diff options
Diffstat (limited to 'eigen/Eigen/src/Eigen2Support/Geometry')
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/AlignedBox.h | 159 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/All.h | 115 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/AngleAxis.h | 214 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt | 6 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/Hyperplane.h | 254 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h | 141 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/Quaternion.h | 495 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/Rotation2D.h | 145 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/RotationBase.h | 123 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/Scaling.h | 167 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/Transform.h | 786 | ||||
| -rw-r--r-- | eigen/Eigen/src/Eigen2Support/Geometry/Translation.h | 184 |
12 files changed, 0 insertions, 2789 deletions
diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/AlignedBox.h b/eigen/Eigen/src/Eigen2Support/Geometry/AlignedBox.h deleted file mode 100644 index 2e4309d..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/AlignedBox.h +++ /dev/null @@ -1,159 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -/** \geometry_module \ingroup Geometry_Module - * \nonstableyet - * - * \class AlignedBox - * - * \brief An axis aligned box - * - * \param _Scalar the type of the scalar coefficients - * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. - * - * This class represents an axis aligned box as a pair of the minimal and maximal corners. - */ -template <typename _Scalar, int _AmbientDim> -class AlignedBox -{ -public: -EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1) - enum { AmbientDimAtCompileTime = _AmbientDim }; - typedef _Scalar Scalar; - typedef typename NumTraits<Scalar>::Real RealScalar; - typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; - - /** Default constructor initializing a null box. */ - inline AlignedBox() - { if (AmbientDimAtCompileTime!=Dynamic) setNull(); } - - /** Constructs a null box with \a _dim the dimension of the ambient space. */ - inline explicit AlignedBox(int _dim) : m_min(_dim), m_max(_dim) - { setNull(); } - - /** Constructs a box with extremities \a _min and \a _max. */ - inline AlignedBox(const VectorType& _min, const VectorType& _max) : m_min(_min), m_max(_max) {} - - /** Constructs a box containing a single point \a p. */ - inline explicit AlignedBox(const VectorType& p) : m_min(p), m_max(p) {} - - ~AlignedBox() {} - - /** \returns the dimension in which the box holds */ - inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size()-1 : AmbientDimAtCompileTime; } - - /** \returns true if the box is null, i.e, empty. */ - inline bool isNull() const { return (m_min.cwise() > m_max).any(); } - - /** Makes \c *this a null/empty box. */ - inline void setNull() - { - m_min.setConstant( (std::numeric_limits<Scalar>::max)()); - m_max.setConstant(-(std::numeric_limits<Scalar>::max)()); - } - - /** \returns the minimal corner */ - inline const VectorType& (min)() const { return m_min; } - /** \returns a non const reference to the minimal corner */ - inline VectorType& (min)() { return m_min; } - /** \returns the maximal corner */ - inline const VectorType& (max)() const { return m_max; } - /** \returns a non const reference to the maximal corner */ - inline VectorType& (max)() { return m_max; } - - /** \returns true if the point \a p is inside the box \c *this. */ - inline bool contains(const VectorType& p) const - { return (m_min.cwise()<=p).all() && (p.cwise()<=m_max).all(); } - - /** \returns true if the box \a b is entirely inside the box \c *this. */ - inline bool contains(const AlignedBox& b) const - { return (m_min.cwise()<=(b.min)()).all() && ((b.max)().cwise()<=m_max).all(); } - - /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */ - inline AlignedBox& extend(const VectorType& p) - { m_min = (m_min.cwise().min)(p); m_max = (m_max.cwise().max)(p); return *this; } - - /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */ - inline AlignedBox& extend(const AlignedBox& b) - { m_min = (m_min.cwise().min)(b.m_min); m_max = (m_max.cwise().max)(b.m_max); return *this; } - - /** Clamps \c *this by the box \a b and returns a reference to \c *this. */ - inline AlignedBox& clamp(const AlignedBox& b) - { m_min = (m_min.cwise().max)(b.m_min); m_max = (m_max.cwise().min)(b.m_max); return *this; } - - /** Translate \c *this by the vector \a t and returns a reference to \c *this. */ - inline AlignedBox& translate(const VectorType& t) - { m_min += t; m_max += t; return *this; } - - /** \returns the squared distance between the point \a p and the box \c *this, - * and zero if \a p is inside the box. - * \sa exteriorDistance() - */ - inline Scalar squaredExteriorDistance(const VectorType& p) const; - - /** \returns the distance between the point \a p and the box \c *this, - * and zero if \a p is inside the box. - * \sa squaredExteriorDistance() - */ - inline Scalar exteriorDistance(const VectorType& p) const - { return ei_sqrt(squaredExteriorDistance(p)); } - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<AlignedBox, - AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const - { - return typename internal::cast_return_type<AlignedBox, - AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this); - } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other) - { - m_min = (other.min)().template cast<Scalar>(); - m_max = (other.max)().template cast<Scalar>(); - } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); } - -protected: - - VectorType m_min, m_max; -}; - -template<typename Scalar,int AmbiantDim> -inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const VectorType& p) const -{ - Scalar dist2(0); - Scalar aux; - for (int k=0; k<dim(); ++k) - { - if ((aux = (p[k]-m_min[k]))<Scalar(0)) - dist2 += aux*aux; - else if ( (aux = (m_max[k]-p[k]))<Scalar(0)) - dist2 += aux*aux; - } - return dist2; -} - -} // end namespace Eigen diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/All.h b/eigen/Eigen/src/Eigen2Support/Geometry/All.h deleted file mode 100644 index e0b00fc..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/All.h +++ /dev/null @@ -1,115 +0,0 @@ -#ifndef EIGEN2_GEOMETRY_MODULE_H -#define EIGEN2_GEOMETRY_MODULE_H - -#include <limits> - -#ifndef M_PI -#define M_PI 3.14159265358979323846 -#endif - -#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS -#include "RotationBase.h" -#include "Rotation2D.h" -#include "Quaternion.h" -#include "AngleAxis.h" -#include "Transform.h" -#include "Translation.h" -#include "Scaling.h" -#include "AlignedBox.h" -#include "Hyperplane.h" -#include "ParametrizedLine.h" -#endif - - -#define RotationBase eigen2_RotationBase -#define Rotation2D eigen2_Rotation2D -#define Rotation2Df eigen2_Rotation2Df -#define Rotation2Dd eigen2_Rotation2Dd - -#define Quaternion eigen2_Quaternion -#define Quaternionf eigen2_Quaternionf -#define Quaterniond eigen2_Quaterniond - -#define AngleAxis eigen2_AngleAxis -#define AngleAxisf eigen2_AngleAxisf -#define AngleAxisd eigen2_AngleAxisd - -#define Transform eigen2_Transform -#define Transform2f eigen2_Transform2f -#define Transform2d eigen2_Transform2d -#define Transform3f eigen2_Transform3f -#define Transform3d eigen2_Transform3d - -#define Translation eigen2_Translation -#define Translation2f eigen2_Translation2f -#define Translation2d eigen2_Translation2d -#define Translation3f eigen2_Translation3f -#define Translation3d eigen2_Translation3d - -#define Scaling eigen2_Scaling -#define Scaling2f eigen2_Scaling2f -#define Scaling2d eigen2_Scaling2d -#define Scaling3f eigen2_Scaling3f -#define Scaling3d eigen2_Scaling3d - -#define AlignedBox eigen2_AlignedBox - -#define Hyperplane eigen2_Hyperplane -#define ParametrizedLine eigen2_ParametrizedLine - -#define ei_toRotationMatrix eigen2_ei_toRotationMatrix -#define ei_quaternion_assign_impl eigen2_ei_quaternion_assign_impl -#define ei_transform_product_impl eigen2_ei_transform_product_impl - -#include "RotationBase.h" -#include "Rotation2D.h" -#include "Quaternion.h" -#include "AngleAxis.h" -#include "Transform.h" -#include "Translation.h" -#include "Scaling.h" -#include "AlignedBox.h" -#include "Hyperplane.h" -#include "ParametrizedLine.h" - -#undef ei_toRotationMatrix -#undef ei_quaternion_assign_impl -#undef ei_transform_product_impl - -#undef RotationBase -#undef Rotation2D -#undef Rotation2Df -#undef Rotation2Dd - -#undef Quaternion -#undef Quaternionf -#undef Quaterniond - -#undef AngleAxis -#undef AngleAxisf -#undef AngleAxisd - -#undef Transform -#undef Transform2f -#undef Transform2d -#undef Transform3f -#undef Transform3d - -#undef Translation -#undef Translation2f -#undef Translation2d -#undef Translation3f -#undef Translation3d - -#undef Scaling -#undef Scaling2f -#undef Scaling2d -#undef Scaling3f -#undef Scaling3d - -#undef AlignedBox - -#undef Hyperplane -#undef ParametrizedLine - -#endif // EIGEN2_GEOMETRY_MODULE_H diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/AngleAxis.h b/eigen/Eigen/src/Eigen2Support/Geometry/AngleAxis.h deleted file mode 100644 index af598a4..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/AngleAxis.h +++ /dev/null @@ -1,214 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -/** \geometry_module \ingroup Geometry_Module - * - * \class AngleAxis - * - * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis - * - * \param _Scalar the scalar type, i.e., the type of the coefficients. - * - * The following two typedefs are provided for convenience: - * \li \c AngleAxisf for \c float - * \li \c AngleAxisd for \c double - * - * \addexample AngleAxisForEuler \label How to define a rotation from Euler-angles - * - * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily - * mimic Euler-angles. Here is an example: - * \include AngleAxis_mimic_euler.cpp - * Output: \verbinclude AngleAxis_mimic_euler.out - * - * \note This class is not aimed to be used to store a rotation transformation, - * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix) - * and transformation objects. - * - * \sa class Quaternion, class Transform, MatrixBase::UnitX() - */ - -template<typename _Scalar> struct ei_traits<AngleAxis<_Scalar> > -{ - typedef _Scalar Scalar; -}; - -template<typename _Scalar> -class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3> -{ - typedef RotationBase<AngleAxis<_Scalar>,3> Base; - -public: - - using Base::operator*; - - enum { Dim = 3 }; - /** the scalar type of the coefficients */ - typedef _Scalar Scalar; - typedef Matrix<Scalar,3,3> Matrix3; - typedef Matrix<Scalar,3,1> Vector3; - typedef Quaternion<Scalar> QuaternionType; - -protected: - - Vector3 m_axis; - Scalar m_angle; - -public: - - /** Default constructor without initialization. */ - AngleAxis() {} - /** Constructs and initialize the angle-axis rotation from an \a angle in radian - * and an \a axis which must be normalized. */ - template<typename Derived> - inline AngleAxis(Scalar angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {} - /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */ - inline AngleAxis(const QuaternionType& q) { *this = q; } - /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */ - template<typename Derived> - inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; } - - Scalar angle() const { return m_angle; } - Scalar& angle() { return m_angle; } - - const Vector3& axis() const { return m_axis; } - Vector3& axis() { return m_axis; } - - /** Concatenates two rotations */ - inline QuaternionType operator* (const AngleAxis& other) const - { return QuaternionType(*this) * QuaternionType(other); } - - /** Concatenates two rotations */ - inline QuaternionType operator* (const QuaternionType& other) const - { return QuaternionType(*this) * other; } - - /** Concatenates two rotations */ - friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b) - { return a * QuaternionType(b); } - - /** Concatenates two rotations */ - inline Matrix3 operator* (const Matrix3& other) const - { return toRotationMatrix() * other; } - - /** Concatenates two rotations */ - inline friend Matrix3 operator* (const Matrix3& a, const AngleAxis& b) - { return a * b.toRotationMatrix(); } - - /** Applies rotation to vector */ - inline Vector3 operator* (const Vector3& other) const - { return toRotationMatrix() * other; } - - /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */ - AngleAxis inverse() const - { return AngleAxis(-m_angle, m_axis); } - - AngleAxis& operator=(const QuaternionType& q); - template<typename Derived> - AngleAxis& operator=(const MatrixBase<Derived>& m); - - template<typename Derived> - AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m); - Matrix3 toRotationMatrix(void) const; - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const - { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other) - { - m_axis = other.axis().template cast<Scalar>(); - m_angle = Scalar(other.angle()); - } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const AngleAxis& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return m_axis.isApprox(other.m_axis, prec) && ei_isApprox(m_angle,other.m_angle, prec); } -}; - -/** \ingroup Geometry_Module - * single precision angle-axis type */ -typedef AngleAxis<float> AngleAxisf; -/** \ingroup Geometry_Module - * double precision angle-axis type */ -typedef AngleAxis<double> AngleAxisd; - -/** Set \c *this from a quaternion. - * The axis is normalized. - */ -template<typename Scalar> -AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionType& q) -{ - Scalar n2 = q.vec().squaredNorm(); - if (n2 < precision<Scalar>()*precision<Scalar>()) - { - m_angle = 0; - m_axis << 1, 0, 0; - } - else - { - m_angle = 2*std::acos(q.w()); - m_axis = q.vec() / ei_sqrt(n2); - } - return *this; -} - -/** Set \c *this from a 3x3 rotation matrix \a mat. - */ -template<typename Scalar> -template<typename Derived> -AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat) -{ - // Since a direct conversion would not be really faster, - // let's use the robust Quaternion implementation: - return *this = QuaternionType(mat); -} - -/** Constructs and \returns an equivalent 3x3 rotation matrix. - */ -template<typename Scalar> -typename AngleAxis<Scalar>::Matrix3 -AngleAxis<Scalar>::toRotationMatrix(void) const -{ - Matrix3 res; - Vector3 sin_axis = ei_sin(m_angle) * m_axis; - Scalar c = ei_cos(m_angle); - Vector3 cos1_axis = (Scalar(1)-c) * m_axis; - - Scalar tmp; - tmp = cos1_axis.x() * m_axis.y(); - res.coeffRef(0,1) = tmp - sin_axis.z(); - res.coeffRef(1,0) = tmp + sin_axis.z(); - - tmp = cos1_axis.x() * m_axis.z(); - res.coeffRef(0,2) = tmp + sin_axis.y(); - res.coeffRef(2,0) = tmp - sin_axis.y(); - - tmp = cos1_axis.y() * m_axis.z(); - res.coeffRef(1,2) = tmp - sin_axis.x(); - res.coeffRef(2,1) = tmp + sin_axis.x(); - - res.diagonal() = (cos1_axis.cwise() * m_axis).cwise() + c; - - return res; -} - -} // end namespace Eigen diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt b/eigen/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt deleted file mode 100644 index c347a8f..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/CMakeLists.txt +++ /dev/null @@ -1,6 +0,0 @@ -FILE(GLOB Eigen_Eigen2Support_Geometry_SRCS "*.h") - -INSTALL(FILES - ${Eigen_Eigen2Support_Geometry_SRCS} - DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Eigen2Support/Geometry - ) diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/Hyperplane.h b/eigen/Eigen/src/Eigen2Support/Geometry/Hyperplane.h deleted file mode 100644 index b95bf00..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/Hyperplane.h +++ /dev/null @@ -1,254 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -/** \geometry_module \ingroup Geometry_Module - * - * \class Hyperplane - * - * \brief A hyperplane - * - * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n. - * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane. - * - * \param _Scalar the scalar type, i.e., the type of the coefficients - * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. - * Notice that the dimension of the hyperplane is _AmbientDim-1. - * - * This class represents an hyperplane as the zero set of the implicit equation - * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part) - * and \f$ d \f$ is the distance (offset) to the origin. - */ -template <typename _Scalar, int _AmbientDim> -class Hyperplane -{ -public: - EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1) - enum { AmbientDimAtCompileTime = _AmbientDim }; - typedef _Scalar Scalar; - typedef typename NumTraits<Scalar>::Real RealScalar; - typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; - typedef Matrix<Scalar,int(AmbientDimAtCompileTime)==Dynamic - ? Dynamic - : int(AmbientDimAtCompileTime)+1,1> Coefficients; - typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType; - - /** Default constructor without initialization */ - inline Hyperplane() {} - - /** Constructs a dynamic-size hyperplane with \a _dim the dimension - * of the ambient space */ - inline explicit Hyperplane(int _dim) : m_coeffs(_dim+1) {} - - /** Construct a plane from its normal \a n and a point \a e onto the plane. - * \warning the vector normal is assumed to be normalized. - */ - inline Hyperplane(const VectorType& n, const VectorType& e) - : m_coeffs(n.size()+1) - { - normal() = n; - offset() = -e.eigen2_dot(n); - } - - /** Constructs a plane from its normal \a n and distance to the origin \a d - * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$. - * \warning the vector normal is assumed to be normalized. - */ - inline Hyperplane(const VectorType& n, Scalar d) - : m_coeffs(n.size()+1) - { - normal() = n; - offset() = d; - } - - /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space - * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made. - */ - static inline Hyperplane Through(const VectorType& p0, const VectorType& p1) - { - Hyperplane result(p0.size()); - result.normal() = (p1 - p0).unitOrthogonal(); - result.offset() = -result.normal().eigen2_dot(p0); - return result; - } - - /** Constructs a hyperplane passing through the three points. The dimension of the ambient space - * is required to be exactly 3. - */ - static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2) - { - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3) - Hyperplane result(p0.size()); - result.normal() = (p2 - p0).cross(p1 - p0).normalized(); - result.offset() = -result.normal().eigen2_dot(p0); - return result; - } - - /** Constructs a hyperplane passing through the parametrized line \a parametrized. - * If the dimension of the ambient space is greater than 2, then there isn't uniqueness, - * so an arbitrary choice is made. - */ - // FIXME to be consitent with the rest this could be implemented as a static Through function ?? - explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized) - { - normal() = parametrized.direction().unitOrthogonal(); - offset() = -normal().eigen2_dot(parametrized.origin()); - } - - ~Hyperplane() {} - - /** \returns the dimension in which the plane holds */ - inline int dim() const { return int(AmbientDimAtCompileTime)==Dynamic ? m_coeffs.size()-1 : int(AmbientDimAtCompileTime); } - - /** normalizes \c *this */ - void normalize(void) - { - m_coeffs /= normal().norm(); - } - - /** \returns the signed distance between the plane \c *this and a point \a p. - * \sa absDistance() - */ - inline Scalar signedDistance(const VectorType& p) const { return p.eigen2_dot(normal()) + offset(); } - - /** \returns the absolute distance between the plane \c *this and a point \a p. - * \sa signedDistance() - */ - inline Scalar absDistance(const VectorType& p) const { return ei_abs(signedDistance(p)); } - - /** \returns the projection of a point \a p onto the plane \c *this. - */ - inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); } - - /** \returns a constant reference to the unit normal vector of the plane, which corresponds - * to the linear part of the implicit equation. - */ - inline const NormalReturnType normal() const { return NormalReturnType(*const_cast<Coefficients*>(&m_coeffs),0,0,dim(),1); } - - /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds - * to the linear part of the implicit equation. - */ - inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); } - - /** \returns the distance to the origin, which is also the "constant term" of the implicit equation - * \warning the vector normal is assumed to be normalized. - */ - inline const Scalar& offset() const { return m_coeffs.coeff(dim()); } - - /** \returns a non-constant reference to the distance to the origin, which is also the constant part - * of the implicit equation */ - inline Scalar& offset() { return m_coeffs(dim()); } - - /** \returns a constant reference to the coefficients c_i of the plane equation: - * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$ - */ - inline const Coefficients& coeffs() const { return m_coeffs; } - - /** \returns a non-constant reference to the coefficients c_i of the plane equation: - * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$ - */ - inline Coefficients& coeffs() { return m_coeffs; } - - /** \returns the intersection of *this with \a other. - * - * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines. - * - * \note If \a other is approximately parallel to *this, this method will return any point on *this. - */ - VectorType intersection(const Hyperplane& other) - { - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2) - Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0); - // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests - // whether the two lines are approximately parallel. - if(ei_isMuchSmallerThan(det, Scalar(1))) - { // special case where the two lines are approximately parallel. Pick any point on the first line. - if(ei_abs(coeffs().coeff(1))>ei_abs(coeffs().coeff(0))) - return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0)); - else - return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0)); - } - else - { // general case - Scalar invdet = Scalar(1) / det; - return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)), - invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2))); - } - } - - /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this. - * - * \param mat the Dim x Dim transformation matrix - * \param traits specifies whether the matrix \a mat represents an Isometry - * or a more generic Affine transformation. The default is Affine. - */ - template<typename XprType> - inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine) - { - if (traits==Affine) - normal() = mat.inverse().transpose() * normal(); - else if (traits==Isometry) - normal() = mat * normal(); - else - { - ei_assert("invalid traits value in Hyperplane::transform()"); - } - return *this; - } - - /** Applies the transformation \a t to \c *this and returns a reference to \c *this. - * - * \param t the transformation of dimension Dim - * \param traits specifies whether the transformation \a t represents an Isometry - * or a more generic Affine transformation. The default is Affine. - * Other kind of transformations are not supported. - */ - inline Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime>& t, - TransformTraits traits = Affine) - { - transform(t.linear(), traits); - offset() -= t.translation().eigen2_dot(normal()); - return *this; - } - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<Hyperplane, - Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type cast() const - { - return typename internal::cast_return_type<Hyperplane, - Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type(*this); - } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime>& other) - { m_coeffs = other.coeffs().template cast<Scalar>(); } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const Hyperplane& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return m_coeffs.isApprox(other.m_coeffs, prec); } - -protected: - - Coefficients m_coeffs; -}; - -} // end namespace Eigen diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h b/eigen/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h deleted file mode 100644 index 9b57b7e..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h +++ /dev/null @@ -1,141 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -/** \geometry_module \ingroup Geometry_Module - * - * \class ParametrizedLine - * - * \brief A parametrized line - * - * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit - * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to - * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ l \in \mathbf{R} \f$. - * - * \param _Scalar the scalar type, i.e., the type of the coefficients - * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. - */ -template <typename _Scalar, int _AmbientDim> -class ParametrizedLine -{ -public: - EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) - enum { AmbientDimAtCompileTime = _AmbientDim }; - typedef _Scalar Scalar; - typedef typename NumTraits<Scalar>::Real RealScalar; - typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; - - /** Default constructor without initialization */ - inline ParametrizedLine() {} - - /** Constructs a dynamic-size line with \a _dim the dimension - * of the ambient space */ - inline explicit ParametrizedLine(int _dim) : m_origin(_dim), m_direction(_dim) {} - - /** Initializes a parametrized line of direction \a direction and origin \a origin. - * \warning the vector direction is assumed to be normalized. - */ - ParametrizedLine(const VectorType& origin, const VectorType& direction) - : m_origin(origin), m_direction(direction) {} - - explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane); - - /** Constructs a parametrized line going from \a p0 to \a p1. */ - static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1) - { return ParametrizedLine(p0, (p1-p0).normalized()); } - - ~ParametrizedLine() {} - - /** \returns the dimension in which the line holds */ - inline int dim() const { return m_direction.size(); } - - const VectorType& origin() const { return m_origin; } - VectorType& origin() { return m_origin; } - - const VectorType& direction() const { return m_direction; } - VectorType& direction() { return m_direction; } - - /** \returns the squared distance of a point \a p to its projection onto the line \c *this. - * \sa distance() - */ - RealScalar squaredDistance(const VectorType& p) const - { - VectorType diff = p-origin(); - return (diff - diff.eigen2_dot(direction())* direction()).squaredNorm(); - } - /** \returns the distance of a point \a p to its projection onto the line \c *this. - * \sa squaredDistance() - */ - RealScalar distance(const VectorType& p) const { return ei_sqrt(squaredDistance(p)); } - - /** \returns the projection of a point \a p onto the line \c *this. */ - VectorType projection(const VectorType& p) const - { return origin() + (p-origin()).eigen2_dot(direction()) * direction(); } - - Scalar intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane); - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<ParametrizedLine, - ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type cast() const - { - return typename internal::cast_return_type<ParametrizedLine, - ParametrizedLine<NewScalarType,AmbientDimAtCompileTime> >::type(*this); - } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime>& other) - { - m_origin = other.origin().template cast<Scalar>(); - m_direction = other.direction().template cast<Scalar>(); - } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const ParametrizedLine& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); } - -protected: - - VectorType m_origin, m_direction; -}; - -/** Constructs a parametrized line from a 2D hyperplane - * - * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line - */ -template <typename _Scalar, int _AmbientDim> -inline ParametrizedLine<_Scalar, _AmbientDim>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane) -{ - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2) - direction() = hyperplane.normal().unitOrthogonal(); - origin() = -hyperplane.normal()*hyperplane.offset(); -} - -/** \returns the parameter value of the intersection between \c *this and the given hyperplane - */ -template <typename _Scalar, int _AmbientDim> -inline _Scalar ParametrizedLine<_Scalar, _AmbientDim>::intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane) -{ - return -(hyperplane.offset()+origin().eigen2_dot(hyperplane.normal())) - /(direction().eigen2_dot(hyperplane.normal())); -} - -} // end namespace Eigen diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/Quaternion.h b/eigen/Eigen/src/Eigen2Support/Geometry/Quaternion.h deleted file mode 100644 index 4b6390c..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/Quaternion.h +++ /dev/null @@ -1,495 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -template<typename Other, - int OtherRows=Other::RowsAtCompileTime, - int OtherCols=Other::ColsAtCompileTime> -struct ei_quaternion_assign_impl; - -/** \geometry_module \ingroup Geometry_Module - * - * \class Quaternion - * - * \brief The quaternion class used to represent 3D orientations and rotations - * - * \param _Scalar the scalar type, i.e., the type of the coefficients - * - * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of - * orientations and rotations of objects in three dimensions. Compared to other representations - * like Euler angles or 3x3 matrices, quatertions offer the following advantages: - * \li \b compact storage (4 scalars) - * \li \b efficient to compose (28 flops), - * \li \b stable spherical interpolation - * - * The following two typedefs are provided for convenience: - * \li \c Quaternionf for \c float - * \li \c Quaterniond for \c double - * - * \sa class AngleAxis, class Transform - */ - -template<typename _Scalar> struct ei_traits<Quaternion<_Scalar> > -{ - typedef _Scalar Scalar; -}; - -template<typename _Scalar> -class Quaternion : public RotationBase<Quaternion<_Scalar>,3> -{ - typedef RotationBase<Quaternion<_Scalar>,3> Base; - -public: - EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,4) - - using Base::operator*; - - /** the scalar type of the coefficients */ - typedef _Scalar Scalar; - - /** the type of the Coefficients 4-vector */ - typedef Matrix<Scalar, 4, 1> Coefficients; - /** the type of a 3D vector */ - typedef Matrix<Scalar,3,1> Vector3; - /** the equivalent rotation matrix type */ - typedef Matrix<Scalar,3,3> Matrix3; - /** the equivalent angle-axis type */ - typedef AngleAxis<Scalar> AngleAxisType; - - /** \returns the \c x coefficient */ - inline Scalar x() const { return m_coeffs.coeff(0); } - /** \returns the \c y coefficient */ - inline Scalar y() const { return m_coeffs.coeff(1); } - /** \returns the \c z coefficient */ - inline Scalar z() const { return m_coeffs.coeff(2); } - /** \returns the \c w coefficient */ - inline Scalar w() const { return m_coeffs.coeff(3); } - - /** \returns a reference to the \c x coefficient */ - inline Scalar& x() { return m_coeffs.coeffRef(0); } - /** \returns a reference to the \c y coefficient */ - inline Scalar& y() { return m_coeffs.coeffRef(1); } - /** \returns a reference to the \c z coefficient */ - inline Scalar& z() { return m_coeffs.coeffRef(2); } - /** \returns a reference to the \c w coefficient */ - inline Scalar& w() { return m_coeffs.coeffRef(3); } - - /** \returns a read-only vector expression of the imaginary part (x,y,z) */ - inline const Block<const Coefficients,3,1> vec() const { return m_coeffs.template start<3>(); } - - /** \returns a vector expression of the imaginary part (x,y,z) */ - inline Block<Coefficients,3,1> vec() { return m_coeffs.template start<3>(); } - - /** \returns a read-only vector expression of the coefficients (x,y,z,w) */ - inline const Coefficients& coeffs() const { return m_coeffs; } - - /** \returns a vector expression of the coefficients (x,y,z,w) */ - inline Coefficients& coeffs() { return m_coeffs; } - - /** Default constructor leaving the quaternion uninitialized. */ - inline Quaternion() {} - - /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from - * its four coefficients \a w, \a x, \a y and \a z. - * - * \warning Note the order of the arguments: the real \a w coefficient first, - * while internally the coefficients are stored in the following order: - * [\c x, \c y, \c z, \c w] - */ - inline Quaternion(Scalar w, Scalar x, Scalar y, Scalar z) - { m_coeffs << x, y, z, w; } - - /** Copy constructor */ - inline Quaternion(const Quaternion& other) { m_coeffs = other.m_coeffs; } - - /** Constructs and initializes a quaternion from the angle-axis \a aa */ - explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; } - - /** Constructs and initializes a quaternion from either: - * - a rotation matrix expression, - * - a 4D vector expression representing quaternion coefficients. - * \sa operator=(MatrixBase<Derived>) - */ - template<typename Derived> - explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; } - - Quaternion& operator=(const Quaternion& other); - Quaternion& operator=(const AngleAxisType& aa); - template<typename Derived> - Quaternion& operator=(const