529 lines
15 KiB
C++
529 lines
15 KiB
C++
/*M///////////////////////////////////////////////////////////////////////////////////////
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//
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// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
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//
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// By downloading, copying, installing or using the software you agree to this license.
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// If you do not agree to this license, do not download, install,
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// copy or use the software.
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//
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//
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// License Agreement
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// For Open Source Computer Vision Library
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//
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// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
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// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
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// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
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// Third party copyrights are property of their respective owners.
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//
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// Redistribution and use in source and binary forms, with or without modification,
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// are permitted provided that the following conditions are met:
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//
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// * Redistribution's of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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//
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// * Redistribution's in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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//
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// * The name of the copyright holders may not be used to endorse or promote products
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// derived from this software without specific prior written permission.
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//
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// This software is provided by the copyright holders and contributors "as is" and
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// any express or implied warranties, including, but not limited to, the implied
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// warranties of merchantability and fitness for a particular purpose are disclaimed.
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// In no event shall the Intel Corporation or contributors be liable for any direct,
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// indirect, incidental, special, exemplary, or consequential damages
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// (including, but not limited to, procurement of substitute goods or services;
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// loss of use, data, or profits; or business interruption) however caused
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// and on any theory of liability, whether in contract, strict liability,
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// or tort (including negligence or otherwise) arising in any way out of
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// the use of this software, even if advised of the possibility of such damage.
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//
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//M*/
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#ifndef OPENCV_CORE_AFFINE3_HPP
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#define OPENCV_CORE_AFFINE3_HPP
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#ifdef __cplusplus
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#include <opencv2/core.hpp>
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namespace cv
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{
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//! @addtogroup core
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//! @{
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/** @brief Affine transform
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@todo document
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*/
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template<typename T>
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class Affine3
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{
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public:
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typedef T float_type;
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typedef Matx<float_type, 3, 3> Mat3;
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typedef Matx<float_type, 4, 4> Mat4;
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typedef Vec<float_type, 3> Vec3;
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Affine3();
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//! Augmented affine matrix
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Affine3(const Mat4& affine);
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//! Rotation matrix
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Affine3(const Mat3& R, const Vec3& t = Vec3::all(0));
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//! Rodrigues vector
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Affine3(const Vec3& rvec, const Vec3& t = Vec3::all(0));
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//! Combines all contructors above. Supports 4x4, 4x3, 3x3, 1x3, 3x1 sizes of data matrix
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explicit Affine3(const Mat& data, const Vec3& t = Vec3::all(0));
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//! From 16th element array
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explicit Affine3(const float_type* vals);
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//! Create identity transform
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static Affine3 Identity();
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//! Rotation matrix
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void rotation(const Mat3& R);
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//! Rodrigues vector
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void rotation(const Vec3& rvec);
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//! Combines rotation methods above. Suports 3x3, 1x3, 3x1 sizes of data matrix;
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void rotation(const Mat& data);
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void linear(const Mat3& L);
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void translation(const Vec3& t);
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Mat3 rotation() const;
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Mat3 linear() const;
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Vec3 translation() const;
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//! Rodrigues vector
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Vec3 rvec() const;
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Affine3 inv(int method = cv::DECOMP_SVD) const;
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//! a.rotate(R) is equivalent to Affine(R, 0) * a;
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Affine3 rotate(const Mat3& R) const;
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//! a.rotate(rvec) is equivalent to Affine(rvec, 0) * a;
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Affine3 rotate(const Vec3& rvec) const;
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//! a.translate(t) is equivalent to Affine(E, t) * a;
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Affine3 translate(const Vec3& t) const;
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//! a.concatenate(affine) is equivalent to affine * a;
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Affine3 concatenate(const Affine3& affine) const;
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template <typename Y> operator Affine3<Y>() const;
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template <typename Y> Affine3<Y> cast() const;
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Mat4 matrix;
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#if defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H
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Affine3(const Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>& affine);
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Affine3(const Eigen::Transform<T, 3, Eigen::Affine>& affine);
