Java tutorial
/******************************************************************************* * Copyright 2011 See AUTHORS file. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. ******************************************************************************/ package com.badlogic.gdx.math; /** Takes a linear value in the range of 0-1 and outputs a (usually) non-linear, interpolated value. * @author Nathan Sweet */ public abstract class Interpolation { /** @param a Alpha value between 0 and 1. */ abstract public float apply(float a); /** @param a Alpha value between 0 and 1. */ public float apply(float start, float end, float a) { return start + (end - start) * apply(a); } static public final Interpolation linear = new Interpolation() { public float apply(float a) { return a; } }; static public final Interpolation fade = new Interpolation() { public float apply(float a) { return MathUtils.clamp(a * a * a * (a * (a * 6 - 15) + 10), 0, 1); } }; static public final Pow pow2 = new Pow(2); static public final PowIn pow2In = new PowIn(2); static public final PowOut pow2Out = new PowOut(2); static public final Pow pow3 = new Pow(3); static public final PowIn pow3In = new PowIn(3); static public final PowOut pow3Out = new PowOut(3); static public final Pow pow4 = new Pow(4); static public final PowIn pow4In = new PowIn(4); static public final PowOut pow4Out = new PowOut(4); static public final Pow pow5 = new Pow(5); static public final PowIn pow5In = new PowIn(5); static public final PowOut pow5Out = new PowOut(5); static public final Interpolation sine = new Interpolation() { public float apply(float a) { return (1 - MathUtils.cos(a * MathUtils.PI)) / 2; } }; static public final Interpolation sineIn = new Interpolation() { public float apply(float a) { return 1 - MathUtils.cos(a * MathUtils.PI / 2); } }; static public final Interpolation sineOut = new Interpolation() { public float apply(float a) { return MathUtils.sin(a * MathUtils.PI / 2); } }; static public final Interpolation exp10 = new Exp(2, 10); static public final Interpolation exp10In = new ExpIn(2, 10); static public final Interpolation exp10Out = new ExpOut(2, 10); static public final Interpolation exp5 = new Exp(2, 5); static public final Interpolation exp5In = new ExpIn(2, 5); static public final Interpolation exp5Out = new ExpOut(2, 5); static public final Interpolation circle = new Interpolation() { public float apply(float a) { if (a <= 0.5f) { a *= 2; return (1 - (float) Math.sqrt(1 - a * a)) / 2; } a--; a *= 2; return ((float) Math.sqrt(1 - a * a) + 1) / 2; } }; static public final Interpolation circleIn = new Interpolation() { public float apply(float a) { return 1 - (float) Math.sqrt(1 - a * a); } }; static public final Interpolation circleOut = new Interpolation() { public float apply(float a) { a--; return (float) Math.sqrt(1 - a * a); } }; static public final Elastic elastic = new Elastic(2, 10, 7, 1); static public final Elastic elasticIn = new ElasticIn(2, 10, 7, 1); static public final Elastic elasticOut = new ElasticOut(2, 10, 7, 1); static public final Interpolation swing = new Swing(1.5f); static public final Interpolation swingIn = new SwingIn(2f); static public final Interpolation swingOut = new SwingOut(2f); static public final Interpolation bounce = new Bounce(4); static public final Interpolation bounceIn = new BounceIn(4); static public final Interpolation bounceOut = new BounceOut(4); // static public class Pow extends Interpolation { final int power; public Pow(int power) { this.power = power; } public float apply(float a) { if (a <= 0.5f) return (float) Math.pow(a * 2, power) / 2; return (float) Math.pow((a - 1) * 2, power) / (power % 2 == 0 ? -2 : 2) + 1; } } static public class PowIn extends Pow { public PowIn(int power) { super(power); } public float apply(float a) { return (float) Math.pow(a, power); } } static public class PowOut extends Pow { public PowOut(int power) { super(power); } public float apply(float a) { return (float) Math.pow(a - 1, power) * (power % 2 == 0 ? -1 : 1) + 1; } } // static public class Exp extends Interpolation { final float value, power, min, scale; public Exp(float value, float power) { this.value = value; this.power = power; min = (float) Math.pow(value, -power); scale = 1 / (1 - min); } public float apply(float a) { if (a <= 0.5f) return ((float) Math.pow(value, power * (a * 2 - 1)) - min) * scale / 