MatrixBase<Derived>& m); - - /** \returns a quaternion representing an identity rotation - * \sa MatrixBase::Identity() - */ - static inline Quaternion Identity() { return Quaternion(1, 0, 0, 0); } - - /** \sa Quaternion::Identity(), MatrixBase::setIdentity() - */ - inline Quaternion& setIdentity() { m_coeffs << 0, 0, 0, 1; return *this; } - - /** \returns the squared norm of the quaternion's coefficients - * \sa Quaternion::norm(), MatrixBase::squaredNorm() - */ - inline Scalar squaredNorm() const { return m_coeffs.squaredNorm(); } - - /** \returns the norm of the quaternion's coefficients - * \sa Quaternion::squaredNorm(), MatrixBase::norm() - */ - inline Scalar norm() const { return m_coeffs.norm(); } - - /** Normalizes the quaternion \c *this - * \sa normalized(), MatrixBase::normalize() */ - inline void normalize() { m_coeffs.normalize(); } - /** \returns a normalized version of \c *this - * \sa normalize(), MatrixBase::normalized() */ - inline Quaternion normalized() const { return Quaternion(m_coeffs.normalized()); } - - /** \returns the dot product of \c *this and \a other - * Geometrically speaking, the dot product of two unit quaternions - * corresponds to the cosine of half the angle between the two rotations. - * \sa angularDistance() - */ - inline Scalar eigen2_dot(const Quaternion& other) const { return m_coeffs.eigen2_dot(other.m_coeffs); } - - inline Scalar angularDistance(const Quaternion& other) const; - - Matrix3 toRotationMatrix(void) const; - - template<typename Derived1, typename Derived2> - Quaternion& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b); - - inline Quaternion operator* (const Quaternion& q) const; - inline Quaternion& operator*= (const Quaternion& q); - - Quaternion inverse(void) const; - Quaternion conjugate(void) const; - - Quaternion slerp(Scalar t, const Quaternion& other) const; - - template<typename Derived> - Vector3 operator* (const MatrixBase<Derived>& vec) const; - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<Quaternion,Quaternion<NewScalarType> >::type cast() const - { return typename internal::cast_return_type<Quaternion,Quaternion<NewScalarType> >::type(*this); } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit Quaternion(const Quaternion<OtherScalarType>& other) - { m_coeffs = other.coeffs().template cast<Scalar>(); } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const Quaternion& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return m_coeffs.isApprox(other.m_coeffs, prec); } - -protected: - Coefficients m_coeffs; -}; - -/** \ingroup Geometry_Module - * single precision quaternion type */ -typedef Quaternion<float> Quaternionf; -/** \ingroup Geometry_Module - * double precision quaternion type */ -typedef Quaternion<double> Quaterniond; - -// Generic Quaternion * Quaternion product -template<typename Scalar> inline Quaternion<Scalar> -ei_quaternion_product(const Quaternion<Scalar>& a, const Quaternion<Scalar>& b) -{ - return Quaternion<Scalar> - ( - a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(), - a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(), - a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(), - a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x() - ); -} - -/** \returns the concatenation of two rotations as a quaternion-quaternion product */ -template <typename Scalar> -inline Quaternion<Scalar> Quaternion<Scalar>::operator* (const Quaternion& other) const -{ - return ei_quaternion_product(*this,other); -} - -/** \sa operator*(Quaternion) */ -template <typename Scalar> -inline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& other) -{ - return (*this = *this * other); -} - -/** Rotation of a vector by a quaternion. - * \remarks If the quaternion is used to rotate several points (>1) - * then it is much more efficient to first convert it to a 3x3 Matrix. - * Comparison of the operation cost for n transformations: - * - Quaternion: 30n - * - Via a Matrix3: 24 + 15n - */ -template <typename Scalar> -template<typename Derived> -inline typename Quaternion<Scalar>::Vector3 -Quaternion<Scalar>::operator* (const MatrixBase<Derived>& v) const -{ - // Note that this algorithm comes from the optimization by hand - // of the conversion to a Matrix followed by a Matrix/Vector product. - // It appears to be much faster than the common algorithm found - // in the litterature (30 versus 39 flops). It also requires two - // Vector3 as temporaries. - Vector3 uv; - uv = 2 * this->vec().cross(v); - return v + this->w() * uv + this->vec().cross(uv); -} - -template<typename Scalar> -inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const Quaternion& other) -{ - m_coeffs = other.m_coeffs; - return *this; -} - -/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this - */ -template<typename Scalar> -inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa) -{ - Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings - this->w() = ei_cos(ha); - this->vec() = ei_sin(ha) * aa.axis(); - return *this; -} - -/** Set \c *this from the expression \a xpr: - * - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion - * - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix - * and \a xpr is converted to a quaternion - */ -template<typename Scalar> -template<typename Derived> -inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const MatrixBase<Derived>& xpr) -{ - ei_quaternion_assign_impl<Derived>::run(*this, xpr.derived()); - return *this; -} - -/** Convert the quaternion to a 3x3 rotation matrix */ -template<typename Scalar> -inline typename Quaternion<Scalar>::Matrix3 -Quaternion<Scalar>::toRotationMatrix(void) const -{ - // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!) - // if not inlined then the cost of the return by value is huge ~ +35%, - // however, not inlining this function is an order of magnitude slower, so - // it has to be inlined, and so the return by value is not an issue - Matrix3 res; - - const Scalar tx = Scalar(2)*this->x(); - const Scalar ty = Scalar(2)*this->y(); - const Scalar tz = Scalar(2)*this->z(); - const Scalar twx = tx*this->w(); - const Scalar twy = ty*this->w(); - const Scalar twz = tz*this->w(); - const Scalar txx = tx*this->x(); - const Scalar txy = ty*this->x(); - const Scalar txz = tz*this->x(); - const Scalar tyy = ty*this->y(); - const Scalar tyz = tz*this->y(); - const Scalar tzz = tz*this->z(); - - res.coeffRef(0,0) = Scalar(1)-(tyy+tzz); - res.coeffRef(0,1) = txy-twz; - res.coeffRef(0,2) = txz+twy; - res.coeffRef(1,0) = txy+twz; - res.coeffRef(1,1) = Scalar(1)-(txx+tzz); - res.coeffRef(1,2) = tyz-twx; - res.coeffRef(2,0) = txz-twy; - res.coeffRef(2,1) = tyz+twx; - res.coeffRef(2,2) = Scalar(1)-(txx+tyy); - - return res; -} - -/** Sets *this to be a quaternion representing a rotation sending the vector \a a to the vector \a b. - * - * \returns a reference to *this. - * - * Note that the two input vectors do \b not have to be normalized. - */ -template<typename Scalar> -template<typename Derived1, typename Derived2> -inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b) -{ - Vector3 v0 = a.normalized(); - Vector3 v1 = b.normalized(); - Scalar c = v0.eigen2_dot(v1); - - // if dot == 1, vectors are the same - if (ei_isApprox(c,Scalar(1))) - { - // set to identity - this->w() = 1; this->vec().setZero(); - return *this; - } - // if dot == -1, vectors are opposites - if (ei_isApprox(c,Scalar(-1))) - { - this->vec() = v0.unitOrthogonal(); - this->w() = 0; - return *this; - } - - Vector3 axis = v0.cross(v1); - Scalar s = ei_sqrt((Scalar(1)+c)*Scalar(2)); - Scalar invs = Scalar(1)/s; - this->vec() = axis * invs; - this->w() = s * Scalar(0.5); - - return *this; -} - -/** \returns the multiplicative inverse of \c *this - * Note that in most cases, i.e., if you simply want the opposite rotation, - * and/or the quaternion is normalized, then it is enough to use the conjugate. - * - * \sa Quaternion::conjugate() - */ -template <typename Scalar> -inline Quaternion<Scalar> Quaternion<Scalar>::inverse() const -{ - // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ?? - Scalar n2 = this->squaredNorm(); - if (n2 > 0) - return Quaternion(conjugate().coeffs() / n2); - else - { - // return an invalid result to flag the error - return Quaternion(Coefficients::Zero()); - } -} - -/** \returns the conjugate of the \c *this which is equal to the multiplicative inverse - * if the quaternion is normalized. - * The conjugate of a quaternion represents the opposite rotation. - * - * \sa Quaternion::inverse() - */ -template <typename Scalar> -inline Quaternion<Scalar> Quaternion<Scalar>::conjugate() const -{ - return Quaternion(this->w(),-this->x(),-this->y(),-this->z()); -} - -/** \returns the angle (in radian) between two rotations - * \sa eigen2_dot() - */ -template <typename Scalar> -inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const -{ - double d = ei_abs(this->eigen2_dot(other)); - if (d>=1.0) - return 0; - return Scalar(2) * std::acos(d); -} - -/** \returns the spherical linear interpolation between the two quaternions - * \c *this and \a other at the parameter \a t - */ -template <typename Scalar> -Quaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other) const -{ - static const Scalar one = Scalar(1) - machine_epsilon<Scalar>(); - Scalar d = this->eigen2_dot(other); - Scalar absD = ei_abs(d); - - Scalar scale0; - Scalar scale1; - - if (absD>=one) - { - scale0 = Scalar(1) - t; - scale1 = t; - } - else - { - // theta is the angle between the 2 quaternions - Scalar theta = std::acos(absD); - Scalar sinTheta = ei_sin(theta); - - scale0 = ei_sin( ( Scalar(1) - t ) * theta) / sinTheta; - scale1 = ei_sin( ( t * theta) ) / sinTheta; - if (d<0) - scale1 = -scale1; - } - - return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs()); -} - -// set from a rotation matrix -template<typename Other> -struct ei_quaternion_assign_impl<Other,3,3> -{ - typedef typename Other::Scalar Scalar; - static inline void run(Quaternion<Scalar>& q, const Other& mat) - { - // This algorithm comes from "Quaternion Calculus and Fast Animation", - // Ken Shoemake, 1987 SIGGRAPH course notes - Scalar t = mat.trace(); - if (t > 0) - { - t = ei_sqrt(t + Scalar(1.0)); - q.w() = Scalar(0.5)*t; - t = Scalar(0.5)/t; - q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t; - q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t; - q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t; - } - else - { - int i = 0; - if (mat.coeff(1,1) > mat.coeff(0,0)) - i = 1; - if (mat.coeff(2,2) > mat.coeff(i,i)) - i = 2; - int j = (i+1)%3; - int k = (j+1)%3; - - t = ei_sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0)); - q.coeffs().coeffRef(i) = Scalar(0.5) * t; - t = Scalar(0.5)/t; - q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t; - q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t; - q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t; - } - } -}; - -// set from a vector of coefficients assumed to be a quaternion -template<typename Other> -struct ei_quaternion_assign_impl<Other,4,1> -{ - typedef typename Other::Scalar Scalar; - static inline void run(Quaternion<Scalar>& q, const Other& vec) - { - q.coeffs() = vec; - } -}; - -} // end namespace Eigen diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/Rotation2D.h b/eigen/Eigen/src/Eigen2Support/Geometry/Rotation2D.h deleted file mode 100644 index 19b8582..