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import eigen2 Geometry module into Eigen2Support.
fix build of geometry tests
This commit is contained in:
Benoit Jacob
parent
5bfde30e48
commit
bd12ac4ffc
@ -33,22 +33,29 @@ namespace Eigen {
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*/
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#include "src/Geometry/OrthoMethods.h"
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#include "src/Geometry/Homogeneous.h"
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#include "src/Geometry/RotationBase.h"
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#include "src/Geometry/Rotation2D.h"
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#include "src/Geometry/Quaternion.h"
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#include "src/Geometry/AngleAxis.h"
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#include "src/Geometry/EulerAngles.h"
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#include "src/Geometry/Transform.h"
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#include "src/Geometry/Translation.h"
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#include "src/Geometry/Scaling.h"
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#include "src/Geometry/Hyperplane.h"
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#include "src/Geometry/ParametrizedLine.h"
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#include "src/Geometry/AlignedBox.h"
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#include "src/Geometry/Umeyama.h"
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#if defined EIGEN_VECTORIZE_SSE
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#include "src/Geometry/arch/Geometry_SSE.h"
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#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
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#include "src/Geometry/Homogeneous.h"
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#include "src/Geometry/RotationBase.h"
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#include "src/Geometry/Rotation2D.h"
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#include "src/Geometry/Quaternion.h"
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#include "src/Geometry/AngleAxis.h"
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#include "src/Geometry/Transform.h"
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#include "src/Geometry/Translation.h"
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#include "src/Geometry/Scaling.h"
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#include "src/Geometry/Hyperplane.h"
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#include "src/Geometry/ParametrizedLine.h"
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#include "src/Geometry/AlignedBox.h"
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#include "src/Geometry/Umeyama.h"
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#if defined EIGEN_VECTORIZE_SSE
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#include "src/Geometry/arch/Geometry_SSE.h"
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#endif
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#endif
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#ifdef EIGEN2_SUPPORT
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#include "src/Eigen2Support/Geometry/All.h"
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#endif
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} // namespace Eigen
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@ -376,7 +376,15 @@ template<typename Derived> class MatrixBase
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PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
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PlainObject unitOrthogonal(void) const;
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Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
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#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
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ScalarMultipleReturnType operator*(const UniformScaling<Scalar>& s) const;
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// put this as separate enum value to work around possible GCC 4.3 bug (?)
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enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1?Vertical:Horizontal };
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typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
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HomogeneousReturnType homogeneous() const;
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#endif
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enum {
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SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
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};
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@ -384,16 +392,10 @@ template<typename Derived> class MatrixBase
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internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
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internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
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typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>,
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ConstStartMinusOne > HNormalizedReturnType;
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const ConstStartMinusOne > HNormalizedReturnType;
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const HNormalizedReturnType hnormalized() const;
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// put this as separate enum value to work around possible GCC 4.3 bug (?)
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enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1?Vertical:Horizontal };
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typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
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HomogeneousReturnType homogeneous() const;
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////////// Householder module ///////////
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void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
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@ -449,13 +451,13 @@ template<typename Derived> class MatrixBase
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inline Cwise<Derived> cwise();
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VectorBlock<Derived> start(Index size);
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const VectorBlock<Derived> start(Index size) const;
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const VectorBlock<const Derived> start(Index size) const;
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VectorBlock<Derived> end(Index size);
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const VectorBlock<Derived> end(Index size) const;
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const VectorBlock<const Derived> end(Index size) const;
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template<int Size> VectorBlock<Derived,Size> start();
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template<int Size> const VectorBlock<Derived,Size> start() const;
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template<int Size> const VectorBlock<const Derived,Size> start() const;
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template<int Size> VectorBlock<Derived,Size> end();
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template<int Size> const VectorBlock<Derived,Size> end() const;
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template<int Size> const VectorBlock<const Derived,Size> end() const;
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Minor<Derived> minor(Index row, Index col);
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const Minor<Derived> minor(Index row, Index col) const;
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@ -468,7 +468,9 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
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/////////// Geometry module ///////////
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#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
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Homogeneous<ExpressionType,Direction> homogeneous() const;
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#endif
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typedef typename ExpressionType::PlainObject CrossReturnType;
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template<typename OtherDerived>
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@ -490,8 +492,8 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
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Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
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HNormalized_Factors;
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typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,
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HNormalized_Block,
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Replicate<HNormalized_Factors,
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const HNormalized_Block,
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const Replicate<HNormalized_Factors,
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Direction==Vertical ? HNormalized_SizeMinusOne : 1,
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Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >
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HNormalizedReturnType;
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@ -219,12 +219,35 @@ template<typename Derived> class QuaternionBase;
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template<typename Scalar> class Quaternion;
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template<typename Scalar> class Rotation2D;
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template<typename Scalar> class AngleAxis;
