82 lines
2.3 KiB
C++
82 lines
2.3 KiB
C++
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/*
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* Copyright 2016 Nu-book Inc.
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* Copyright 2016 ZXing authors
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* Copyright 2020 Axel Waggershauser
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*/
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// SPDX-License-Identifier: Apache-2.0
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#include "PerspectiveTransform.h"
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#include <array>
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namespace ZXing {
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PerspectiveTransform PerspectiveTransform::inverse() const
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{
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// Here, the adjoint serves as the inverse:
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// Adjoint is the transpose of the cofactor matrix:
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return {
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a22 * a33 - a23 * a32,
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a23 * a31 - a21 * a33,
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a21 * a32 - a22 * a31,
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a13 * a32 - a12 * a33,
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a11 * a33 - a13 * a31,
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a12 * a31 - a11 * a32,
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a12 * a23 - a13 * a22,
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a13 * a21 - a11 * a23,
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a11 * a22 - a12 * a21
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};
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}
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PerspectiveTransform PerspectiveTransform::times(const PerspectiveTransform& other) const
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{
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return {
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a11 * other.a11 + a21 * other.a12 + a31 * other.a13,
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a11 * other.a21 + a21 * other.a22 + a31 * other.a23,
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a11 * other.a31 + a21 * other.a32 + a31 * other.a33,
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a12 * other.a11 + a22 * other.a12 + a32 * other.a13,
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a12 * other.a21 + a22 * other.a22 + a32 * other.a23,
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a12 * other.a31 + a22 * other.a32 + a32 * other.a33,
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a13 * other.a11 + a23 * other.a12 + a33 * other.a13,
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a13 * other.a21 + a23 * other.a22 + a33 * other.a23,
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a13 * other.a31 + a23 * other.a32 + a33 * other.a33
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};
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}
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PerspectiveTransform PerspectiveTransform::UnitSquareTo(const QuadrilateralF& q)
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{
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auto [x0, y0, x1, y1, x2, y2, x3, y3] = reinterpret_cast<const std::array<PointF::value_t, 8>&>(q);
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auto d3 = q[0] - q[1] + q[2] - q[3];
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if (d3 == PointF(0, 0)) {
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// Affine
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return {x1 - x0, x2 - x1, x0,
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y1 - y0, y2 - y1, y0,
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0.0f, 0.0f, 1.0f};
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} else {
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auto d1 = q[1] - q[2];
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auto d2 = q[3] - q[2];
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auto denominator = cross(d1, d2);
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auto a13 = cross(d3, d2) / denominator;
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auto a23 = cross(d1, d3) / denominator;
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return {x1 - x0 + a13 * x1, x3 - x0 + a23 * x3, x0,
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y1 - y0 + a13 * y1, y3 - y0 + a23 * y3, y0,
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a13, a23, 1.0f};
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}
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}
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PerspectiveTransform::PerspectiveTransform(const QuadrilateralF& src, const QuadrilateralF& dst)
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{
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if (!IsConvex(src) || !IsConvex(dst))
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return;
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*this = UnitSquareTo(dst).times(UnitSquareTo(src).inverse());
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}
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PointF PerspectiveTransform::operator()(PointF p) const
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{
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auto denominator = a13 * p.x + a23 * p.y + a33;
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return {(a11 * p.x + a21 * p.y + a31) / denominator, (a12 * p.x + a22 * p.y + a32) / denominator};
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}
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} // ZXing
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