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/Rotation2D.h +++ /dev/null @@ -1,145 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -/** \geometry_module \ingroup Geometry_Module - * - * \class Rotation2D - * - * \brief Represents a rotation/orientation in a 2 dimensional space. - * - * \param _Scalar the scalar type, i.e., the type of the coefficients - * - * This class is equivalent to a single scalar representing a counter clock wise rotation - * as a single angle in radian. It provides some additional features such as the automatic - * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar - * interface to Quaternion in order to facilitate the writing of generic algorithms - * dealing with rotations. - * - * \sa class Quaternion, class Transform - */ -template<typename _Scalar> struct ei_traits<Rotation2D<_Scalar> > -{ - typedef _Scalar Scalar; -}; - -template<typename _Scalar> -class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2> -{ - typedef RotationBase<Rotation2D<_Scalar>,2> Base; - -public: - - using Base::operator*; - - enum { Dim = 2 }; - /** the scalar type of the coefficients */ - typedef _Scalar Scalar; - typedef Matrix<Scalar,2,1> Vector2; - typedef Matrix<Scalar,2,2> Matrix2; - -protected: - - Scalar m_angle; - -public: - - /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */ - inline Rotation2D(Scalar a) : m_angle(a) {} - - /** \returns the rotation angle */ - inline Scalar angle() const { return m_angle; } - - /** \returns a read-write reference to the rotation angle */ - inline Scalar& angle() { return m_angle; } - - /** \returns the inverse rotation */ - inline Rotation2D inverse() const { return -m_angle; } - - /** Concatenates two rotations */ - inline Rotation2D operator*(const Rotation2D& other) const - { return m_angle + other.m_angle; } - - /** Concatenates two rotations */ - inline Rotation2D& operator*=(const Rotation2D& other) - { return m_angle += other.m_angle; return *this; } - - /** Applies the rotation to a 2D vector */ - Vector2 operator* (const Vector2& vec) const - { return toRotationMatrix() * vec; } - - template<typename Derived> - Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m); - Matrix2 toRotationMatrix(void) const; - - /** \returns the spherical interpolation between \c *this and \a other using - * parameter \a t. It is in fact equivalent to a linear interpolation. - */ - inline Rotation2D slerp(Scalar t, const Rotation2D& other) const - { return m_angle * (1-t) + other.angle() * t; } - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const - { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other) - { - m_angle = Scalar(other.angle()); - } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return ei_isApprox(m_angle,other.m_angle, prec); } -}; - -/** \ingroup Geometry_Module - * single precision 2D rotation type */ -typedef Rotation2D<float> Rotation2Df; -/** \ingroup Geometry_Module - * double precision 2D rotation type */ -typedef Rotation2D<double> Rotation2Dd; - -/** Set \c *this from a 2x2 rotation matrix \a mat. - * In other words, this function extract the rotation angle - * from the rotation matrix. - */ -template<typename Scalar> -template<typename Derived> -Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat) -{ - EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE) - m_angle = ei_atan2(mat.coeff(1,0), mat.coeff(0,0)); - return *this; -} - -/** Constructs and \returns an equivalent 2x2 rotation matrix. - */ -template<typename Scalar> -typename Rotation2D<Scalar>::Matrix2 -Rotation2D<Scalar>::toRotationMatrix(void) const -{ - Scalar sinA = ei_sin(m_angle); - Scalar cosA = ei_cos(m_angle); - return (Matrix2() << cosA, -sinA, sinA, cosA).finished(); -} - -} // end namespace Eigen diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/RotationBase.h b/eigen/Eigen/src/Eigen2Support/Geometry/RotationBase.h deleted file mode 100644 index b1c8f38..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/RotationBase.h +++ /dev/null @@ -1,123 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -// this file aims to contains the various representations of rotation/orientation -// in 2D and 3D space excepted Matrix and Quaternion. - -/** \class RotationBase - * - * \brief Common base class for compact rotation representations - * - * \param Derived is the derived type, i.e., a rotation type - * \param _Dim the dimension of the space - */ -template<typename Derived, int _Dim> -class RotationBase -{ - public: - enum { Dim = _Dim }; - /** the scalar type of the coefficients */ - typedef typename ei_traits<Derived>::Scalar Scalar; - - /** corresponding linear transformation matrix type */ - typedef Matrix<Scalar,Dim,Dim> RotationMatrixType; - - inline const Derived& derived() const { return *static_cast<const Derived*>(this); } - inline Derived& derived() { return *static_cast<Derived*>(this); } - - /** \returns an equivalent rotation matrix */ - inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); } - - /** \returns the inverse rotation */ - inline Derived inverse() const { return derived().inverse(); } - - /** \returns the concatenation of the rotation \c *this with a translation \a t */ - inline Transform<Scalar,Dim> operator*(const Translation<Scalar,Dim>& t) const - { return toRotationMatrix() * t; } - - /** \returns the concatenation of the rotation \c *this with a scaling \a s */ - inline RotationMatrixType operator*(const Scaling<Scalar,Dim>& s) const - { return toRotationMatrix() * s; } - - /** \returns the concatenation of the rotation \c *this with an affine transformation \a t */ - inline Transform<Scalar,Dim> operator*(const Transform<Scalar,Dim>& t) const - { return toRotationMatrix() * t; } -}; - -/** \geometry_module - * - * Constructs a Dim x Dim rotation matrix from the rotation \a r - */ -template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols> -template<typename OtherDerived> -Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols> -::Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r) -{ - EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim)) - *this = r.toRotationMatrix(); -} - -/** \geometry_module - * - * Set a Dim x Dim rotation matrix from the rotation \a r - */ -template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols> -template<typename OtherDerived> -Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>& -Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols> -::operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r) -{ - EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim)) - return *this = r.toRotationMatrix(); -} - -/** \internal - * - * Helper function to return an arbitrary rotation object to a rotation matrix. - * - * \param Scalar the numeric type of the matrix coefficients - * \param Dim the dimension of the current space - * - * It returns a Dim x Dim fixed size matrix. - * - * Default specializations are provided for: - * - any scalar type (2D), - * - any matrix expression, - * - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D) - * - * Currently ei_toRotationMatrix is only used by Transform. - * - * \sa class Transform, class Rotation2D, class Quaternion, class AngleAxis - */ -template<typename Scalar, int Dim> -static inline Matrix<Scalar,2,2> ei_toRotationMatrix(const Scalar& s) -{ - EIGEN_STATIC_ASSERT(Dim==2,YOU_MADE_A_PROGRAMMING_MISTAKE) - return Rotation2D<Scalar>(s).toRotationMatrix(); -} - -template<typename Scalar, int Dim, typename OtherDerived> -static inline Matrix<Scalar,Dim,Dim> ei_toRotationMatrix(const RotationBase<OtherDerived,Dim>& r) -{ - return r.toRotationMatrix(); -} - -template<typename Scalar, int Dim, typename OtherDerived> -static inline const MatrixBase<OtherDerived>& ei_toRotationMatrix(const MatrixBase<OtherDerived>& mat) -{ - EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime==Dim && OtherDerived::ColsAtCompileTime==Dim, - YOU_MADE_A_PROGRAMMING_MISTAKE) - return mat; -} - -} // end namespace Eigen diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/Scaling.h b/eigen/Eigen/src/Eigen2Support/Geometry/Scaling.h deleted file mode 100644 index b8fa6cd..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/Scaling.h +++ /dev/null @@ -1,167 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -/** \geometry_module \ingroup Geometry_Module - * - * \class Scaling - * - * \brief Represents a possibly non uniform scaling transformation - * - * \param _Scalar the scalar type, i.e., the type of the coefficients. - * \param _Dim the dimension of the space, can be a compile time value or Dynamic - * - * \note This class is not aimed to be used to store a scaling transformation, - * but rather to make easier the constructions and updates of Transform objects. - * - * \sa class Translation, class Transform - */ -template<typename _Scalar, int _Dim> -class Scaling -{ -public: - EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim) - /** dimension of the space */ - enum { Dim = _Dim }; - /** the scalar type of the coefficients */ - typedef _Scalar Scalar; - /** corresponding vector type */ - typedef Matrix<Scalar,Dim,1> VectorType; - /** corresponding linear transformation matrix type */ - typedef Matrix<Scalar,Dim,Dim> LinearMatrixType; - /** corresponding translation type */ - typedef Translation<Scalar,Dim> TranslationType; - /** corresponding affine transformation type */ - typedef Transform<Scalar,Dim> TransformType; - -protected: - - VectorType m_coeffs; - -public: - - /** Default constructor without initialization. */ - Scaling() {} - /** Constructs and initialize a uniform scaling transformation */ - explicit inline Scaling(const Scalar& s) { m_coeffs.setConstant(s); } - /** 2D only */ - inline Scaling(const Scalar& sx, const Scalar& sy) - { - ei_assert(Dim==2); - m_coeffs.x() = sx; - m_coeffs.y() = sy; - } - /** 3D only */ - inline Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz) - { - ei_assert(Dim==3); - m_coeffs.x() = sx; - m_coeffs.y() = sy; - m_coeffs.z() = sz; - } - /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */ - explicit inline Scaling(const VectorType& coeffs) : m_coeffs(coeffs) {} - - const VectorType& coeffs() const { return m_coeffs; } - VectorType& coeffs() { return m_coeffs; } - - /** Concatenates two scaling */ - inline Scaling operator* (const Scaling& other) const - { return Scaling(coeffs().cwise() * other.coeffs()); } - - /** Concatenates a scaling and a translation */ - inline TransformType operator* (const TranslationType& t) const; - - /** Concatenates a scaling and an affine transformation */ - inline TransformType operator* (const TransformType& t) const; - - /** Concatenates a scaling and a linear transformation matrix */ - // TODO returns an expression - inline LinearMatrixType operator* (const LinearMatrixType& other) const - { return