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operator Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>() const;
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operator Eigen::Transform<T, 3, Eigen::Affine>() const;
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#endif
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};
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template<typename T> static
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Affine3<T> operator*(const Affine3<T>& affine1, const Affine3<T>& affine2);
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template<typename T, typename V> static
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V operator*(const Affine3<T>& affine, const V& vector);
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typedef Affine3<float> Affine3f;
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typedef Affine3<double> Affine3d;
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static Vec3f operator*(const Affine3f& affine, const Vec3f& vector);
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static Vec3d operator*(const Affine3d& affine, const Vec3d& vector);
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template<typename _Tp> class DataType< Affine3<_Tp> >
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{
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public:
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typedef Affine3<_Tp> value_type;
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typedef Affine3<typename DataType<_Tp>::work_type> work_type;
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typedef _Tp channel_type;
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enum { generic_type = 0,
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channels = 16,
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fmt = traits::SafeFmt<channel_type>::fmt + ((channels - 1) << 8)
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#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
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,depth = DataType<channel_type>::depth
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,type = CV_MAKETYPE(depth, channels)
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#endif
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};
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typedef Vec<channel_type, channels> vec_type;
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};
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namespace traits {
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template<typename _Tp>
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struct Depth< Affine3<_Tp> > { enum { value = Depth<_Tp>::value }; };
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template<typename _Tp>
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struct Type< Affine3<_Tp> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, 16) }; };
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} // namespace
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//! @} core
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}
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//! @cond IGNORED
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///////////////////////////////////////////////////////////////////////////////////
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// Implementaiton
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template<typename T> inline
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cv::Affine3<T>::Affine3()
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: matrix(Mat4::eye())
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{}
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template<typename T> inline
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cv::Affine3<T>::Affine3(const Mat4& affine)
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: matrix(affine)
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{}
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template<typename T> inline
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cv::Affine3<T>::Affine3(const Mat3& R, const Vec3& t)
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{
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rotation(R);
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translation(t);
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matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
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matrix.val[15] = 1;
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}
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template<typename T> inline
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cv::Affine3<T>::Affine3(const Vec3& _rvec, const Vec3& t)
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{
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rotation(_rvec);
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translation(t);
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matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
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matrix.val[15] = 1;
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}
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template<typename T> inline
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cv::Affine3<T>::Affine3(const cv::Mat& data, const Vec3& t)
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{
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CV_Assert(data.type() == cv::traits::Type<T>::value);
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if (data.cols == 4 && data.rows == 4)
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{
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data.copyTo(matrix);
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return;
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}
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else if (data.cols == 4 && data.rows == 3)
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{
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rotation(data(Rect(0, 0, 3, 3)));
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translation(data(Rect(3, 0, 1, 3)));
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}
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else
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{
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rotation(data);
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translation(t);
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}
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matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
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matrix.val[15] = 1;
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}
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template<typename T> inline
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cv::Affine3<T>::Affine3(const float_type* vals) : matrix(vals)
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{}
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template<typename T> inline
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cv::Affine3<T> cv::Affine3<T>::Identity()
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{
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return Affine3<T>(cv::Affine3<T>::Mat4::eye());
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}
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template<typename T> inline
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void cv::Affine3<T>::rotation(const Mat3& R)
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{
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linear(R);
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}
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template<typename T> inline
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void cv::Affine3<T>::rotation(const Vec3& _rvec)
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{
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double theta = norm(_rvec);
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if (theta < DBL_EPSILON)
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rotation(Mat3::eye());
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else
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{
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double c = std::cos(theta);
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double s = std::sin(theta);
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double c1 = 1. - c;
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double itheta = (theta != 0) ? 1./theta : 0.;
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Point3_<T> r = _rvec*itheta;
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Mat3 rrt( r.x*r.x, r.x*r.y, r.x*r.z, r.x*r.y, r.y*r.y, r.y*r.z, r.x*r.z, r.y*r.z, r.z*r.z );
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Mat3 r_x( 0, -r.z, r.y, r.z, 0, -r.x, -r.y, r.x, 0 );
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// R = cos(theta)*I + (1 - cos(theta))*r*rT + sin(theta)*[r_x]