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template<typename Scalar,int Dim> class Translation;
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#ifdef EIGEN2_SUPPORT
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template<typename Derived, int _Dim> class eigen2_RotationBase;
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template<typename Lhs, typename Rhs> class eigen2_Cross;
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template<typename Scalar> class eigen2_Quaternion;
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template<typename Scalar> class eigen2_Rotation2D;
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template<typename Scalar> class eigen2_AngleAxis;
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template<typename Scalar,int Dim> class eigen2_Transform;
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template <typename _Scalar, int _AmbientDim> class eigen2_ParametrizedLine;
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template <typename _Scalar, int _AmbientDim> class eigen2_Hyperplane;
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template<typename Scalar,int Dim> class eigen2_Translation;
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template<typename Scalar,int Dim> class eigen2_Scaling;
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#endif
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#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
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template<typename Scalar,int Dim> class Transform;
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template <typename _Scalar, int _AmbientDim> class ParametrizedLine;
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template <typename _Scalar, int _AmbientDim> class Hyperplane;
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template<typename Scalar,int Dim> class Scaling;
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#endif
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#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
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template<typename Scalar,int Dim,int Mode> class Transform;
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template <typename _Scalar, int _AmbientDim> class ParametrizedLine;
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template <typename _Scalar, int _AmbientDim> class Hyperplane;
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template<typename Scalar,int Dim> class Translation;
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template<typename Scalar> class UniformScaling;
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template<typename MatrixType,int Direction> class Homogeneous;
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#endif
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// MatrixFunctions module
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template<typename Derived> struct MatrixExponentialReturnValue;
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173
Eigen/src/Eigen2Support/Geometry/AlignedBox.h
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173
Eigen/src/Eigen2Support/Geometry/AlignedBox.h
Normal file
@ -0,0 +1,173 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_ALIGNEDBOX_H
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#define EIGEN_ALIGNEDBOX_H
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/** \geometry_module \ingroup Geometry_Module
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* \nonstableyet
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*
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* \class AlignedBox
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*
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* \brief An axis aligned box
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*
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* \param _Scalar the type of the scalar coefficients
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* \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
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*
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* This class represents an axis aligned box as a pair of the minimal and maximal corners.
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*/
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template <typename _Scalar, int _AmbientDim>
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class AlignedBox
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{
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public:
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
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enum { AmbientDimAtCompileTime = _AmbientDim };
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typedef _Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
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/** Default constructor initializing a null box. */
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inline explicit AlignedBox()
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{ if (AmbientDimAtCompileTime!=Dynamic) setNull(); }
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/** Constructs a null box with \a _dim the dimension of the ambient space. */
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inline explicit AlignedBox(int _dim) : m_min(_dim), m_max(_dim)
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{ setNull(); }
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/** Constructs a box with extremities \a _min and \a _max. */
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inline AlignedBox(const VectorType& _min, const VectorType& _max) : m_min(_min), m_max(_max) {}
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/** Constructs a box containing a single point \a p. */
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inline explicit AlignedBox(const VectorType& p) : m_min(p), m_max(p) {}
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~AlignedBox() {}
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/** \returns the dimension in which the box holds */
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inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size()-1 : AmbientDimAtCompileTime; }
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/** \returns true if the box is null, i.e, empty. */
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inline bool isNull() const { return (m_min.cwise() > m_max).any(); }
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/** Makes \c *this a null/empty box. */
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inline void setNull()
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{
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m_min.setConstant( std::numeric_limits<Scalar>::max());
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m_max.setConstant(-std::numeric_limits<Scalar>::max());
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}
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/** \returns the minimal corner */
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inline const VectorType& min() const { return m_min; }
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/** \returns a non const reference to the minimal corner */
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inline VectorType& min() { return m_min; }
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/** \returns the maximal corner */
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inline const VectorType& max() const { return m_max; }
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/** \returns a non const reference to the maximal corner */
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inline VectorType& max() { return m_max; }
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/** \returns true if the point \a p is inside the box \c *this. */
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inline bool contains(const VectorType& p) const
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{ return (m_min.cwise()<=p).all() && (p.cwise()<=m_max).all(); }
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/** \returns true if the box \a b is entirely inside the box \c *this. */
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inline bool contains(const AlignedBox& b) const
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{ return (m_min.cwise()<=b.min()).all() && (b.max().cwise()<=m_max).all(); }
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/** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
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inline AlignedBox& extend(const VectorType& p)
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{ m_min = m_min.cwise().min(p); m_max = m_max.cwise().max(p); return *this; }
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/** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
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inline AlignedBox& extend(const AlignedBox& b)
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{ m_min = m_min.cwise().min(b.m_min); m_max = m_max.cwise().max(b.m_max); return *this; }
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/** Clamps \c *this by the box \a b and returns a reference to \c *this. */
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inline AlignedBox& clamp(const AlignedBox& b)
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{ m_min = m_min.cwise().max(b.m_min); m_max = m_max.cwise().min(b.m_max); return *this; }
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/** Translate \c *this by the vector \a t and returns a reference to \c *this. */
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inline AlignedBox& translate(const VectorType& t)
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{ m_min += t; m_max += t; return *this; }
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/** \returns the squared distance between the point \a p and the box \c *this,
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* and zero if \a p is inside the box.