coeffs().asDiagonal() * other; } - - /** Concatenates a linear transformation matrix and a scaling */ - // TODO returns an expression - friend inline LinearMatrixType operator* (const LinearMatrixType& other, const Scaling& s) - { return other * s.coeffs().asDiagonal(); } - - template<typename Derived> - inline LinearMatrixType operator*(const RotationBase<Derived,Dim>& r) const - { return *this * r.toRotationMatrix(); } - - /** Applies scaling to vector */ - inline VectorType operator* (const VectorType& other) const - { return coeffs().asDiagonal() * other; } - - /** \returns the inverse scaling */ - inline Scaling inverse() const - { return Scaling(coeffs().cwise().inverse()); } - - inline Scaling& operator=(const Scaling& other) - { - m_coeffs = other.m_coeffs; - return *this; - } - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type cast() const - { return typename internal::cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type(*this); } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit Scaling(const Scaling<OtherScalarType,Dim>& other) - { m_coeffs = other.coeffs().template cast<Scalar>(); } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const Scaling& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return m_coeffs.isApprox(other.m_coeffs, prec); } - -}; - -/** \addtogroup Geometry_Module */ -//@{ -typedef Scaling<float, 2> Scaling2f; -typedef Scaling<double,2> Scaling2d; -typedef Scaling<float, 3> Scaling3f; -typedef Scaling<double,3> Scaling3d; -//@} - -template<typename Scalar, int Dim> -inline typename Scaling<Scalar,Dim>::TransformType -Scaling<Scalar,Dim>::operator* (const TranslationType& t) const -{ - TransformType res; - res.matrix().setZero(); - res.linear().diagonal() = coeffs(); - res.translation() = m_coeffs.cwise() * t.vector(); - res(Dim,Dim) = Scalar(1); - return res; -} - -template<typename Scalar, int Dim> -inline typename Scaling<Scalar,Dim>::TransformType -Scaling<Scalar,Dim>::operator* (const TransformType& t) const -{ - TransformType res = t; - res.prescale(m_coeffs); - return res; -} - -} // end namespace Eigen diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/Transform.h b/eigen/Eigen/src/Eigen2Support/Geometry/Transform.h deleted file mode 100644 index fab60b2..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/Transform.h +++ /dev/null @@ -1,786 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -// Note that we have to pass Dim and HDim because it is not allowed to use a template -// parameter to define a template specialization. To be more precise, in the following -// specializations, it is not allowed to use Dim+1 instead of HDim. -template< typename Other, - int Dim, - int HDim, - int OtherRows=Other::RowsAtCompileTime, - int OtherCols=Other::ColsAtCompileTime> -struct ei_transform_product_impl; - -/** \geometry_module \ingroup Geometry_Module - * - * \class Transform - * - * \brief Represents an homogeneous transformation in a N dimensional space - * - * \param _Scalar the scalar type, i.e., the type of the coefficients - * \param _Dim the dimension of the space - * - * The homography is internally represented and stored as a (Dim+1)^2 matrix which - * is available through the matrix() method. - * - * Conversion methods from/to Qt's QMatrix and QTransform are available if the - * preprocessor token EIGEN_QT_SUPPORT is defined. - * - * \sa class Matrix, class Quaternion - */ -template<typename _Scalar, int _Dim> -class Transform -{ -public: - EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1)) - enum { - Dim = _Dim, ///< space dimension in which the transformation holds - HDim = _Dim+1 ///< size of a respective homogeneous vector - }; - /** the scalar type of the coefficients */ - typedef _Scalar Scalar; - /** type of the matrix used to represent the transformation */ - typedef Matrix<Scalar,HDim,HDim> MatrixType; - /** type of the matrix used to represent the linear part of the transformation */ - typedef Matrix<Scalar,Dim,Dim> LinearMatrixType; - /** type of read/write reference to the linear part of the transformation */ - typedef Block<MatrixType,Dim,Dim> LinearPart; - /** type of read/write reference to the linear part of the transformation */ - typedef const Block<const MatrixType,Dim,Dim> ConstLinearPart; - /** type of a vector */ - typedef Matrix<Scalar,Dim,1> VectorType; - /** type of a read/write reference to the translation part of the rotation */ - typedef Block<MatrixType,Dim,1> TranslationPart; - /** type of a read/write reference to the translation part of the rotation */ - typedef const Block<const MatrixType,Dim,1> ConstTranslationPart; - /** corresponding translation type */ - typedef Translation<Scalar,Dim> TranslationType; - /** corresponding scaling transformation type */ - typedef Scaling<Scalar,Dim> ScalingType; - -protected: - - MatrixType m_matrix; - -public: - - /** Default constructor without initialization of the coefficients. */ - inline Transform() { } - - inline Transform(const Transform& other) - { - m_matrix = other.m_matrix; - } - - inline explicit Transform(const TranslationType& t) { *this = t; } - inline explicit Transform(const ScalingType& s) { *this = s; } - template<typename Derived> - inline explicit Transform(const RotationBase<Derived, Dim>& r) { *this = r; } - - inline Transform& operator=(const Transform& other) - { m_matrix = other.m_matrix; return *this; } - - template<typename OtherDerived, bool BigMatrix> // MSVC 2005 will commit suicide if BigMatrix has a default value - struct construct_from_matrix - { - static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other) - { - transform->matrix() = other; - } - }; - - template<typename OtherDerived> struct construct_from_matrix<OtherDerived, true> - { - static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other) - { - transform->linear() = other; - transform->translation().setZero(); - transform->matrix()(Dim,Dim) = Scalar(1); - transform->matrix().template block<1,Dim>(Dim,0).setZero(); - } - }; - - /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */ - template<typename OtherDerived> - inline explicit Transform(const MatrixBase<OtherDerived>& other) - { - construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other); - } - - /** Set \c *this from a (Dim+1)^2 matrix. */ - template<typename OtherDerived> - inline Transform& operator=(const MatrixBase<OtherDerived>& other) - { m_matrix = other; return *this; } - - #ifdef EIGEN_QT_SUPPORT - inline Transform(const QMatrix& other); - inline Transform& operator=(const QMatrix& other); - inline QMatrix toQMatrix(void) const; - inline Transform(const QTransform& other); - inline Transform& operator=(const QTransform& other); - inline QTransform toQTransform(void) const; - #endif - - /** shortcut for m_matrix(row,col); - * \sa MatrixBase::operaror(int,int) const */ - inline Scalar operator() (int row, int col) const { return m_matrix(row,col); } - /** shortcut for m_matrix(row,col); - * \sa MatrixBase::operaror(int,int) */ - inline Scalar& operator() (int row, int col) { return m_matrix(row,col); } - - /** \returns a read-only expression of the transformation matrix */ - inline const MatrixType& matrix() const { return m_matrix; } - /** \returns a writable expression of the transformation matrix */ - inline MatrixType& matrix() { return m_matrix; } - - /** \returns a read-only expression of the linear (linear) part of the transformation */ - inline ConstLinearPart linear() const { return m_matrix.template block<Dim,Dim>(0,0); } - /** \returns a writable expression of the linear (linear) part of the transformation */ - inline LinearPart linear() { return m_matrix.template block<Dim,Dim>(0,0); } - - /** \returns a read-only expression of the translation vector of the transformation */ - inline ConstTranslationPart translation() const { return m_matrix.template block<Dim,1>(0,Dim); } - /** \returns a writable expression of the translation vector of the transformation */ - inline TranslationPart translation() { return m_matrix.template block<Dim,1>(0,Dim); } - - /** \returns an expression of the product between the transform \c *this and a matrix expression \a other - * - * The right hand side \a other might be either: - * \li a vector of size Dim, - * \li an homogeneous vector of size Dim+1, - * \li a transformation matrix of size Dim+1 x Dim+1. - */ - // note: this function is defined here because some compilers cannot find the respective declaration - template<typename OtherDerived> - inline const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType - operator * (const MatrixBase<OtherDerived> &other) const - { return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); } - - /** \returns the product expression of a transformation matrix \a a times a transform \a b - * The transformation matrix \a a must have a Dim+1 x Dim+1 sizes. */ - template<typename OtherDerived> - friend inline const typename ProductReturnType<OtherDerived,MatrixType>::Type - operator * (const MatrixBase<OtherDerived> &a, const Transform &b) - { return a.derived() * b.matrix(); } - - /** Contatenates two transformations */ - inline const Transform - operator * (const Transform& other) const - { return Transform(m_matrix * other.matrix()); } - - /** \sa MatrixBase::setIdentity() */ - void setIdentity() { m_matrix.setIdentity(); } - static const typename MatrixType::IdentityReturnType Identity() - { - return MatrixType::Identity(); - } - - template<typename OtherDerived> - inline Transform& scale(const MatrixBase<OtherDerived> &other); - - template<typename OtherDerived> - inline Transform& prescale(const MatrixBase<OtherDerived> &other); - - inline Transform& scale(Scalar s); - inline Transform& prescale(Scalar s); - - template<typename OtherDerived> - inline Transform& translate(const MatrixBase<OtherDerived> &other); - - template<typename OtherDerived> - inline Transform& pretranslate(const MatrixBase<OtherDerived> &other); - - template<typename RotationType> - inline Transform& rotate(const RotationType& rotation); - - template<typename RotationType> - inline Transform& prerotate(const RotationType& rotation); - - Transform& shear(Scalar sx, Scalar sy); - Transform& preshear(Scalar sx, Scalar sy); - - inline Transform& operator=(const TranslationType& t); - inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); } - inline Transform operator*(const TranslationType& t) const; - - inline Transform& operator=(const ScalingType& t); - inline Transform& operator*=(const ScalingType& s) { return scale(s.coeffs()); } - inline Transform operator*(const ScalingType& s) const; - friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t) - { - Transform res = t; - res.matrix().row(Dim) = t.matrix().row(Dim); - res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy(); - return res; - } - - template<typename Derived> - inline Transform& operator=(const RotationBase<Derived,Dim>& r); - template<typename Derived> - inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); } - template<typename Derived> - inline Transform operator*(const RotationBase<Derived,Dim>& r) const; - - LinearMatrixType