affine.hpp

00001 /*M///////////////////////////////////////////////////////////////////////////////////////
00002 //
00003 //  IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
00004 //
00005 //  By downloading, copying, installing or using the software you agree to this license.
00006 //  If you do not agree to this license, do not download, install,
00007 //  copy or use the software.
00008 //
00009 //
00010 //                          License Agreement
00011 //                For Open Source Computer Vision Library
00012 //
00013 // Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
00014 // Copyright (C) 2009, Willow Garage Inc., all rights reserved.
00015 // Copyright (C) 2013, OpenCV Foundation, all rights reserved.
00016 // Third party copyrights are property of their respective owners.
00017 //
00018 // Redistribution and use in source and binary forms, with or without modification,
00019 // are permitted provided that the following conditions are met:
00020 //
00021 //   * Redistribution's of source code must retain the above copyright notice,
00022 //     this list of conditions and the following disclaimer.
00023 //
00024 //   * Redistribution's in binary form must reproduce the above copyright notice,
00025 //     this list of conditions and the following disclaimer in the documentation
00026 //     and/or other materials provided with the distribution.
00027 //
00028 //   * The name of the copyright holders may not be used to endorse or promote products
00029 //     derived from this software without specific prior written permission.
00030 //
00031 // This software is provided by the copyright holders and contributors "as is" and
00032 // any express or implied warranties, including, but not limited to, the implied
00033 // warranties of merchantability and fitness for a particular purpose are disclaimed.
00034 // In no event shall the Intel Corporation or contributors be liable for any direct,
00035 // indirect, incidental, special, exemplary, or consequential damages
00036 // (including, but not limited to, procurement of substitute goods or services;
00037 // loss of use, data, or profits; or business interruption) however caused
00038 // and on any theory of liability, whether in contract, strict liability,
00039 // or tort (including negligence or otherwise) arising in any way out of
00040 // the use of this software, even if advised of the possibility of such damage.
00041 //
00042 //M*/
00043 
00044 #ifndef OPENCV_CORE_AFFINE3_HPP
00045 #define OPENCV_CORE_AFFINE3_HPP
00046 
00047 #ifdef __cplusplus
00048 
00049 #include <opencv2/core.hpp>
00050 
00051 namespace cv
00052 {
00053 
00054 //! @addtogroup core
00055 //! @{
00056 
00057     /** @brief Affine transform
00058       @todo document
00059      */
00060     template<typename T>
00061     class Affine3
00062     {
00063     public:
00064         typedef T float_type;
00065         typedef Matx<float_type, 3, 3> Mat3;
00066         typedef Matx<float_type, 4, 4>  Mat4 ;
00067         typedef Vec<float_type, 3> Vec3;
00068 
00069         Affine3();
00070 
00071         //! Augmented affine matrix
00072         Affine3(const Mat4 & affine);
00073 
00074         //! Rotation matrix
00075         Affine3(const Mat3& R, const Vec3& t = Vec3::all(0));
00076 
00077         //! Rodrigues vector
00078         Affine3(const Vec3& rvec, const Vec3& t = Vec3::all(0));
00079 
00080         //! Combines all contructors above. Supports 4x4, 4x3, 3x3, 1x3, 3x1 sizes of data matrix
00081         explicit Affine3(const Mat& data, const Vec3& t = Vec3::all(0));
00082 
00083         //! From 16th element array
00084         explicit Affine3(const float_type* vals);