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* \sa exteriorDistance()
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*/
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inline Scalar squaredExteriorDistance(const VectorType& p) const;
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/** \returns the distance between the point \a p and the box \c *this,
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* and zero if \a p is inside the box.
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* \sa squaredExteriorDistance()
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*/
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inline Scalar exteriorDistance(const VectorType& p) const
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{ return ei_sqrt(squaredExteriorDistance(p)); }
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/** \returns \c *this with scalar type casted to \a NewScalarType
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*
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* Note that if \a NewScalarType is equal to the current scalar type of \c *this
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* then this function smartly returns a const reference to \c *this.
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*/
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template<typename NewScalarType>
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inline typename internal::cast_return_type<AlignedBox,
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AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
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{
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return typename internal::cast_return_type<AlignedBox,
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AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
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}
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/** Copy constructor with scalar type conversion */
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template<typename OtherScalarType>
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inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
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{
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m_min = other.min().template cast<Scalar>();
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m_max = other.max().template cast<Scalar>();
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}
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/** \returns \c true if \c *this is approximately equal to \a other, within the precision
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* determined by \a prec.
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*
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* \sa MatrixBase::isApprox() */
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bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
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{ return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
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protected:
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VectorType m_min, m_max;
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};
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template<typename Scalar,int AmbiantDim>
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inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const VectorType& p) const
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{
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Scalar dist2 = 0.;
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Scalar aux;
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for (int k=0; k<dim(); ++k)
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{
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if ((aux = (p[k]-m_min[k]))<0.)
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dist2 += aux*aux;
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else if ( (aux = (m_max[k]-p[k]))<0. )
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dist2 += aux*aux;
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}
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return dist2;
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}
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#endif // EIGEN_ALIGNEDBOX_H
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108
Eigen/src/Eigen2Support/Geometry/All.h
Normal file
108
Eigen/src/Eigen2Support/Geometry/All.h
Normal file
@ -0,0 +1,108 @@
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#ifndef EIGEN2_GEOMETRY_MODULE_H
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#define EIGEN2_GEOMETRY_MODULE_H
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#include <limits>
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#ifndef M_PI
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#define M_PI 3.14159265358979323846
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#endif
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#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
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#include "RotationBase.h"
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#include "Rotation2D.h"
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#include "Quaternion.h"
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#include "AngleAxis.h"
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#include "Transform.h"
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#include "Translation.h"
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#include "Scaling.h"
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#include "AlignedBox.h"
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#include "Hyperplane.h"
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#include "ParametrizedLine.h"
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#endif
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#define RotationBase eigen2_RotationBase
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#define Rotation2D eigen2_Rotation2D
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#define Rotation2Df eigen2_Rotation2Df
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#define Rotation2Dd eigen2_Rotation2Dd
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#define Quaternion eigen2_Quaternion
