, 0.3478548451, 0.6521451549, 0.6521451549,
		0.2369268851, 0.2369268851, 0.4786286705, 0.4786286705, 0.5688888888,
		0.1713244924, 0.1713244924, 0.3607615730, 0.3607615730, 0.4679139346, 0.4679139346,
		0.1294849662, 0.1294849662, 0.2797053915, 0.2797053915, 0.3818300505, 0.3818300505, 0.4179591837,
		0.1012285363, 0.1012285363, 0.2223810345, 0.2223810345, 0.3137066459, 0.3137066459, 0.3626837834, 0.3626837834
	];

	return {
		EPSILON: Math.pow(2, -maxDepth + 1),

		gauss: function(f, a, b, n) {
			n = Math.min(Math.max(n, 2), 8);

			var l = n == 2 ? 0 : n * (n - 1) / 2 - 1,
				sum = 0,
				mul = 0.5 * (b - a),
				ab2 = mul + a;
			for(var i = 0; i < n; i++)
				sum += f(ab2 + mul * abscissa[l + i]) * weight[l + i];

			return mul * sum;
		}
	}
};