rotation() const; - template<typename RotationMatrixType, typename ScalingMatrixType> - void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const; - template<typename ScalingMatrixType, typename RotationMatrixType> - void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const; - - template<typename PositionDerived, typename OrientationType, typename ScaleDerived> - Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position, - const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale); - - inline const MatrixType inverse(TransformTraits traits = Affine) const; - - /** \returns a const pointer to the column major internal matrix */ - const Scalar* data() const { return m_matrix.data(); } - /** \returns a non-const pointer to the column major internal matrix */ - Scalar* data() { return m_matrix.data(); } - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type cast() const - { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type(*this); } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit Transform(const Transform<OtherScalarType,Dim>& other) - { m_matrix = other.matrix().template cast<Scalar>(); } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return m_matrix.isApprox(other.m_matrix, prec); } - - #ifdef EIGEN_TRANSFORM_PLUGIN - #include EIGEN_TRANSFORM_PLUGIN - #endif - -protected: - -}; - -/** \ingroup Geometry_Module */ -typedef Transform<float,2> Transform2f; -/** \ingroup Geometry_Module */ -typedef Transform<float,3> Transform3f; -/** \ingroup Geometry_Module */ -typedef Transform<double,2> Transform2d; -/** \ingroup Geometry_Module */ -typedef Transform<double,3> Transform3d; - -/************************** -*** Optional QT support *** -**************************/ - -#ifdef EIGEN_QT_SUPPORT -/** Initialises \c *this from a QMatrix assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>::Transform(const QMatrix& other) -{ - *this = other; -} - -/** Set \c *this from a QMatrix assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QMatrix& other) -{ - EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - m_matrix << other.m11(), other.m21(), other.dx(), - other.m12(), other.m22(), other.dy(), - 0, 0, 1; - return *this; -} - -/** \returns a QMatrix from \c *this assuming the dimension is 2. - * - * \warning this convertion might loss data if \c *this is not affine - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -QMatrix Transform<Scalar,Dim>::toQMatrix(void) const -{ - EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0), - m_matrix.coeff(0,1), m_matrix.coeff(1,1), - m_matrix.coeff(0,2), m_matrix.coeff(1,2)); -} - -/** Initialises \c *this from a QTransform assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>::Transform(const QTransform& other) -{ - *this = other; -} - -/** Set \c *this from a QTransform assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QTransform& other) -{ - EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - m_matrix << other.m11(), other.m21(), other.dx(), - other.m12(), other.m22(), other.dy(), - other.m13(), other.m23(), other.m33(); - return *this; -} - -/** \returns a QTransform from \c *this assuming the dimension is 2. - * - * This function is available only if the token EIGEN_QT_SUPPORT is defined. - */ -template<typename Scalar, int Dim> -QTransform Transform<Scalar,Dim>::toQTransform(void) const -{ - EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0), - m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1), - m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2)); -} -#endif - -/********************* -*** Procedural API *** -*********************/ - -/** Applies on the right the non uniform scale transformation represented - * by the vector \a other to \c *this and returns a reference to \c *this. - * \sa prescale() - */ -template<typename Scalar, int Dim> -template<typename OtherDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::scale(const MatrixBase<OtherDerived> &other) -{ - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim)) - linear() = (linear() * other.asDiagonal()).lazy(); - return *this; -} - -/** Applies on the right a uniform scale of a factor \a c to \c *this - * and returns a reference to \c *this. - * \sa prescale(Scalar) - */ -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::scale(Scalar s) -{ - linear() *= s; - return *this; -} - -/** Applies on the left the non uniform scale transformation represented - * by the vector \a other to \c *this and returns a reference to \c *this. - * \sa scale() - */ -template<typename Scalar, int Dim> -template<typename OtherDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::prescale(const MatrixBase<OtherDerived> &other) -{ - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim)) - m_matrix.template block<Dim,HDim>(0,0) = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0)).lazy(); - return *this; -} - -/** Applies on the left a uniform scale of a factor \a c to \c *this - * and returns a reference to \c *this. - * \sa scale(Scalar) - */ -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::prescale(Scalar s) -{ - m_matrix.template corner<Dim,HDim>(TopLeft) *= s; - return *this; -} - -/** Applies on the right the translation matrix represented by the vector \a other - * to \c *this and returns a reference to \c *this. - * \sa pretranslate() - */ -template<typename Scalar, int Dim> -template<typename OtherDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::translate(const MatrixBase<OtherDerived> &other) -{ - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim)) - translation() += linear() * other; - return *this; -} - -/** Applies on the left the translation matrix represented by the vector \a other - * to \c *this and returns a reference to \c *this. - * \sa translate() - */ -template<typename Scalar, int Dim> -template<typename OtherDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::pretranslate(const MatrixBase<OtherDerived> &other) -{ - EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim)) - translation() += other; - return *this; -} - -/** Applies on the right the rotation represented by the rotation \a rotation - * to \c *this and returns a reference to \c *this. - * - * The template parameter \a RotationType is the type of the rotation which - * must be known by ei_toRotationMatrix<>. - * - * Natively supported types includes: - * - any scalar (2D), - * - a Dim x Dim matrix expression, - * - a Quaternion (3D), - * - a AngleAxis (3D) - * - * This mechanism is easily extendable to support user types such as Euler angles, - * or a pair of Quaternion for 4D rotations. - * - * \sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType) - */ -template<typename Scalar, int Dim> -template<typename RotationType> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::rotate(const RotationType& rotation) -{ - linear() *= ei_toRotationMatrix<Scalar,Dim>(rotation); - return *this; -} - -/** Applies on the left the rotation represented by the rotation \a rotation - * to \c *this and returns a reference to \c *this. - * - * See rotate() for further details. - * - * \sa rotate() - */ -template<typename Scalar, int Dim> -template<typename RotationType> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::prerotate(const RotationType& rotation) -{ - m_matrix.template block<Dim,HDim>(0,0) = ei_toRotationMatrix<Scalar,Dim>(rotation) - * m_matrix.template block<Dim,HDim>(0,0); - return *this; -} - -/** Applies on the right the shear transformation represented - * by the vector \a other to \c *this and returns a reference to \c *this. - * \warning 2D only. - * \sa preshear() - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::shear(Scalar sx, Scalar sy) -{ - EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - VectorType tmp = linear().col(0)*sy + linear().col(1); - linear() << linear().col(0) + linear().col(1)*sx, tmp; - return *this; -} - -/** Applies on the left the shear transformation represented - * by the vector \a other to \c *this and returns a reference to \c *this. - * \warning 2D only. - * \sa shear() - */ -template<typename Scalar, int Dim> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::preshear(Scalar sx, Scalar sy) -{ - EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE) - m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0); - return *this; -} - -/****************************************************** -*** Scaling, Translation and Rotation compatibility *** -******************************************************/ - -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const TranslationType& t) -{ - linear().setIdentity(); - translation() = t.vector(); - m_matrix.template block<1,Dim>(Dim,0).setZero(); - m_matrix(Dim,Dim) = Scalar(1); - return *this; -} - -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const TranslationType& t) const -{ - Transform res = *this; - res.translate(t.vector()); - return res; -} - -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const ScalingType& s) -{ - m_matrix.setZero(); - linear().diagonal() = s.coeffs(); - m_matrix.coeffRef(Dim,Dim) = Scalar(1); - return *this; -} - -template<typename Scalar, int Dim> -inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const ScalingType& s) const -{ - Transform res = *this; - res.scale(s.coeffs()); - return res; -} - -template<typename Scalar, int Dim> -template<typename Derived> -inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const RotationBase<Derived,Dim>& r) -{ - linear() = ei_toRotationMatrix<Scalar,Dim>(r); - translation().setZero(); - m_matrix.template block<1,Dim>(Dim,0).setZero(); - m_matrix.coeffRef(Dim,Dim) = Scalar(1); - return *this; -} - -template<typename Scalar, int Dim> -template<typename Derived> -inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const RotationBase<Derived,Dim>& r) const -{ - Transform res = *this; - res.rotate(r.derived()); - return res; -} - -/************************ -*** Special functions *** -************************/ - -/** \returns the rotation part of the transformation - * \nonstableyet - * - * \svd_module - * - * \sa computeRotationScaling(), computeScalingRotation(), class SVD - */ -template<typename Scalar, int Dim> -typename Transform<Scalar,Dim>::LinearMatrixType -Transform<Scalar,Dim>::rotation() const -{ - LinearMatrixType result; - computeRotationScaling(&result, (LinearMatrixType*)0); - return result; -} - - -/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being - * not necessarily positive. - * - * If either pointer is zero, the corresponding computation is skipped. - * - * \nonstableyet - * - * \svd_module - * - * \sa computeScalingRotation(), rotation(), class SVD - */ -template<typename Scalar, int Dim> -template<typename RotationMatrixType, typename ScalingMatrixType> -void Transform<Scalar,Dim>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const -{ - JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV); - Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1 - Matrix<Scalar, Dim, 