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#define Quaternionf eigen2_Quaternionf
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#define Quaterniond eigen2_Quaterniond
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#define AngleAxis eigen2_AngleAxis
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#define AngleAxisf eigen2_AngleAxisf
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#define AngleAxisd eigen2_AngleAxisd
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#define Transform eigen2_Transform
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#define Transform2f eigen2_Transform2f
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#define Transform2d eigen2_Transform2d
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#define Transform3f eigen2_Transform3f
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#define Transform3d eigen2_Transform3d
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#define Translation eigen2_Translation
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#define Translation2f eigen2_Translation2f
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#define Translation2d eigen2_Translation2d
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#define Translation3f eigen2_Translation3f
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#define Translation3d eigen2_Translation3d
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#define Scaling eigen2_Scaling
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#define Scaling2f eigen2_Scaling2f
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#define Scaling2d eigen2_Scaling2d
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#define Scaling3f eigen2_Scaling3f
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#define Scaling3d eigen2_Scaling3d
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#define AlignedBox eigen2_AlignedBox
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#define Hyperplane eigen2_Hyperplane
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#define ParametrizedLine eigen2_ParametrizedLine
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#include "RotationBase.h"
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#include "Rotation2D.h"
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#include "Quaternion.h"
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#include "AngleAxis.h"
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#include "Transform.h"
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#include "Translation.h"
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#include "Scaling.h"
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#include "AlignedBox.h"
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#include "Hyperplane.h"
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#include "ParametrizedLine.h"
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#undef RotationBase
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#undef Rotation2D
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#undef Rotation2Df
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#undef Rotation2Dd
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#undef Quaternion
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#undef Quaternionf
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#undef Quaterniond
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#undef AngleAxis
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#undef AngleAxisf
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#undef AngleAxisd
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#undef Transform
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#undef Transform2f
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#undef Transform2d
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#undef Transform3f
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#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
|
||||
228
Eigen/src/Eigen2Support/Geometry/AngleAxis.h
Normal file
228
Eigen/src/Eigen2Support/Geometry/AngleAxis.h
Normal file
@ -0,0 +1,228 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra. Eigen itself is part of the KDE project.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_ANGLEAXIS_H
|
||||
#define EIGEN_ANGLEAXIS_H
|
||||
|
||||
/** \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;
|
||||
}
|
||||
|
||||
#endif // EIGEN_ANGLEAXIS_H
|
||||
6
Eigen/src/Eigen2Support/Geometry/CMakeLists.txt
Normal file
6
Eigen/src/Eigen2Support/Geometry/CMakeLists.txt
Normal file
@ -0,0 +1,6 @@
|
||||
FILE(GLOB Eigen_Geometry_SRCS "*.h")
|
||||
|
||||
INSTALL(FILES
|
||||
${Eigen_Geometry_SRCS}
|
||||
DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Eigen2Support/Geometry
|
||||
)
|
||||
268
Eigen/src/Eigen2Support/Geometry/Hyperplane.h
Normal file
268
Eigen/src/Eigen2Support/Geometry/Hyperplane.h
Normal file
@ -0,0 +1,268 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra. Eigen itself is part of the KDE project.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
|
||||
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_HYPERPLANE_H
|
||||
#define EIGEN_HYPERPLANE_H
|
||||
|
||||
/** \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 explicit 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.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().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().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().dot(parametrized.origin());
|
||||
}
|
||||
|
||||
~Hyperplane() {}
|
||||
|
||||
/** \returns the dimension in which the plane holds */
|
||||
inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_coeffs.size()-1 : 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.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(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().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;
|
||||
};
|
||||
|
||||
#endif // EIGEN_HYPERPLANE_H
|
||||
155
Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h
Normal file
155
Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h
Normal file
@ -0,0 +1,155 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra. Eigen itself is part of the KDE project.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
|
||||
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_PARAMETRIZEDLINE_H
|
||||
#define EIGEN_PARAMETRIZEDLINE_H
|
||||
|
