2 * Copyright 2007 ZXing authors
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4 * Licensed under the Apache License, Version 2.0 (the "License");
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5 * you may not use this file except in compliance with the License.
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6 * You may obtain a copy of the License at
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8 * http://www.apache.org/licenses/LICENSE-2.0
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10 * Unless required by applicable law or agreed to in writing, software
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11 * distributed under the License is distributed on an "AS IS" BASIS,
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12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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13 * See the License for the specific language governing permissions and
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14 * limitations under the License.
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17 package com.google.zxing.common;
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20 * <p>This class implements a perspective transform in two dimensions. Given four source and four
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21 * destination points, it will compute the transformation implied between them. The code is based
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22 * directly upon section 3.4.2 of George Wolberg's "Digital Image Warping"; see pages 54-56.</p>
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26 public final class PerspectiveTransform {
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28 private final float a11, a12, a13, a21, a22, a23, a31, a32, a33;
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30 private PerspectiveTransform(float a11, float a21, float a31,
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31 float a12, float a22, float a32,
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32 float a13, float a23, float a33) {
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44 public static PerspectiveTransform quadrilateralToQuadrilateral(float x0, float y0,
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48 float x0p, float y0p,
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49 float x1p, float y1p,
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50 float x2p, float y2p,
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51 float x3p, float y3p) {
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53 PerspectiveTransform qToS = quadrilateralToSquare(x0, y0, x1, y1, x2, y2, x3, y3);
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54 PerspectiveTransform sToQ = squareToQuadrilateral(x0p, y0p, x1p, y1p, x2p, y2p, x3p, y3p);
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55 return sToQ.times(qToS);
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58 public void transformPoints(float[] points) {
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59 int max = points.length;
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60 float a11 = this.a11;
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61 float a12 = this.a12;
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62 float a13 = this.a13;
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63 float a21 = this.a21;
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64 float a22 = this.a22;
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65 float a23 = this.a23;
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66 float a31 = this.a31;
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67 float a32 = this.a32;
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68 float a33 = this.a33;
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69 for (int i = 0; i < max; i += 2) {
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70 float x = points[i];
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71 float y = points[i + 1];
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72 float denominator = a13 * x + a23 * y + a33;
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73 points[i] = (a11 * x + a21 * y + a31) / denominator;
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74 points[i + 1] = (a12 * x + a22 * y + a32) / denominator;
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78 /** Convenience method, not optimized for performance. */
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79 public void transformPoints(float[] xValues, float[] yValues) {
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80 int n = xValues.length;
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81 for (int i = 0; i < n; i ++) {
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82 float x = xValues[i];
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83 float y = yValues[i];
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84 float denominator = a13 * x + a23 * y + a33;
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85 xValues[i] = (a11 * x + a21 * y + a31) / denominator;
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86 yValues[i] = (a12 * x + a22 * y + a32) / denominator;
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90 public static PerspectiveTransform squareToQuadrilateral(float x0, float y0,
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93 float x3, float y3) {
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94 float dy2 = y3 - y2;
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95 float dy3 = y0 - y1 + y2 - y3;
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96 if (dy2 == 0.0f && dy3 == 0.0f) {
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97 return new PerspectiveTransform(x1 - x0, x2 - x1, x0,
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98 y1 - y0, y2 - y1, y0,
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101 float dx1 = x1 - x2;
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102 float dx2 = x3 - x2;
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103 float dx3 = x0 - x1 + x2 - x3;
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104 float dy1 = y1 - y2;
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105 float denominator = dx1 * dy2 - dx2 * dy1;
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106 float a13 = (dx3 * dy2 - dx2 * dy3) / denominator;
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107 float a23 = (dx1 * dy3 - dx3 * dy1) / denominator;
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108 return new PerspectiveTransform(x1 - x0 + a13 * x1, x3 - x0 + a23 * x3, x0,
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109 y1 - y0 + a13 * y1, y3 - y0 + a23 * y3, y0,
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114 public static PerspectiveTransform quadrilateralToSquare(float x0, float y0,
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115 float x1, float y1,
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116 float x2, float y2,
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117 float x3, float y3) {
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118 // Here, the adjoint serves as the inverse:
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119 return squareToQuadrilateral(x0, y0, x1, y1, x2, y2, x3, y3).buildAdjoint();
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122 PerspectiveTransform buildAdjoint() {
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123 // Adjoint is the transpose of the cofactor matrix:
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124 return new PerspectiveTransform(a22 * a33 - a23 * a32,
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125 a23 * a31 - a21 * a33,
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126 a21 * a32 - a22 * a31,
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127 a13 * a32 - a12 * a33,
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128 a11 * a33 - a13 * a31,
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129 a12 * a31 - a11 * a32,
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130 a12 * a23 - a13 * a22,
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131 a13 * a21 - a11 * a23,
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132 a11 * a22 - a12 * a21);
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135 PerspectiveTransform times(PerspectiveTransform other) {
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136 return new PerspectiveTransform(a11 * other.a11 + a21 * other.a12 + a31 * other.a13,
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137 a11 * other.a21 + a21 * other.a22 + a31 * other.a23,
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138 a11 * other.a31 + a21 * other.a32 + a31 * other.a33,
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139 a12 * other.a11 + a22 * other.a12 + a32 * other.a13,
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140 a12 * other.a21 + a22 * other.a22 + a32 * other.a23,
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141 a12 * other.a31 + a22 * other.a32 + a32 * other.a33,
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142 a13 * other.a11 + a23 * other.a12 + a33 * other.a13,
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143 a13 * other.a21 + a23 * other.a22 + a33 * other.a23,
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144 a13 * other.a31 + a23 * other.a32 + a33 * other.a33);
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