diff options
Diffstat (limited to 'meowpp/math/Transformations.h')
| -rw-r--r-- | meowpp/math/Transformations.h | 550 |
1 files changed, 0 insertions, 550 deletions
diff --git a/meowpp/math/Transformations.h b/meowpp/math/Transformations.h deleted file mode 100644 index 99d6483..0000000 --- a/meowpp/math/Transformations.h +++ /dev/null @@ -1,550 +0,0 @@ -#ifndef math_Transformations_H__ -#define math_Transformations_H__ - -#include "Transformation.h" -#include "Matrix.h" -#include "utility.h" -#include "../Self.h" - -#include <cstdlib> - -namespace meow { - -/*! - * @brief A ball projection is to project the given vector to a hyper-sphere - * - * Assume: - * - The dimension of a ball projection is \f$ N \f$ - * - The radius of the hyper-sphere is \f$ R \f$ - * . - * Then the transformation is like below: \n - * \f[ - * \left[ - * \begin{array}{c} - * x_1 \\ - * x_2 \\ - * x_3 \\ - * . \\ - * . \\ - * . \\ - * x_N \\ - * \end{array} - * \right] - * \stackrel{transformate}{\rightarrow} - * \left[ - * \begin{array}{c} - * \frac{x_1 \times R}{L} \\ - * \frac{x_2 \times R}{L} \\ - * \frac{x_3 \times R}{L} \\ - * . \\ - * . \\ - * . \\ - * \frac{x_N \times R}{L} \\ - * \end{array} - * \right] \\ - * \f] - * where \f$ L=\sqrt{x_1^2 + x_2^2 + x_3^2 + ... + x_N^2 } \f$ - * @author cat_leopard - */ -template<class Scalar> -class BallProjection: public Transformation<Scalar> { -private: - struct Myself { - size_t dimension_; - Scalar radius_; - - Myself(size_t d): dimension_(1), radius_(1) { - } - - Myself(size_t d, Scalar const& r): dimension_(d), radius_(r) { - } - - Myself(Myself const& m): dimension_(m.dimension_), radius_(m.radius_) { - } - }; - - Self<Myself> const self; -public: - /*! - * Constructor, copy settings from given BallProjection - * @param [in] b another ball projection class - */ - BallProjection(BallProjection const& b): Transformation<Scalar>(b), - self(b.self, Self<Myself>::COPY_FROM) { - } - - /*! - * Constructor and setup, radius = 1 - * @param [in] d Dimension of the input/output vector - */ - BallProjection(size_t d): Transformation<Scalar>(d, 1, d, 1, 1), - self(Myself(d)) { - radius(1); - } - - /*! - * Constructor and setup - * @param [in] d Dimension of the input/output vector - * @param [in] r Radius of the hyper-sphere - */ - BallProjection(size_t d, Scalar const& r): Transformation<Scalar>(d,1,d,1,1), - self(Myself(d, r)) { - radius(r); - } - - /*! - * @brief Copy settings from another one - * @param [in] b Another one - * @return \c *this - */ - BallProjection& copyFrom(BallProjection const& b) { - Transformation<Scalar>::copyFrom(b); - copyFrom(b); - return *this; - } - - /*! - * @brief Reference settings from another one - * @param [in] b Another one - * @return \c *this - */ - BallProjection& referenceFrom(BallProjection const& b) { - Transformation<Scalar>::referenceFrom(b); - referenceFrom(b); - return *this; - } - - /*! - * @brief same as \c radius() - */ - Scalar parameter(size_t i) const { - return radius(); - } - - /*! - * @brief same as \c radius(s) - */ - Scalar parameter(size_t i, Scalar const& s) { - return radius(s); - } - - /*! - * @brief Return the value of the radius - */ - Scalar radius() const { - return self->radius_; - } - - /*! - * @brief Setup the radius - * - * @param [in] r New value of the radius - * @return New radius - */ - Scalar radius(Scalar const& r) { - self()->radius_ = r; - return radius(); - } - - /*! - * @brief Get the dimension of this projection - */ - size_t dimension() const { - return self->dimension_; - } - - - /*! - * @brief Project the input vector(s) onto the hyper-sphere and return it. - * - * If the number of columns of the input matrix is larger than 1, this - * method will think that you want to transform multiple vector once - * and the number of columns of the output matrix will be the same of - * the number of columns of the input one. - * - * @param [in] x The input matrix. - * @return The output matrix. - * @note Take into account that too much safty checking will lead to - * inefficient, this method will not checking whether the dimension - * of the input vector/matrix is right. So be sure the data is valid - * before you call this method. - */ - Matrix<Scalar> transformate(Matrix<Scalar> const& x) const { - Matrix<Scalar> ret(x); - for (size_t c = 0, C = ret.cols(); c < C; c++) { - Scalar sum(0); - for (size_t i = 0; i < self->dimension_; i++) { - sum = sum + squ(ret(i, c)); - } - Scalar len(sqrt(double(sum))); - for (size_t i = 0; i < self->dimension_; i++) { - ret(i, c, ret(i, c) * radius() / len); - } - } - return ret; - } - - /*! - * @brief Return the jacobian matrix (derivate by the input vector) - * of this projection. - * - * This method only allow a vector-like matrix be input. - * Assume: - * - The dimension of a ball projection is \f$ N \f$ - * - The length of the input vector is \f$ L=\sqrt{x_1^2+x_2^2+...+x_N^2} \f$ - * - The radius of the hyper-sphere is \f$ R \f$ - * . - * Then the jacobian matrix is like below: \n - * \f[ - * \frac{R}{L^3} \times \left[ - * \begin{array}{ccccc} - * L^2-x_1^2 & -x_1x_2 & -x_1x_3 & ... & -x_1x_N \\ - * -x_2x_1 & L^2-x_2^2 & -x_2x_3 & ... & -x_2x_N \\ - * -x_3x_1 & -x_3x_2 & L^2-x_3^2 & ... & -x_3x_N \\ - * . & . & . & & . \\ - * . & . & . & & . \\ - * . & . & . & & . \\ - * -x_Nx_1 & -x_Nx_2 & -x_Nx_3 & ... & L^2-x_N^2 \\ - * \end{array} - * \right] - * \f] - * - * @param [in] x The input matrix. - * @return The output matrix. - */ - Matrix<Scalar> jacobian(Matrix<Scalar> const& x) const { - Scalar sum(0); - for(size_t i = 0, I = dimension(); i < I; ++i) - sum = sum + squ(x(i, 0)); - Scalar len(sqrt(double(sum))); - Matrix<Scalar> ret(dimension(), dimension(), Scalar(0.0)); - for(size_t i = 0, I = dimension(); i < I; ++i) - for(size_t j = 0; j < I; ++j) - if (i == j) { - ret(i, j, radius() * (squ(len) - squ(x(i, 0))) / cub(len)); - } - else { - ret(i, j, radius() * (-x(i, 0) * x(j, 0) / cub(len))); - } - return ret; - } - - /*! - * @brief Return the jacobian matrix (derivate by radius) of this projection. - * - * This method only allow a vector-like matrix be input. - * Assume: - * - The dimension of a ball projection is \f$ N \f$ - * - The length of the input vector is \f$ L=\sqrt{x_1^2+x_2^2+...+x_N^2} \f$ - * - The radius of the hyper-sphere is \f$ R \f$ - * . - * Then the jacobian matrix is like below: \n - * \f[ - * R \times \left[ - * \begin{array}{c} - * \frac{x_1}{L} \\ - * \frac{x_2}{L} \\ - * \frac{x_3}{L} \\ - * . \\ - * . \\ - * . \\ - * \frac{x_N}{L} \\ - * \end{array} - * \right] - * \f] - * - * @param [in] x The input matrix. - * @param [in] i Useless parameter - * @return The output matrix. - */ - Matrix<Scalar> jacobian(Matrix<Scalar> const& x, size_t i) const { - Matrix<Scalar> ret(dimension(), 