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// where [r_x] is [0 -rz ry; rz 0 -rx; -ry rx 0]
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Mat3 R = c*Mat3::eye() + c1*rrt + s*r_x;
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rotation(R);
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}
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}
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//Combines rotation methods above. Suports 3x3, 1x3, 3x1 sizes of data matrix;
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template<typename T> inline
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void cv::Affine3<T>::rotation(const cv::Mat& data)
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{
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CV_Assert(data.type() == cv::traits::Type<T>::value);
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if (data.cols == 3 && data.rows == 3)
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{
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Mat3 R;
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data.copyTo(R);
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rotation(R);
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}
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else if ((data.cols == 3 && data.rows == 1) || (data.cols == 1 && data.rows == 3))
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{
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Vec3 _rvec;
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data.reshape(1, 3).copyTo(_rvec);
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rotation(_rvec);
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}
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else
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CV_Assert(!"Input marix can be 3x3, 1x3 or 3x1");
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}
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template<typename T> inline
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void cv::Affine3<T>::linear(const Mat3& L)
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{
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matrix.val[0] = L.val[0]; matrix.val[1] = L.val[1]; matrix.val[ 2] = L.val[2];
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matrix.val[4] = L.val[3]; matrix.val[5] = L.val[4]; matrix.val[ 6] = L.val[5];
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matrix.val[8] = L.val[6]; matrix.val[9] = L.val[7]; matrix.val[10] = L.val[8];
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}
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template<typename T> inline
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void cv::Affine3<T>::translation(const Vec3& t)
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{
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matrix.val[3] = t[0]; matrix.val[7] = t[1]; matrix.val[11] = t[2];
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}
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template<typename T> inline
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typename cv::Affine3<T>::Mat3 cv::Affine3<T>::rotation() const
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{
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return linear();
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}
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template<typename T> inline
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typename cv::Affine3<T>::Mat3 cv::Affine3<T>::linear() const
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{
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typename cv::Affine3<T>::Mat3 R;
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R.val[0] = matrix.val[0]; R.val[1] = matrix.val[1]; R.val[2] = matrix.val[ 2];
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R.val[3] = matrix.val[4]; R.val[4] = matrix.val[5]; R.val[5] = matrix.val[ 6];
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R.val[6] = matrix.val[8]; R.val[7] = matrix.val[9]; R.val[8] = matrix.val[10];
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return R;
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}
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template<typename T> inline
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typename cv::Affine3<T>::Vec3 cv::Affine3<T>::translation() const
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{
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return Vec3(matrix.val[3], matrix.val[7], matrix.val[11]);
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}
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template<typename T> inline
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typename cv::Affine3<T>::Vec3 cv::Affine3<T>::rvec() const
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{
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cv::Vec3d w;
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cv::Matx33d u, vt, R = rotation();
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cv::SVD::compute(R, w, u, vt, cv::SVD::FULL_UV + cv::SVD::MODIFY_A);
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R = u * vt;
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double rx = R.val[7] - R.val[5];
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double ry = R.val[2] - R.val[6];
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double rz = R.val[3] - R.val[1];
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double s = std::sqrt((rx*rx + ry*ry + rz*rz)*0.25);
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double c = (R.val[0] + R.val[4] + R.val[8] - 1) * 0.5;
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c = c > 1.0 ? 1.0 : c < -1.0 ? -1.0 : c;
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double theta = acos(c);
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if( s < 1e-5 )
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{
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if( c > 0 )
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rx = ry = rz = 0;
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else
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{
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double t;
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t = (R.val[0] + 1) * 0.5;
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rx = std::sqrt(std::max(t, 0.0));
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t = (R.val[4] + 1) * 0.5;
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ry = std::sqrt(std::max(t, 0.0)) * (R.val[1] < 0 ? -1.0 : 1.0);
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t = (R.val[8] + 1) * 0.5;
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rz = std::sqrt(std::max(t, 0.0)) * (R.val[2] < 0 ? -1.0 : 1.0);
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if( fabs(rx) < fabs(ry) && fabs(rx) < fabs(rz) && (R.val[5] > 0) != (ry*rz > 0) )
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rz = -rz;
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theta /= std::sqrt(rx*rx + ry*ry + rz*rz);
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rx *= theta;
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ry *= theta;
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rz *= theta;
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}
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}
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else
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{
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double vth = 1/(2*s);
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vth *= theta;
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rx *= vth; ry *= vth; rz *= vth;
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}
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return cv::Vec3d(rx, ry, rz);
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}
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template<typename T> inline
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cv::Affine3<T> cv::Affine3<T>::inv(int method) const
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{
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return matrix.inv(method);
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}
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template<typename T> inline
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cv::Affine3<T> cv::Affine3<T>::rotate(const Mat3& R) const
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{
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Mat3 Lc = linear();
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Vec3 tc = translation();
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Mat4 result;
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result.val[12] = result.val[13] = result.val[14] = 0;
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result.val[15] = 1;
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for(int j = 0; j < 3; ++j)
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{