00085 
00086         //! Create identity transform
00087         static Affine3 Identity();
00088 
00089         //! Rotation matrix
00090         void rotation(const Mat3& R);
00091 
00092         //! Rodrigues vector
00093         void rotation(const Vec3& rvec);
00094 
00095         //! Combines rotation methods above. Suports 3x3, 1x3, 3x1 sizes of data matrix;
00096         void rotation(const Mat& data);
00097 
00098         void linear(const Mat3& L);
00099         void translation(const Vec3& t);
00100 
00101         Mat3 rotation() const;
00102         Mat3 linear() const;
00103         Vec3 translation() const;
00104 
00105         //! Rodrigues vector
00106         Vec3 rvec() const;
00107 
00108         Affine3 inv(int method = cv::DECOMP_SVD) const;
00109 
00110         //! a.rotate(R) is equivalent to Affine(R, 0) * a;
00111         Affine3 rotate(const Mat3& R) const;
00112 
00113         //! a.rotate(rvec) is equivalent to Affine(rvec, 0) * a;
00114         Affine3 rotate(const Vec3& rvec) const;
00115 
00116         //! a.translate(t) is equivalent to Affine(E, t) * a;
00117         Affine3 translate(const Vec3& t) const;
00118 
00119         //! a.concatenate(affine) is equivalent to affine * a;
00120         Affine3 concatenate(const Affine3& affine) const;
00121 
00122         template <typename Y> operator Affine3<Y>() const;
00123 
00124         template <typename Y> Affine3<Y> cast() const;
00125 
00126         Mat4  matrix;
00127 
00128 #if defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H
00129         Affine3(const Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>& affine);
00130         Affine3(const Eigen::Transform<T, 3, Eigen::Affine>& affine);
00131         operator Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>() const;
00132         operator Eigen::Transform<T, 3, Eigen::Affine>() const;
00133 #endif
00134     };
00135 
00136     template<typename T> static
00137     Affine3<T> operator*(const Affine3<T>& affine1, const Affine3<T>& affine2);
00138 
00139     template<typename T, typename V> static
00140     V operator*(const Affine3<T>& affine, const V& vector);
00141 
00142     typedef Affine3<float> Affine3f;
00143     typedef Affine3<double> Affine3d;
00144 
00145     static Vec3f operator*(const Affine3f& affine, const Vec3f& vector);
00146     static Vec3d operator*(const Affine3d& affine, const Vec3d& vector);
00147 
00148     template<typename _Tp> class DataType< Affine3<_Tp> >
00149     {
00150     public:
00151         typedef Affine3<_Tp>                               value_type;
00152         typedef Affine3<typename DataType<_Tp>::work_type> work_type;
00153         typedef _Tp                                        channel_type;
00154 
00155         enum { generic_type = 0,
00156                depth        = DataType<channel_type>::depth,
00157                channels     = 16,
00158                fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
00159                type         = CV_MAKETYPE(depth, channels)
00160              };
00161 
00162         typedef Vec<channel_type, channels> vec_type;
00163     };
00164 
00165 //! @} core
00166 
00167 }
00168 
00169 //! @cond IGNORED
00170 
00171 ///////////////////////////////////////////////////////////////////////////////////
00172 // Implementaiton
00173 
00174 template<typename T> inline
00175 cv::Affine3<T>::Affine3()
00176     : matrix(Mat4::eye())
00177 {}
00178 
00179 template<typename T> inline
00180 cv::Affine3<T>::Affine3(const Mat4& affine)
00181     : matrix(affine)
00182 {}
00183 
00184 template<typename T> inline
00185 cv::Affine3<T>::Affine3(const Mat3& R, const Vec3& t)
