84 lines
2.3 KiB
Java
84 lines
2.3 KiB
Java
/*
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* opsu! - an open-source osu! client
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* Copyright (C) 2014, 2015 Jeffrey Han
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*
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* opsu! is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* opsu! is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with opsu!. If not, see <http://www.gnu.org/licenses/>.
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*/
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package itdelatrisu.opsu.objects.curves;
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/**
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* Representation of a Bezier curve with the distance between each point calculated.
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*
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* @author fluddokt (https://github.com/fluddokt)
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*/
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public class Bezier2 extends CurveType {
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/** The control points of the Bezier curve. */
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private Vec2f[] points;
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/**
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* Constructor.
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* @param points the control points
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*/
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public Bezier2(Vec2f[] points) {
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this.points = points;
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// approximate by finding the length of all points
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// (which should be the max possible length of the curve)
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float approxlength = 0;
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for (int i = 0; i < points.length - 1; i++)
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approxlength += points[i].cpy().sub(points[i + 1]).len();
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init(approxlength);
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}
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@Override
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public Vec2f pointAt(float t) {
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Vec2f c = new Vec2f();
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int n = points.length - 1;
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for (int i = 0; i <= n; i++) {
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double b = bernstein(i, n, t);
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c.x += points[i].x * b;
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c.y += points[i].y * b;
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}
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return c;
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}
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/**
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* Calculates the binomial coefficient.
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* http://en.wikipedia.org/wiki/Binomial_coefficient#Binomial_coefficient_in_programming_languages
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*/
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private static long binomialCoefficient(int n, int k) {
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if (k < 0 || k > n)
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return 0;
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if (k == 0 || k == n)
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return 1;
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k = Math.min(k, n - k); // take advantage of symmetry
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long c = 1;
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for (int i = 0; i < k; i++)
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c = c * (n - i) / (i + 1);
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return c;
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}
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/**
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* Calculates the Bernstein polynomial.
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* @param i the index
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* @param n the degree of the polynomial (i.e. number of points)
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* @param t the t value [0, 1]
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*/
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private static double bernstein(int i, int n, float t) {
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return binomialCoefficient(n, i) * Math.pow(t, i) * Math.pow(1 - t, n - i);
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}
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}
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