2 * Copyright 2007 Google Inc.
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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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18 * <p>This class implements a perspective transform in two dimensions. Given four source and four destination
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19 * points, it will compute the transformation implied between them. The code is based directly upon section
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20 * 3.4.2 of George Wolberg's "Digital Image Warping"; see pages 54-56.</p>
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22 * @author srowen@google.com (Sean Owen)
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24 package com.google.zxing.qrcode.detector;
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26 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 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 PerspectiveTransform product = sToQ.times(qToS);
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59 void transformPoints(float[] points) {
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60 int max = points.length;
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61 float a11 = this.a11;
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62 float a12 = this.a12;
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63 float a13 = this.a13;
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64 float a21 = this.a21;
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65 float a22 = this.a22;
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66 float a23 = this.a23;
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67 float a31 = this.a31;
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68 float a32 = this.a32;
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69 float a33 = this.a33;
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70 for (int i = 0; i < max; i += 2) {
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71 float x = points[i];
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72 float y = points[i+1];
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73 float denominator = a13*x + a23*y + a33;
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74 points[i] = (a11*x + a21*y + a31) / denominator;
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75 points[i+1] = (a12*x + a22*y + a32) / denominator;
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79 static PerspectiveTransform squareToQuadrilateral(float x0, float y0,
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82 float x3, float y3) {
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83 float dy2 = y3 - y2;
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84 float dy3 = y0 - y1 + y2 - y3;
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85 if (dy2 == 0.0f && dy3 == 0.0f) {
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86 return new PerspectiveTransform(x1 - x0, x2 - x1, x0,
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87 y1 - y0, y2 - y1, y0,
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90 float dx1 = x1 - x2;
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91 float dx2 = x3 - x2;
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92 float dx3 = x0 - x1 + x2 - x3;
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93 float dy1 = y1 - y2;
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94 float denominator = dx1*dy2 - dx2*dy1;
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95 float a13 = (dx3*dy2 - dx2*dy3) / denominator;
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96 float a23 = (dx1*dy3 - dx3*dy1) / denominator;
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97 return new PerspectiveTransform(x1 - x0 + a13*x1, x3 - x0 + a23*x3, x0,
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98 y1 - y0 + a13*y1, y3 - y0 + a23*y3, y0,
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103 static PerspectiveTransform quadrilateralToSquare(float x0, float y0,
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104 float x1, float y1,
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105 float x2, float y2,
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106 float x3, float y3) {
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107 // Here, the adjoint serves as the inverse:
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108 return squareToQuadrilateral(x0, y0, x1, y1, x2, y2, x3, y3).buildAdjoint();
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111 PerspectiveTransform buildAdjoint() {
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112 // Adjoint is the transpose of the cofactor matrix:
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113 return new PerspectiveTransform(a22*a33 - a23*a32,
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121 a11*a22 - a12*a21);
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124 PerspectiveTransform times(PerspectiveTransform other) {
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125 return new PerspectiveTransform(a11*other.a11 + a21*other.a12 + a31*other.a13,
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126 a11*other.a21 + a21*other.a22 + a31*other.a23,
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127 a11*other.a31 + a21*other.a32 + a31*other.a33,
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128 a12*other.a11 + a22*other.a12 + a32*other.a13,
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129 a12*other.a21 + a22*other.a22 + a32*other.a23,
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130 a12*other.a31 + a22*other.a32 + a32*other.a33,
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131 a13*other.a11 + a23*other.a12 + a33*other.a13,
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132 a13*other.a21 + a23*other.a22 + a33*other.a23,
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133 a13*other.a31 + a23*other.a32 + a33*other.a33);
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