00186 {
00187     rotation(R);
00188     translation(t);
00189     matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
00190     matrix.val[15] = 1;
00191 }
00192 
00193 template<typename T> inline
00194 cv::Affine3<T>::Affine3(const Vec3& _rvec, const Vec3& t)
00195 {
00196     rotation(_rvec);
00197     translation(t);
00198     matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
00199     matrix.val[15] = 1;
00200 }
00201 
00202 template<typename T> inline
00203 cv::Affine3<T>::Affine3(const cv::Mat& data, const Vec3& t)
00204 {
00205     CV_Assert(data.type() == cv::DataType<T>::type);
00206 
00207     if (data.cols == 4 && data.rows == 4)
00208     {
00209         data.copyTo(matrix);
00210         return;
00211     }
00212     else if (data.cols == 4 && data.rows == 3)
00213     {
00214         rotation(data(Rect(0, 0, 3, 3)));
00215         translation(data(Rect(3, 0, 1, 3)));
00216         return;
00217     }
00218 
00219     rotation(data);
00220     translation(t);
00221     matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
00222     matrix.val[15] = 1;
00223 }
00224 
00225 template<typename T> inline
00226 cv::Affine3<T>::Affine3(const float_type* vals) : matrix(vals)
00227 {}
00228 
00229 template<typename T> inline
00230 cv::Affine3<T> cv::Affine3<T>::Identity()
00231 {
00232     return Affine3<T>(cv::Affine3<T>::Mat4::eye());
00233 }
00234 
00235 template<typename T> inline
00236 void cv::Affine3<T>::rotation(const Mat3& R)
00237 {
00238     linear(R);
00239 }
00240 
00241 template<typename T> inline
00242 void cv::Affine3<T>::rotation(const Vec3& _rvec)
00243 {
00244     double theta = norm(_rvec);
00245 
00246     if (theta < DBL_EPSILON)
00247         rotation(Mat3::eye());
00248     else
00249     {
00250         double c = std::cos(theta);
00251         double s = std::sin(theta);
00252         double c1 = 1. - c;
00253         double itheta = (theta != 0) ? 1./theta : 0.;
00254 
00255         Point3_<T> r = _rvec*itheta;
00256 
00257         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 );
00258         Mat3 r_x( 0, -r.z, r.y, r.z, 0, -r.x, -r.y, r.x, 0 );
00259 
00260         // R = cos(theta)*I + (1 - cos(theta))*r*rT + sin(theta)*[r_x]
00261         // where [r_x] is [0 -rz ry; rz 0 -rx; -ry rx 0]
00262         Mat3 R = c*Mat3::eye() + c1*rrt + s*r_x;
00263 
00264         rotation(R);
00265     }
00266 }
00267 
00268 //Combines rotation methods above. Suports 3x3, 1x3, 3x1 sizes of data matrix;
00269 template<typename T> inline
00270 void cv::Affine3<T>::rotation(const cv::Mat& data)
00271 {
00272     CV_Assert(data.type() == cv::DataType<T>::type);
00273 
00274     if (data.cols == 3 && data.rows == 3)
00275     {
00276         Mat3 R;
00277         data.copyTo(R);
00278         rotation(R);
00279     }
00280     else if ((data.cols == 3 && data.rows == 1) || (data.cols == 1 && data.rows == 3))
00281     {
00282         Vec3 _rvec;
00283         data.reshape(1, 3).copyTo(_rvec);
00284         rotation(_rvec);
00285     }
00286     else
00287         CV_Assert(!"Input marix can be 3x3, 1x3 or 3x1");
00288 }
00289 
00290 template<typename T> inline
00291 void cv::Affine3<T>::linear(const Mat3& L)
00292 {
00293     matrix.val[0] = L.val[0]; matrix.val[1] = L.val[1];  matrix.val[ 2] = L.val[2];
00294     matrix.val[4] = L.val[3]; matrix.val[5] = L.val[4];  matrix.val[ 6] = L.val[5];
00295     matrix.val[8] = L.val[6]; matrix.val[9] = L.val[7];  matrix.val[10] = L.val[8];
00296 }
00297 
00298 template<typename T> inline
00299 void cv::Affine3<T>::translation(const Vec3& t)
00300 {
00301     matrix.val[3] = t[0]; matrix.val[7] = t[1]; matrix.val[11] = t[2];
00302 }
00303 