2; return (2 - ((float) Math.pow(value, -power * (a * 2 - 1)) - min) * scale) / 2; } }; static public class ExpIn extends Exp { public ExpIn(float value, float power) { super(value, power); } public float apply(float a) { return ((float) Math.pow(value, power * (a - 1)) - min) * scale; } } static public class ExpOut extends Exp { public ExpOut(float value, float power) { super(value, power); } public float apply(float a) { return 1 - ((float) Math.pow(value, -power * a) - min) * scale; } } // static public class Elastic extends Interpolation { final float value, power, scale, bounces; public Elastic(float value, float power, int bounces, float scale) { this.value = value; this.power = power; this.scale = scale; this.bounces = bounces * MathUtils.PI * (bounces % 2 == 0 ? 1 : -1); } public float apply(float a) { if (a <= 0.5f) { a *= 2; return (float) Math.pow(value, power * (a - 1)) * MathUtils.sin(a * bounces) * scale / 2; } a = 1 - a; a *= 2; return 1 - (float) Math.pow(value, power * (a - 1)) * MathUtils.sin((a) * bounces) * scale / 2; } } static public class ElasticIn extends Elastic { public ElasticIn(float value, float power, int bounces, float scale) { super(value, power, bounces, scale); } public float apply(float a) { return (float) Math.pow(value, power * (a - 1)) * MathUtils.sin(a * bounces) * scale; } } static public class ElasticOut extends Elastic { public ElasticOut(float value, float power, int bounces, float scale) { super(value, power, bounces, scale); } public float apply(float a) { a = 1 - a; return (1 - (float) Math.pow(value, power * (a - 1)) * MathUtils.sin(a * bounces) * scale); } } // static public class Bounce extends BounceOut { public Bounce(float[] widths, float[] heights) { super(widths, heights); } public Bounce(int bounces) { super(bounces); } private float out(float a) { float test = a + widths[0] / 2; if (test < widths[0]) return test / (widths[0] / 2) - 1; return super.apply(a); } public float apply(float a) { if (a <= 0.5f) return (1 - out(1 - a * 2)) / 2; return out(a * 2 - 1) / 2 + 0.5f; } } static public class BounceOut extends Interpolation { final float[] widths, heights; public BounceOut(float[] widths, float[] heights) { if (widths.length != heights.length) throw new IllegalArgumentException("Must be the same number of widths and heights."); this.widths = widths; this.heights = heights; } public BounceOut(int bounces) { if (bounces < 2 || bounces > 5) throw new IllegalArgumentException("bounces cannot be < 2 or > 5: " + bounces); widths = new float[bounces]; heights = new float[bounces]; heights[0] = 1; switch (bounces) { case 2: widths[0] = 0.6f; widths[1] = 0.4f; heights[1] = 0.33f; break; case 3: widths[0] = 0.4f; widths[1] = 0.4f; widths[2] = 0.2f; heights[1] = 0.33f; heights[2] = 0.1f; break; case 4: widths[0] = 0.34f; widths[1] = 0.34f; widths[2] = 0.2f; widths[3] = 0.15f; heights[1] = 0.26f; heights[2] = 0.11f; heights[3] = 0.03f; break; case 5: widths[0] = 0.3f; widths[1] = 0.3f; widths[2] = 0.2f; widths[3] = 0.1f; widths[4] = 0.1f; heights[1] = 0.45f; heights[2] = 0.3f; heights[3] = 0.15f; heights[4] = 0.06f; break; } widths[0] *= 2; } public float apply(float a) { a += widths[0] / 2; float width = 0, height = 0; for (int i = 0, n = widths.length; i < n; i++) { width = widths[i]; if (a <= width) { height = heights[i]; break; } a -= width; } a /= width; float z = 4 / width * height * a; return 1 - (z - z * a) * width; } } static public class BounceIn extends BounceOut { public BounceIn(float[] widths, float[] heights) { super(widths, heights); } public BounceIn(int bounces) { super(bounces); } public float apply(float a) { return 1 - super.apply(1 - a); } } // static public class Swing extends Interpolation { private final float scale; public Swing(float scale) { this.scale = scale * 2; } public float apply(float a) { if (a <= 0.5f) { a *= 2; return a * a * ((scale + 1) * a - scale) / 2; } a--; a *= 2; return a * a * ((scale + 1) * a + scale) / 2 + 1; } } static public class SwingOut extends Interpolation { private final float scale; public SwingOut(float scale) { this.scale = scale; } public float apply(float a) { a--; return a * a * ((scale + 1) * a + scale) + 1; } } static public class SwingIn extends Interpolation { private final float scale; public SwingIn(float scale) { this.scale = scale; } public float apply(float a) { return a * a * ((scale + 1) * a - scale); } } }