1 /* 2 * Copyright (C) 2013 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.inputmethod.keyboard.internal; 18 19 /** 20 * Interpolates XY-coordinates using Cubic Hermite Curve. 21 */ 22 public final class HermiteInterpolator { 23 private int[] mXCoords; 24 private int[] mYCoords; 25 private int mMinPos; 26 private int mMaxPos; 27 28 // Working variable to calculate interpolated value. 29 /** The coordinates of the start point of the interval. */ 30 public int mP1X, mP1Y; 31 /** The coordinates of the end point of the interval. */ 32 public int mP2X, mP2Y; 33 /** The slope of the tangent at the start point. */ 34 public float mSlope1X, mSlope1Y; 35 /** The slope of the tangent at the end point. */ 36 public float mSlope2X, mSlope2Y; 37 /** The interpolated coordinates. 38 * The return variables of {@link #interpolate(float)} to avoid instantiations. 39 */ 40 public float mInterpolatedX, mInterpolatedY; 41 42 public HermiteInterpolator() { 43 // Nothing to do with here. 44 } 45 46 /** 47 * Reset this interpolator to point XY-coordinates data. 48 * @param xCoords the array of x-coordinates. Valid data are in left-open interval 49 * <code>[minPos, maxPos)</code>. 50 * @param yCoords the array of y-coordinates. Valid data are in left-open interval 51 * <code>[minPos, maxPos)</code>. 52 * @param minPos the minimum index of left-open interval of valid data. 53 * @param maxPos the maximum index of left-open interval of valid data. 54 */ 55 public void reset(final int[] xCoords, final int[] yCoords, final int minPos, 56 final int maxPos) { 57 mXCoords = xCoords; 58 mYCoords = yCoords; 59 mMinPos = minPos; 60 mMaxPos = maxPos; 61 } 62 63 /** 64 * Set interpolation interval. 65 * <p> 66 * The start and end coordinates of the interval will be set in {@link #mP1X}, {@link #mP1Y}, 67 * {@link #mP2X}, and {@link #mP2Y}. The slope of the tangents at start and end points will be 68 * set in {@link #mSlope1X}, {@link #mSlope1Y}, {@link #mSlope2X}, and {@link #mSlope2Y}. 69 * 70 * @param p0 the index just before interpolation interval. If <code>p1</code> points the start 71 * of valid points, <code>p0</code> must be less than <code>minPos</code> of 72 * {@link #reset(int[],int[],int,int)}. 73 * @param p1 the start index of interpolation interval. 74 * @param p2 the end index of interpolation interval. 75 * @param p3 the index just after interpolation interval. If <code>p2</code> points the end of 76 * valid points, <code>p3</code> must be equal or greater than <code>maxPos</code> of 77 * {@link #reset(int[],int[],int,int)}. 78 */ 79 public void setInterval(final int p0, final int p1, final int p2, final int p3) { 80 mP1X = mXCoords[p1]; 81 mP1Y = mYCoords[p1]; 82 mP2X = mXCoords[p2]; 83 mP2Y = mYCoords[p2]; 84 // A(ax,ay) is the vector p1->p2. 85 final int ax = mP2X - mP1X; 86 final int ay = mP2Y - mP1Y; 87 88 // Calculate the slope of the tangent at p1. 89 if (p0 >= mMinPos) { 90 // p1 has previous valid point p0. 91 // The slope of the tangent is half of the vector p0->p2. 92 mSlope1X = (mP2X - mXCoords[p0]) / 2.0f; 93 mSlope1Y = (mP2Y - mYCoords[p0]) / 2.0f; 94 } else if (p3 < mMaxPos) { 95 // p1 has no previous valid point, but p2 has next valid point p3. 96 // B(bx,by) is the slope vector of the tangent at p2. 97 final float bx = (mXCoords[p3] - mP1X) / 2.0f; 98 final float by = (mYCoords[p3] - mP1Y) / 2.0f; 99 final float crossProdAB = ax * by - ay * bx; 100 final float dotProdAB = ax * bx + ay * by; 101 final float normASquare = ax * ax + ay * ay; 102 final float invHalfNormASquare = 1.0f / normASquare / 2.0f; 103 // The slope of the tangent is the mirror image of vector B to vector A. 104 mSlope1X = invHalfNormASquare * (dotProdAB * ax + crossProdAB * ay); 105 mSlope1Y = invHalfNormASquare * (dotProdAB * ay - crossProdAB * ax); 106 } else { 107 // p1 and p2 have no previous valid point. (Interval has only point p1 and p2) 108 mSlope1X = ax; 109 mSlope1Y = ay; 110 } 111 112 // Calculate the slope of the tangent at p2. 113 if (p3 < mMaxPos) { 114 // p2 has next valid point p3. 115 // The slope of the tangent is half of the vector p1->p3. 116 mSlope2X = (mXCoords[p3] - mP1X) / 2.0f; 117 mSlope2Y = (mYCoords[p3] - mP1Y) / 2.0f; 118 } else if (p0 >= mMinPos) { 119 // p2 has no next valid point, but p1 has previous valid point p0. 120 // B(bx,by) is the slope vector of the tangent at p1. 121 final float bx = (mP2X - mXCoords[p0]) / 2.0f; 122 final float by = (mP2Y - mYCoords[p0]) / 2.0f; 123 final float crossProdAB = ax * by - ay * bx; 124 final float dotProdAB = ax * bx + ay * by; 125 final float normASquare = ax * ax + ay * ay; 126 final float invHalfNormASquare = 1.0f / normASquare / 2.0f; 127 // The slope of the tangent is the mirror image of vector B to vector A. 128 mSlope2X = invHalfNormASquare * (dotProdAB * ax + crossProdAB * ay); 129 mSlope2Y = invHalfNormASquare * (dotProdAB * ay - crossProdAB * ax); 130 } else { 131 // p1 and p2 has no previous valid point. (Interval has only point p1 and p2) 132 mSlope2X = ax; 133 mSlope2Y = ay; 134 } 135 } 136 137 /** 138 * Calculate interpolation value at <code>t</code> in unit interval <code>[0,1]</code>. 139 * <p> 140 * On the unit interval [0,1], given a starting point p1 at t=0 and an ending point p2 at t=1 141 * with the slope of the tangent m1 at p1 and m2 at p2, the polynomial of cubic Hermite curve 142 * can be defined by 143 * p(t) = (1+2t)(1-t)(1-t)*p1 + t(1-t)(1-t)*m1 + (3-2t)t^2*p2 + (t-1)t^2*m2 144 * where t is an element of [0,1]. 145 * <p> 146 * The interpolated XY-coordinates will be set in {@link #mInterpolatedX} and 147 * {@link #mInterpolatedY}. 148 * 149 * @param t the interpolation parameter. The value must be in close interval <code>[0,1]</code>. 150 */ 151 public void interpolate(final float t) { 152 final float omt = 1.0f - t; 153 final float tm2 = 2.0f * t; 154 final float k1 = 1.0f + tm2; 155 final float k2 = 3.0f - tm2; 156 final float omt2 = omt * omt; 157 final float t2 = t * t; 158 mInterpolatedX = (k1 * mP1X + t * mSlope1X) * omt2 + (k2 * mP2X - omt * mSlope2X) * t2; 159 mInterpolatedY = (k1 * mP1Y + t * mSlope1Y) * omt2 + (k2 * mP2Y - omt * mSlope2Y) * t2; 160 } 161 } 162