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for(int i = 0; i < 3; ++i)
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{
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float_type value = 0;
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for(int k = 0; k < 3; ++k)
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value += R(j, k) * Lc(k, i);
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result(j, i) = value;
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}
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result(j, 3) = R.row(j).dot(tc.t());
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}
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return result;
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}
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template<typename T> inline
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cv::Affine3<T> cv::Affine3<T>::rotate(const Vec3& _rvec) const
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{
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return rotate(Affine3f(_rvec).rotation());
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}
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template<typename T> inline
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cv::Affine3<T> cv::Affine3<T>::translate(const Vec3& t) const
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{
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Mat4 m = matrix;
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m.val[ 3] += t[0];
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m.val[ 7] += t[1];
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m.val[11] += t[2];
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return m;
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}
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template<typename T> inline
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cv::Affine3<T> cv::Affine3<T>::concatenate(const Affine3<T>& affine) const
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{
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return (*this).rotate(affine.rotation()).translate(affine.translation());
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}
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template<typename T> template <typename Y> inline
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cv::Affine3<T>::operator Affine3<Y>() const
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{
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return Affine3<Y>(matrix);
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}
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template<typename T> template <typename Y> inline
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cv::Affine3<Y> cv::Affine3<T>::cast() const
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{
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return Affine3<Y>(matrix);
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}
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template<typename T> inline
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cv::Affine3<T> cv::operator*(const cv::Affine3<T>& affine1, const cv::Affine3<T>& affine2)
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{
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return affine2.concatenate(affine1);
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}
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template<typename T, typename V> inline
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V cv::operator*(const cv::Affine3<T>& affine, const V& v)
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{
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const typename Affine3<T>::Mat4& m = affine.matrix;
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V r;
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r.x = m.val[0] * v.x + m.val[1] * v.y + m.val[ 2] * v.z + m.val[ 3];
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r.y = m.val[4] * v.x + m.val[5] * v.y + m.val[ 6] * v.z + m.val[ 7];
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r.z = m.val[8] * v.x + m.val[9] * v.y + m.val[10] * v.z + m.val[11];
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return r;
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}
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static inline
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cv::Vec3f cv::operator*(const cv::Affine3f& affine, const cv::Vec3f& v)
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{
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const cv::Matx44f& m = affine.matrix;
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cv::Vec3f r;
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r.val[0] = m.val[0] * v[0] + m.val[1] * v[1] + m.val[ 2] * v[2] + m.val[ 3];
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r.val[1] = m.val[4] * v[0] + m.val[5] * v[1] + m.val[ 6] * v[2] + m.val[ 7];
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r.val[2] = m.val[8] * v[0] + m.val[9] * v[1] + m.val[10] * v[2] + m.val[11];
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return r;
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}
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static inline
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cv::Vec3d cv::operator*(const cv::Affine3d& affine, const cv::Vec3d& v)
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{
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const cv::Matx44d& m = affine.matrix;
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cv::Vec3d r;
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r.val[0] = m.val[0] * v[0] + m.val[1] * v[1] + m.val[ 2] * v[2] + m.val[ 3];
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r.val[1] = m.val[4] * v[0] + m.val[5] * v[1] + m.val[ 6] * v[2] + m.val[ 7];
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r.val[2] = m.val[8] * v[0] + m.val[9] * v[1] + m.val[10] * v[2] + m.val[11];
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return r;
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}
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#if defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H
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|
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template<typename T> inline
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cv::Affine3<T>::Affine3(const Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>& affine)
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{
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cv::Mat(4, 4, cv::traits::Type<T>::value, affine.matrix().data()).copyTo(matrix);
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}
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|
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template<typename T> inline
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cv::Affine3<T>::Affine3(const Eigen::Transform<T, 3, Eigen::Affine>& affine)
|
|
{
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Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)> a = affine;
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cv::Mat(4, 4, cv::traits::Type<T>::value, a.matrix().data()).copyTo(matrix);
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}
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|
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template<typename T> inline
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cv::Affine3<T>::operator Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>() const
|
|
{
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Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)> r;
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cv::Mat hdr(4, 4, cv::traits::Type<T>::value, r.matrix().data());
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cv::Mat(matrix, false).copyTo(hdr);
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return r;
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|
}
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|
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template<typename T> inline
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cv::Affine3<T>::operator Eigen::Transform<T, 3, Eigen::Affine>() const
|
|
{
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|
return this->operator Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>();
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|
}
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|
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#endif /* defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H */
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|
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//! @endcond
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|
|
|
#endif /* __cplusplus */
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|
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|
#endif /* OPENCV_CORE_AFFINE3_HPP */
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