1, Scalar(0.0)); - Scalar sum(0); - for(size_t i = 0, I = dimension(); i < I; i++) { - sum = sum + squ(x(i, 0)); - } - return ret / Scalar(sqrt(double(sum))); - } - - /*! - * @brief Same as \c copyFrom(b) - */ - BallProjection& operator=(BallProjection const& b) { - return copyFrom(b); - } - - /*! - * @brief Same as \c transformate(v) - */ - Matrix<Scalar> operator()(Matrix<Scalar> const& v) const { - return transformate(v); - } -}; - - -/*! - * @brief A \b photo \b projection is a kind of transformation that project - * point/vector to a flat \b photo - * - * Assume: - * - The dimension of a photo projection is \f$ N \f$ - * - The length of the input vector is \f$ L \f$ - * - The focal length is \f$ f \f$ - * . - * Then transformation is like below: \n - * \f[ - * \left[ - * \begin{array}{c} - * x_1 \\ - * x_2 \\ - * x_3 \\ - * . \\ - * . \\ - * . \\ - * x_N \\ - * \end{array} - * \right] - * \stackrel{transformate}{\rightarrow} - * \left[ - * \begin{array}{c} - * \frac{-x_1 \times f}{x_N} \\ - * \frac{-x_2 \times f}{x_N} \\ - * \frac{-x_3 \times f}{x_N} \\ - * . \\ - * . \\ - * . \\ - * -f \\ - * \end{array} - * \right] \\ - * \f] - * i.e. projecte the vector onto the plane \f$ x_N = -f \f$. - * - * @author cat_leopard - */ -template<class Scalar> -class PhotoProjection: public Transformation<Scalar> { -private: - struct Myself { - Scalar focal_; - size_t dimension_; - - Myself() { - } - - Myself(size_t d, Scalar f): focal_(f), dimension_(d) { - } - - Myself(Myself const& b): focal_(b.focal_), dimension_(b.dimension_) { - } - - ~Myself() { - } - }; - - Self<Myself> const self; -public: - /*! - * Constructor, focal = 1 - */ - PhotoProjection(size_t dimension): - Transformation<Scalar>(dimension, 1, dimension, 1, 1), - self(Myself(dimension, 1)) { - } - - /*! - * Constructor - */ - PhotoProjection(size_t dimension, Scalar const& f): - Transformation<Scalar>(dimension, 1, dimension, 1, 1), - self(Myself(dimension, f)) { - } - - /*! - * Constructor, copy settings from another PhotoProjection. - */ - PhotoProjection(PhotoProjection const& p): Transformation<Scalar>(p), - self(p.self, Self<Myself>::COPY_FROM) { - } - - /*! - * Copy settings from another one - * @param [in] b another one - * @return \c *this - */ - PhotoProjection& copyFrom(PhotoProjection const& b) { - Transformation<Scalar>::copyFrom(b); - self().copyFrom(b.self); - return *this; - } - - /*! - * Reference settings from another one - * @param [in] b another one - * @return \c *this - */ - PhotoProjection& referenceFrom(PhotoProjection const& b) { - Transformation<Scalar>::referenceFrom(b); - self().referenceFrom(b.self); - return *this; - } - - /*! - * @brief Same as \c focal() - */ - Scalar parameter(size_t i) const { - return focal(); - } - - /*! - * @brief Same as \c focal(s) - */ - Scalar parameter(size_t i, Scalar const& s){ - return focal(s); - } - - /*! - * @brief Get the focal length - * @return Focal length - */ - Scalar focal() const { - return self->focal_; - } - - /*! - * @brief Set the focal length - * - * @param [in] f New focal length - * @return New focal length - */ - Scalar focal(Scalar const& f){ - self()->focal_ = f; - return focal(); - } - - /*! - * @brief Get the dimension of this projection - */ - size_t dimension() const { - return self->dimension_; - } - - /*! - * @brief Project the input vector(s) onto the plane - * - * The equation of the plane is \f$ x_N = -f \f$, where the \f$ N \f$ - * is the dimension of this projection and f is the focal length. \n - * If the number of columns of the input matrix is larger than 1, this - * method will think that you want to transform multiple vector once - * and the number of columns of the output matrix will be the same of - * the number of columns of the input one. - * - * @param [in] x The input matrix. - * @return The output matrix. - * @note Take into account that too much safty checking will lead to - * inefficient, this method will not checking whether the dimension - * of the input vector/matrix is right. So be sure the data is valid - * before you call this method. - */ - Matrix<Scalar> transformate(Matrix<Scalar> const& x) const { - Matrix<Scalar> ret(x); - for (size_t c = 0, C = ret.cols(); c < C; c++) { - for (size_t i = 0, I = dimension(); i < I; ++i) { - ret(i, c, -ret(i, c) * focal() / ret(I - 1, c)); - } - } - return ret; - } - - /*! - * @brief Return the jacobian matrix (derivate by the input vector) - * of this projection. - * - * This method only allow a vector-like matrix be input. - * Assume: - * - The dimension of this projection is \f$ N \f$ - * - The length of the input vector is \f$ L=\sqrt{x_1^2+x_2^2+...+x_N^2} \f$ - * - The focal length of this projection is \f$ f \f$ - * . - * Then the jacobian matrix is like below: \n - * \f[ - * f \times - * \left[ - * \begin{array}{ccccc} - * \frac{-1}{x_N} & 0 & 0 & ... & \frac{1}{x_N^2} \\ - * 0 & \frac{-1}{x_N} & 0 & ... & \frac{1}{x_N^2} \\ - * 0 & 0 & \frac{-1}{x_N} & ... & \frac{1}{x_N^2} \\ - * . & . & . & & . \\ - * . & . & . & & . \\ - * . & . & . & & . \\ - * 0 & 0 & 0 & ... & 0 \\ - * \end{array} - * \right] - * \f] - * - * @param [in] x The input matrix. - * @return The output matrix. - */ - Matrix<Scalar> jacobian(Matrix<Scalar> const& x) const{ - Matrix<Scalar> ret(dimension(), dimension(), Scalar(0.0)); - for(ssize_t i = 0, I = (ssize_t)dimension() - 1; i < I; i++){ - ret(i, i, -focal() / x(I, 0) ); - ret(i, dimension() - 1, focal() / squ(x(I, 0))); - } - return ret; - } - - /*! - * @brief Return the jacobian matrix (derivate by the focus length) - * of this projection. - * - * This method only allow a vector-like matrix be input. - * Assume: - * - The dimension of this projection is \f$ N \f$ - * - The length of the input vector is \f$ L=\sqrt{x_1^2+x_2^2+...+x_N^2} \f$ - * - The focal length of this projection is \f$ f \f$ - * . - * Then the jacobian matrix is like below: \n - * \f[ - * \left[ - * \begin{array}{c} - * \frac{-x_1}{x_N} \\ - * \frac{-x_2}{x_N} \\ - * \frac{-x_3}{x_N} \\ - * . \\ - * . \\ - * . \\ - * -1 \\ - * \end{array} - * \right] - * \f] - * - * @param [in] x The input matrix. - * @param [in] i Useless parameter - * @return The output matrix. - */ - Matrix<Scalar> jacobian(Matrix<Scalar> const& x, size_t i) const{ - Matrix<Scalar> ret(dimension(), 1, Scalar(0.0)); - for(size_t i = 0, I = dimension(); i < I; ++i) { - ret(i, 0, -x(i, 0) / x(I - 1, 0)); - } - return ret; - } - - /*! - * @brief Same as \c copyFrom(b) - */ - PhotoProjection& operator=(PhotoProjection const& b) { - return copyFrom(b); - } - - /*! - * @brief Same as \c transformate(v) - */ - Matrix<Scalar> operator()(Matrix<Scalar> const& v) const { - return transformate(v); - } -}; - -} // meow - -#endif // Transformations_H__ |