00304 template<typename T> inline
00305 typename cv::Affine3<T>::Mat3 cv::Affine3<T>::rotation() const
00306 {
00307     return linear();
00308 }
00309 
00310 template<typename T> inline
00311 typename cv::Affine3<T>::Mat3 cv::Affine3<T>::linear() const
00312 {
00313     typename cv::Affine3<T>::Mat3 R;
00314     R.val[0] = matrix.val[0];  R.val[1] = matrix.val[1];  R.val[2] = matrix.val[ 2];
00315     R.val[3] = matrix.val[4];  R.val[4] = matrix.val[5];  R.val[5] = matrix.val[ 6];
00316     R.val[6] = matrix.val[8];  R.val[7] = matrix.val[9];  R.val[8] = matrix.val[10];
00317     return R;
00318 }
00319 
00320 template<typename T> inline
00321 typename cv::Affine3<T>::Vec3 cv::Affine3<T>::translation() const
00322 {
00323     return Vec3(matrix.val[3], matrix.val[7], matrix.val[11]);
00324 }
00325 
00326 template<typename T> inline
00327 typename cv::Affine3<T>::Vec3 cv::Affine3<T>::rvec() const
00328 {
00329     cv::Vec3d w;
00330     cv::Matx33d u, vt, R = rotation();
00331     cv::SVD::compute(R, w, u, vt, cv::SVD::FULL_UV + cv::SVD::MODIFY_A);
00332     R = u * vt;
00333 
00334     double rx = R.val[7] - R.val[5];
00335     double ry = R.val[2] - R.val[6];
00336     double rz = R.val[3] - R.val[1];
00337 
00338     double s = std::sqrt((rx*rx + ry*ry + rz*rz)*0.25);
00339     double c = (R.val[0] + R.val[4] + R.val[8] - 1) * 0.5;
00340     c = c > 1.0 ? 1.0 : c < -1.0 ? -1.0 : c;
00341     double theta = acos(c);
00342 
00343     if( s < 1e-5 )
00344     {
00345         if( c > 0 )
00346             rx = ry = rz = 0;
00347         else
00348         {
00349             double t;
00350             t = (R.val[0] + 1) * 0.5;
00351             rx = std::sqrt(std::max(t, 0.0));
00352             t = (R.val[4] + 1) * 0.5;
00353             ry = std::sqrt(std::max(t, 0.0)) * (R.val[1] < 0 ? -1.0 : 1.0);
00354             t = (R.val[8] + 1) * 0.5;
00355             rz = std::sqrt(std::max(t, 0.0)) * (R.val[2] < 0 ? -1.0 : 1.0);
00356 
00357             if( fabs(rx) < fabs(ry) && fabs(rx) < fabs(rz) && (R.val[5] > 0) != (ry*rz > 0) )
00358                 rz = -rz;
00359             theta /= std::sqrt(rx*rx + ry*ry + rz*rz);
00360             rx *= theta;
00361             ry *= theta;
00362             rz *= theta;
00363         }
00364     }
00365     else
00366     {
00367         double vth = 1/(2*s);
00368         vth *= theta;
00369         rx *= vth; ry *= vth; rz *= vth;
00370     }
00371 
00372     return cv::Vec3d(rx, ry, rz);
00373 }
00374 
00375 template<typename T> inline
00376 cv::Affine3<T> cv::Affine3<T>::inv(int method) const
00377 {
00378     return matrix.inv(method);
00379 }
00380 
00381 template<typename T> inline
00382 cv::Affine3<T> cv::Affine3<T>::rotate(const Mat3& R) const
00383 {
00384     Mat3 Lc = linear();
00385     Vec3 tc = translation();
00386     Mat4 result;
00387     result.val[12] = result.val[13] = result.val[14] = 0;
00388     result.val[15] = 1;
00389 
00390     for(int j = 0; j < 3; ++j)
00391     {
00392         for(int i = 0; i < 3; ++i)
00393         {
00394             float_type value = 0;
00395             for(int k = 0; k < 3; ++k)
00396                 value += R(j, k) * Lc(k, i);
00397             result(j, i) = value;
00398         }
00399 
00400         result(j, 3) = R.row(j).dot(tc.t());
00401     }
00402     return result;
00403 }
00404 
00405 template<typename T> inline
00406 cv::Affine3<T> cv::Affine3<T>::rotate(const Vec3& _rvec) const
00407 {
00408     return rotate(Affine3f(_rvec).rotation());
00409 }
00410 
00411 template<typename T> inline
00412 cv::Affine3<T> cv::Affine3<T>::translate(const Vec3& t) const
00413 {
00414     Mat4 m = matrix;
00415     m.val[ 3] += t[0];