1> sv(svd.singularValues()); - sv.coeffRef(0) *= x; - if(scaling) - { - scaling->noalias() = svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint(); - } - if(rotation) - { - LinearMatrixType m(svd.matrixU()); - m.col(0) /= x; - rotation->noalias() = m * svd.matrixV().adjoint(); - } -} - -/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being - * not necessarily positive. - * - * If either pointer is zero, the corresponding computation is skipped. - * - * \nonstableyet - * - * \svd_module - * - * \sa computeRotationScaling(), rotation(), class SVD - */ -template<typename Scalar, int Dim> -template<typename ScalingMatrixType, typename RotationMatrixType> -void Transform<Scalar,Dim>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const -{ - JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV); - Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1 - Matrix<Scalar, Dim, 1> sv(svd.singularValues()); - sv.coeffRef(0) *= x; - if(scaling) - { - scaling->noalias() = svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint(); - } - if(rotation) - { - LinearMatrixType m(svd.matrixU()); - m.col(0) /= x; - rotation->noalias() = m * svd.matrixV().adjoint(); - } -} - -/** Convenient method to set \c *this from a position, orientation and scale - * of a 3D object. - */ -template<typename Scalar, int Dim> -template<typename PositionDerived, typename OrientationType, typename ScaleDerived> -Transform<Scalar,Dim>& -Transform<Scalar,Dim>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position, - const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale) -{ - linear() = ei_toRotationMatrix<Scalar,Dim>(orientation); - linear() *= scale.asDiagonal(); - translation() = position; - m_matrix.template block<1,Dim>(Dim,0).setZero(); - m_matrix(Dim,Dim) = Scalar(1); - return *this; -} - -/** \nonstableyet - * - * \returns the inverse transformation matrix according to some given knowledge - * on \c *this. - * - * \param traits allows to optimize the inversion process when the transformion - * is known to be not a general transformation. The possible values are: - * - Projective if the transformation is not necessarily affine, i.e., if the - * last row is not guaranteed to be [0 ... 0 1] - * - Affine is the default, the last row is assumed to be [0 ... 0 1] - * - Isometry if the transformation is only a concatenations of translations - * and rotations. - * - * \warning unless \a traits is always set to NoShear or NoScaling, this function - * requires the generic inverse method of MatrixBase defined in the LU module. If - * you forget to include this module, then you will get hard to debug linking errors. - * - * \sa MatrixBase::inverse() - */ -template<typename Scalar, int Dim> -inline const typename Transform<Scalar,Dim>::MatrixType -Transform<Scalar,Dim>::inverse(TransformTraits traits) const -{ - if (traits == Projective) - { - return m_matrix.inverse(); - } - else - { - MatrixType res; - if (traits == Affine) - { - res.template corner<Dim,Dim>(TopLeft) = linear().inverse(); - } - else if (traits == Isometry) - { - res.template corner<Dim,Dim>(TopLeft) = linear().transpose(); - } - else - { - ei_assert("invalid traits value in Transform::inverse()"); - } - // translation and remaining parts - res.template corner<Dim,1>(TopRight) = - res.template corner<Dim,Dim>(TopLeft) * translation(); - res.template corner<1,Dim>(BottomLeft).setZero(); - res.coeffRef(Dim,Dim) = Scalar(1); - return res; - } -} - -/***************************************************** -*** Specializations of operator* with a MatrixBase *** -*****************************************************/ - -template<typename Other, int Dim, int HDim> -struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim> -{ - typedef Transform<typename Other::Scalar,Dim> TransformType; - typedef typename TransformType::MatrixType MatrixType; - typedef typename ProductReturnType<MatrixType,Other>::Type ResultType; - static ResultType run(const TransformType& tr, const Other& other) - { return tr.matrix() * other; } -}; - -template<typename Other, int Dim, int HDim> -struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim> -{ - typedef Transform<typename Other::Scalar,Dim> TransformType; - typedef typename TransformType::MatrixType MatrixType; - typedef TransformType ResultType; - static ResultType run(const TransformType& tr, const Other& other) - { - TransformType res; - res.translation() = tr.translation(); - res.matrix().row(Dim) = tr.matrix().row(Dim); - res.linear() = (tr.linear() * other).lazy(); - return res; - } -}; - -template<typename Other, int Dim, int HDim> -struct ei_transform_product_impl<Other,Dim,HDim, HDim,1> -{ - typedef Transform<typename Other::Scalar,Dim> TransformType; - typedef typename TransformType::MatrixType MatrixType; - typedef typename ProductReturnType<MatrixType,Other>::Type ResultType; - static ResultType run(const TransformType& tr, const Other& other) - { return tr.matrix() * other; } -}; - -template<typename Other, int Dim, int HDim> -struct ei_transform_product_impl<Other,Dim,HDim, Dim,1> -{ - typedef typename Other::Scalar Scalar; - typedef Transform<Scalar,Dim> TransformType; - typedef Matrix<Scalar,Dim,1> ResultType; - static ResultType run(const TransformType& tr, const Other& other) - { return ((tr.linear() * other) + tr.translation()) - * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); } -}; - -} // end namespace Eigen diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/Translation.h b/eigen/Eigen/src/Eigen2Support/Geometry/Translation.h deleted file mode 100644 index 2b9859f..0000000 --- a/eigen/Eigen/src/Eigen2Support/Geometry/Translation.h +++ /dev/null @@ -1,184 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway - -namespace Eigen { - -/** \geometry_module \ingroup Geometry_Module - * - * \class Translation - * - * \brief Represents a translation transformation - * - * \param _Scalar the scalar type, i.e., the type of the coefficients. - * \param _Dim the dimension of the space, can be a compile time value or Dynamic - * - * \note This class is not aimed to be used to store a translation transformation, - * but rather to make easier the constructions and updates of Transform objects. - * - * \sa class Scaling, class Transform - */ -template<typename _Scalar, int _Dim> -class Translation -{ -public: - EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim) - /** dimension of the space */ - enum { Dim = _Dim }; - /** the scalar type of the coefficients */ - typedef _Scalar Scalar; - /** corresponding vector type */ - typedef Matrix<Scalar,Dim,1> VectorType; - /** corresponding linear transformation matrix type */ - typedef Matrix<Scalar,Dim,Dim> LinearMatrixType; - /** corresponding scaling transformation type */ - typedef Scaling<Scalar,Dim> ScalingType; - /** corresponding affine transformation type */ - typedef Transform<Scalar,Dim> TransformType; - -protected: - - VectorType m_coeffs; - -public: - - /** Default constructor without initialization. */ - Translation() {} - /** */ - inline Translation(const Scalar& sx, const Scalar& sy) - { - ei_assert(Dim==2); - m_coeffs.x() = sx; - m_coeffs.y() = sy; - } - /** */ - inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz) - { - ei_assert(Dim==3); - m_coeffs.x() = sx; - m_coeffs.y() = sy; - m_coeffs.z() = sz; - } - /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */ - explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {} - - const VectorType& vector() const { return m_coeffs; } - VectorType& vector() { return m_coeffs; } - - /** Concatenates two translation */ - inline Translation operator* (const Translation& other) const - { return Translation(m_coeffs + other.m_coeffs); } - - /** Concatenates a translation and a scaling */ - inline TransformType operator* (const ScalingType& other) const; - - /** Concatenates a translation and a linear transformation */ - inline TransformType operator* (const LinearMatrixType& linear) const; - - template<typename Derived> - inline TransformType operator*(const RotationBase<Derived,Dim>& r) const - { return *this * r.toRotationMatrix(); } - - /** Concatenates a linear transformation and a translation */ - // its a nightmare to define a templated friend function outside its declaration - friend inline TransformType operator* (const LinearMatrixType& linear, const Translation& t) - { - TransformType res; - res.matrix().setZero(); - res.linear() = linear; - res.translation() = linear * t.m_coeffs; - res.matrix().row(Dim).setZero(); - res(Dim,Dim) = Scalar(1); - return res; - } - - /** Concatenates a translation and an affine transformation */ - inline TransformType operator* (const TransformType& t) const; - - /** Applies translation to vector */ - inline VectorType operator* (const VectorType& other) const - { return m_coeffs + other; } - - /** \returns the inverse translation (opposite) */ - Translation inverse() const { return Translation(-m_coeffs); } - - Translation& operator=(const Translation& other) - { - m_coeffs = other.m_coeffs; - return *this; - } - - /** \returns \c *this with scalar type casted to \a NewScalarType - * - * Note that if \a NewScalarType is equal to the current scalar type of \c *this - * then this function smartly returns a const reference to \c *this. - */ - template<typename NewScalarType> - inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const - { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); } - - /** Copy constructor with scalar type conversion */ - template<typename OtherScalarType> - inline explicit Translation(const Translation<OtherScalarType,Dim>& other) - { m_coeffs = other.vector().template cast<Scalar>(); } - - /** \returns \c true if \c *this is approximately equal to \a other, within the precision - * determined by \a prec. - * - * \sa MatrixBase::isApprox() */ - bool isApprox(const Translation& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const - { return m_coeffs.isApprox(other.m_coeffs, prec); } - -}; - -/** \addtogroup Geometry_Module */ -//@{ -typedef Translation<float, 2> Translation2f; -typedef Translation<double,2> Translation2d; -typedef Translation<float, 3> Translation3f; -typedef Translation<double,3> Translation3d; -//@} - - -template<typename Scalar, int Dim> -inline typename Translation<Scalar,Dim>::TransformType -Translation<Scalar,Dim>::operator* (const ScalingType& other) const -{ - TransformType res; - res.matrix().setZero(); - res.linear().diagonal() = other.coeffs(); - res.translation() = m_coeffs; - res(Dim,Dim) = Scalar(1); - return res; -} - -template<typename Scalar, int Dim> -inline typename Translation<Scalar,Dim>::TransformType -Translation<Scalar,Dim>::operator* (const LinearMatrixType& linear) const -{ - TransformType res; - res.matrix().setZero(); - res.linear() = linear; - res.translation() = m_coeffs; - res.matrix().row(Dim).setZero(); - res(Dim,Dim) = Scalar(1); - return res; -} - -template<typename Scalar, int Dim> -inline typename Translation<Scalar,Dim>::TransformType -Translation<Scalar,Dim>::operator* (const TransformType& t) const -{ - TransformType res = t; - res.pretranslate(m_coeffs); - return res; -} - -} // end namespace Eigen |