PerspectiveTransform.dart

import 'package:flutter/material.dart';

// Ported from com.google.zxing.common.PerspectiveTransform

/// <p>This class implements a perspective transform in two dimensions. Given four source and four
/// destination points, it will compute the transformation implied between them. The code is based
/// directly upon section 3.4.2 of George Wolberg's "Digital Image Warping"; see pages 54-56.</p>
///
/// @author Sean Owen
class PerspectiveTransform {
  final double a11;
  final double a12;
  final double a13;
  final double a21;
  final double a22;
  final double a23;
  final double a31;
  final double a32;
  final double a33;

  PerspectiveTransform(this.a11, this.a21, this.a31, this.a12, this.a22,
      this.a32, this.a13, this.a23, this.a33);

  static PerspectiveTransform quadrilateralToQuadrilateral(
      double x0,
      double y0,
      double x1,
      double y1,
      double x2,
      double y2,
      double x3,
      double y3,
      double x0p,
      double y0p,
      double x1p,
      double y1p,
      double x2p,
      double y2p,
      double x3p,
      double y3p) {
    PerspectiveTransform qToS =
        quadrilateralToSquare(x0, y0, x1, y1, x2, y2, x3, y3);
    PerspectiveTransform sToQ =
        squareToQuadrilateral(x0p, y0p, x1p, y1p, x2p, y2p, x3p, y3p);
    return sToQ.times(qToS);
  }

  List<double> transformPoints(List<double> points) {
    List<double> out = [];
    double a11 = this.a11;
    double a12 = this.a12;
    double a13 = this.a13;
    double a21 = this.a21;
    double a22 = this.a22;
    double a23 = this.a23;
    double a31 = this.a31;
    double a32 = this.a32;
    double a33 = this.a33;
    int maxI = points.length - 1; // points.length must be even
    for (int i = 0; i < maxI; i += 2) {
      double x = points[i];
      double y = points[i + 1];
      double denominator = a13 * x + a23 * y + a33;
      out.add((a11 * x + a21 * y + a31) / denominator);
      out.add((a12 * x + a22 * y + a32) / denominator);
    }
    return points;
  }

  List<Offset> transformPointsFromOffset(List<Offset> points) {
    List<Offset> out = [];
    for (int i = 0; i <  points.length; i++) {
      double x = points[i].dx;
      double y = points[i].dy;
      double denominator = a13 * x + a23 * y + a33;
      out.add(Offset(
        (a11 * x + a21 * y + a31) / denominator,
        (a12 * x + a22 * y + a32) / denominator
      ));
    }
    return out;
  }

  static PerspectiveTransform squareToQuadrilateral(double x0, double y0,
      double x1, double y1, double x2, double y2, double x3, double y3) {
    double dx3 = x0 - x1 + x2 - x3;
    double dy3 = y0 - y1 + y2 - y3;
    if (dx3 == 0 && dy3 == 0) {
      // Affine
      return new PerspectiveTransform(
          x1 - x0, x2 - x1, x0, y1 - y0, y2 - y1, y0, 0, 0, 1);
    } else {
      double dx1 = x1 - x2;
      double dx2 = x3 - x2;
      double dy1 = y1 - y2;
      double dy2 = y3 - y2;
      double denominator = dx1 * dy2 - dx2 * dy1;
      double a13 = (dx3 * dy2 - dx2 * dy3) / denominator;
      double a23 = (dx1 * dy3 - dx3 * dy1) / denominator;
      return new PerspectiveTransform(x1 - x0 + a13 * x1, x3 - x0 + a23 * x3,
          x0, y1 - y0 + a13 * y1, y3 - y0 + a23 * y3, y0, a13, a23, 1);
    }
  }

  static PerspectiveTransform quadrilateralToSquare(double x0, double y0,
      double x1, double y1, double x2, double y2, double x3, double y3) {
    // Here, the adjoint serves as the inverse:
    return squareToQuadrilateral(x0, y0, x1, y1, x2, y2, x3, y3).buildAdjoint();
  }

  PerspectiveTransform buildAdjoint() {
    // Adjoint is the transpose of the cofactor matrix:
    return new PerspectiveTransform(
        a22 * a33 - a23 * a32,
        a23 * a31 - a21 * a33,
        a21 * a32 - a22 * a31,
        a13 * a32 - a12 * a33,
        a11 * a33 - a13 * a31,
        a12 * a31 - a11 * a32,
        a12 * a23 - a13 * a22,
        a13 * a21 - a11 * a23,
        a11 * a22 - a12 * a21);
  }

  PerspectiveTransform times(PerspectiveTransform other) {
    return new PerspectiveTransform(
        a11 * other.a11 + a21 * other.a12 + a31 * other.a13,
        a11 * other.a21 + a21 * other.a22 + a31 * other.a23,
        a11 * other.a31 + a21 * other.a32 + a31 * other.a33,
        a12 * other.a11 + a22 * other.a12 + a32 * other.a13,
        a12 * other.a21 + a22 * other.a22 + a32 * other.a23,
        a12 * other.a31 + a22 * other.a32 + a32 * other.a33,
        a13 * other.a11 + a23 * other.a12 + a33 * other.a13,
        a13 * other.a21 + a23 * other.a22 + a33 * other.a23,
        a13 * other.a31 + a23 * other.a32 + a33 * other.a33);
  }
}