00416     m.val[ 7] += t[1];
00417     m.val[11] += t[2];
00418     return m;
00419 }
00420 
00421 template<typename T> inline
00422 cv::Affine3<T> cv::Affine3<T>::concatenate(const Affine3<T>& affine) const
00423 {
00424     return (*this).rotate(affine.rotation()).translate(affine.translation());
00425 }
00426 
00427 template<typename T> template <typename Y> inline
00428 cv::Affine3<T>::operator Affine3<Y>() const
00429 {
00430     return Affine3<Y>(matrix);
00431 }
00432 
00433 template<typename T> template <typename Y> inline
00434 cv::Affine3<Y> cv::Affine3<T>::cast() const
00435 {
00436     return Affine3<Y>(matrix);
00437 }
00438 
00439 template<typename T> inline
00440 cv::Affine3<T> cv::operator*(const cv::Affine3<T>& affine1, const cv::Affine3<T>& affine2)
00441 {
00442     return affine2.concatenate(affine1);
00443 }
00444 
00445 template<typename T, typename V> inline
00446 V cv::operator*(const cv::Affine3<T>& affine, const V& v)
00447 {
00448     const typename Affine3<T>::Mat4& m = affine.matrix;
00449 
00450     V r;
00451     r.x = m.val[0] * v.x + m.val[1] * v.y + m.val[ 2] * v.z + m.val[ 3];
00452     r.y = m.val[4] * v.x + m.val[5] * v.y + m.val[ 6] * v.z + m.val[ 7];
00453     r.z = m.val[8] * v.x + m.val[9] * v.y + m.val[10] * v.z + m.val[11];
00454     return r;
00455 }
00456 
00457 static inline
00458 cv::Vec3f cv::operator*(const cv::Affine3f& affine, const cv::Vec3f& v)
00459 {
00460     const cv::Matx44f& m = affine.matrix;
00461     cv::Vec3f r;
00462     r.val[0] = m.val[0] * v[0] + m.val[1] * v[1] + m.val[ 2] * v[2] + m.val[ 3];
00463     r.val[1] = m.val[4] * v[0] + m.val[5] * v[1] + m.val[ 6] * v[2] + m.val[ 7];
00464     r.val[2] = m.val[8] * v[0] + m.val[9] * v[1] + m.val[10] * v[2] + m.val[11];
00465     return r;
00466 }
00467 
00468 static inline
00469 cv::Vec3d cv::operator*(const cv::Affine3d& affine, const cv::Vec3d& v)
00470 {
00471     const cv::Matx44d& m = affine.matrix;
00472     cv::Vec3d r;
00473     r.val[0] = m.val[0] * v[0] + m.val[1] * v[1] + m.val[ 2] * v[2] + m.val[ 3];
00474     r.val[1] = m.val[4] * v[0] + m.val[5] * v[1] + m.val[ 6] * v[2] + m.val[ 7];
00475     r.val[2] = m.val[8] * v[0] + m.val[9] * v[1] + m.val[10] * v[2] + m.val[11];
00476     return r;
00477 }
00478 
00479 
00480 
00481 #if defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H
00482 
00483 template<typename T> inline
00484 cv::Affine3<T>::Affine3(const Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>& affine)
00485 {
00486     cv::Mat(4, 4, cv::DataType<T>::type, affine.matrix().data()).copyTo(matrix);
00487 }
00488 
00489 template<typename T> inline
00490 cv::Affine3<T>::Affine3(const Eigen::Transform<T, 3, Eigen::Affine>& affine)
00491 {
00492     Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)> a = affine;
00493     cv::Mat(4, 4, cv::DataType<T>::type, a.matrix().data()).copyTo(matrix);
00494 }
00495 
00496 template<typename T> inline
00497 cv::Affine3<T>::operator Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>() const
00498 {
00499     Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)> r;
00500     cv::Mat hdr(4, 4, cv::DataType<T>::type, r.matrix().data());
00501     cv::Mat(matrix, false).copyTo(hdr);
00502     return r;
00503 }
00504 
00505 template<typename T> inline
00506 cv::Affine3<T>::operator Eigen::Transform<T, 3, Eigen::Affine>() const
00507 {
00508     return this->operator Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>();
00509 }
00510 
00511 #endif /* defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H */
00512 
00513 //! @endcond
00514 
00515 #endif /* __cplusplus */
00516 
00517 #endif /* OPENCV_CORE_AFFINE3_HPP */