1 /* 2 * Copyright (C) 2014 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17 package com.android.camera.ui.motion; 18 19 /** 20 * This represents is a precomputed cubic bezier curve starting at (0,0) and 21 * going to (1,1) with two configurable control points. Once the instance is 22 * created, the control points cannot be modified. 23 * 24 * Generally, this will be used for computing timing curves for with control 25 * points where an x value will be provide from 0.0 - 1.0, and the y value will 26 * be solved for where y is used as the timing value in some linear 27 * interpolation of a value. 28 */ 29 public class UnitBezier implements UnitCurve { 30 31 private static final float EPSILON = 1e-6f; 32 33 private final DerivableFloatFn mXFn; 34 private final DerivableFloatFn mYFn; 35 36 /** 37 * Build and pre-compute a unit bezier. This assumes a starting point of 38 * (0, 0) and end point of (1.0, 1.0). 39 * 40 * @param c0x control point x value for p0 41 * @param c0y control point y value for p0 42 * @param c1x control point x value for p1 43 * @param c1y control point y value for p1 44 */ UnitBezier(float c0x, float c0y, float c1x, float c1y)45 public UnitBezier(float c0x, float c0y, float c1x, float c1y) { 46 mXFn = new CubicBezierFn(c0x, c1x); 47 mYFn = new CubicBezierFn(c0y, c1y); 48 } 49 50 /** 51 * Given a unit bezier curve find the height of the curve at t (which is 52 * internally represented as the xAxis). 53 * 54 * @param t the x position between 0 and 1 to solve for y. 55 * @return the closest approximate height of the curve at x. 56 */ 57 @Override valueAt(float t)58 public float valueAt(float t) { 59 return mYFn.value(solve(t, mXFn)); 60 } 61 62 /** 63 * Given a unit bezier curve find a value along the x axis such that 64 * valueAt(result) produces the input value. 65 * 66 * @param value the y position between 0 and 1 to solve for x 67 * @return the closest approximate input that will produce value when provided 68 * to the valueAt function. 69 */ 70 @Override tAt(float value)71 public float tAt(float value) { 72 return mXFn.value(solve(value, mYFn)); 73 } 74 solve(float target, DerivableFloatFn fn)75 private float solve(float target, DerivableFloatFn fn) { 76 // For a linear fn, t = value. This makes value a good starting guess. 77 float input = target; 78 79 // Newton's method (Faster than bisection) 80 for (int i = 0; i < 8; i++) { 81 float value = fn.value(input) - target; 82 if (Math.abs(value) < EPSILON) { 83 return input; 84 } 85 float derivative = fn.derivative(input); 86 if (Math.abs(derivative) < EPSILON) { 87 break; 88 } 89 input = input - value / derivative; 90 } 91 92 // Fallback on bi-section 93 float min = 0.0f; 94 float max = 1.0f; 95 input = target; 96 97 if (input < min) { 98 return min; 99 } 100 if (input > max) { 101 return max; 102 } 103 104 while (min < max) { 105 float value = fn.value(input); 106 if (Math.abs(value - target) < EPSILON) { 107 return input; 108 } 109 110 if (target > value) { 111 min = input; 112 } else { 113 max = input; 114 } 115 116 input = (max - min) * .5f + min; 117 } 118 119 // Give up, return the closest match we got too. 120 return input; 121 } 122 123 private interface DerivableFloatFn { value(float x)124 float value(float x); derivative(float x)125 float derivative(float x); 126 } 127 128 /** 129 * Precomputed constants for a given set of control points along a given 130 * cubic bezier axis. 131 */ 132 private static class CubicBezierFn implements DerivableFloatFn { 133 private final float c; 134 private final float a; 135 private final float b; 136 137 /** 138 * Build and pre-compute a single axis for a unit bezier. This assumes p0 139 * is 0 and p1 is 1. 140 * 141 * @param c0 start control point. 142 * @param c1 end control point. 143 */ CubicBezierFn(float c0, float c1)144 public CubicBezierFn(float c0, float c1) { 145 c = 3.0f * c0; 146 b = 3.0f * (c1 - c0) - c; 147 a = 1.0f - c - b; 148 } 149 value(float x)150 public float value(float x) { 151 return ((a * x + b) * x + c) * x; 152 } derivative(float x)153 public float derivative(float x) { 154 return (3.0f * a * x + 2.0f * b) * x + c; 155 } 156 } 157 } 158