||||
/** \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 explicit 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.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()).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().dot(hyperplane.normal()))
|
||||
/(direction().dot(hyperplane.normal()));
|
||||
}
|
||||
|
||||
#endif // EIGEN_PARAMETRIZEDLINE_H
|
||||
509
Eigen/src/Eigen2Support/Geometry/Quaternion.h
Normal file
509
Eigen/src/Eigen2Support/Geometry/Quaternion.h
Normal file
@ -0,0 +1,509 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra. Eigen itself is part of the KDE project.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_QUATERNION_H
|
||||
#define EIGEN_QUATERNION_H
|
||||
|
||||
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()
|
||||
*/
|
||||
inline static 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 dot(const Quaternion& other) const { return m_coeffs.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 = 2*this->x();
|
||||
const Scalar ty = 2*this->y();
|
||||
const Scalar tz = 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) = 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) = 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) = 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.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 dot()
|
||||
*/
|
||||
template <typename Scalar>
|
||||
inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const
|
||||
{
|
||||
double d = ei_abs(this->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->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;
|
||||
inline static 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;
|
||||
inline static void run(Quaternion<Scalar>& q, const Other& vec)
|
||||
{
|
||||
q.coeffs() = vec;
|
||||
}
|
||||
};
|
||||
|
||||
#endif // EIGEN_QUATERNION_H
|
||||
159
Eigen/src/Eigen2Support/Geometry/Rotation2D.h
Normal file
159
Eigen/src/Eigen2Support/Geometry/Rotation2D.h
Normal file
@ -0,0 +1,159 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra. Eigen itself is part of the KDE project.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_ROTATION2D_H
|
||||
#define EIGEN_ROTATION2D_H
|
||||
|
||||
/** \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();
|
||||
}
|
||||
|
||||
#endif // EIGEN_ROTATION2D_H
|
||||
137
Eigen/src/Eigen2Support/Geometry/RotationBase.h
Normal file
137
Eigen/src/Eigen2Support/Geometry/RotationBase.h
Normal file
@ -0,0 +1,137 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra. Eigen itself is part of the KDE project.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_ROTATIONBASE_H
|
||||
#define EIGEN_ROTATIONBASE_H
|
||||
|
||||
// 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>
|
||||
inline static 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>
|
||||
inline static Matrix<Scalar,Dim,Dim> ei_toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)
|
||||
{
|
||||
return r.toRotationMatrix();
|
||||
}
|
||||
|
||||
template<typename Scalar, int Dim, typename OtherDerived>
|
||||
inline static 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;
|
||||
}
|
||||
|
||||
#endif // EIGEN_ROTATIONBASE_H
|
||||
181
Eigen/src/Eigen2Support/Geometry/Scaling.h
Normal file
181
Eigen/src/Eigen2Support/Geometry/Scaling.h
Normal file
@ -0,0 +1,181 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra. Eigen itself is part of the KDE project.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_SCALING_H
|
||||
#define EIGEN_SCALING_H
|
||||
|
||||
/** \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;
|
||||
}
|
||||
|
||||
#endif // EIGEN_SCALING_H
|
||||
800
Eigen/src/Eigen2Support/Geometry/Transform.h
Normal file
800
Eigen/src/Eigen2Support/Geometry/Transform.h
Normal file
@ -0,0 +1,800 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra. Eigen itself is part of the KDE project.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
|
||||
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_TRANSFORM_H
|
||||
#define EIGEN_TRANSFORM_H
|
||||
|
||||
// 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))); }
|
||||
};
|
||||
|
||||
#endif // EIGEN_TRANSFORM_H
|
||||
198
Eigen/src/Eigen2Support/Geometry/Translation.h
Normal file
198
Eigen/src/Eigen2Support/Geometry/Translation.h
Normal file
@ -0,0 +1,198 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra. Eigen itself is part of the KDE project.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_TRANSLATION_H
|
||||
#define EIGEN_TRANSLATION_H
|
||||
|
||||
/** \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;
|
||||
}
|
||||
|
||||
#endif // EIGEN_TRANSLATION_H
|
||||
@ -41,6 +41,7 @@ template<typename T> inline T ei_random () { return internal::random<T>(); }
|
||||
template<typename T> inline T ei_random (const T& x, const T& y) { return internal::random(x, y); }
|
||||
|
||||
template<typename T> inline T precision () { return NumTraits<T>::dummy_precision(); }
|
||||
template<typename T> inline T machine_epsilon () { return NumTraits<T>::epsilon(); }
|
||||
|
||||
|
||||
template<typename Scalar, typename OtherScalar>
|
||||
|
||||
@ -1,37 +0,0 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_TRANSFORM2_H
|
||||
#define EIGEN_TRANSFORM2_H
|
||||
|
||||
/** \ingroup Geometry_Module */
|
||||
typedef Projective2f Transform2f;
|
||||
/** \ingroup Geometry_Module */
|
||||
typedef Projective2d Transform2d;
|
||||
/** \ingroup Geometry_Module */
|
||||
typedef Projective3f Transform3f;
|
||||
/** \ingroup Geometry_Module */
|
||||
typedef Projective3d Transform3d;
|
||||
|
||||
#endif // EIGEN_TRANSFORM2_H
|
||||
@ -23,8 +23,8 @@
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_VECTORBLOCK2_H
|
||||
#define EIGEN_VECTORBLOCK2_H
|
||||
#ifndef EIGEN2_VECTORBLOCK_H
|
||||
#define EIGEN2_VECTORBLOCK_H
|
||||
|
||||
/** \deprecated use DenseMase::head(Index) */
|
||||
template<typename Derived>
|
||||
@ -37,11 +37,11 @@ MatrixBase<Derived>::start(Index size)
|
||||
|
||||
/** \deprecated use DenseMase::head(Index) */
|
||||
template<typename Derived>
|
||||
inline const VectorBlock<Derived>
|
||||
inline const VectorBlock<const Derived>
|
||||
MatrixBase<Derived>::start(Index size) const
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
|
||||
return VectorBlock<Derived>(derived(), 0, size);
|
||||
return VectorBlock<const Derived>(derived(), 0, size);
|
||||
}
|
||||
|
||||
/** \deprecated use DenseMase::tail(Index) */
|
||||
@ -55,11 +55,11 @@ MatrixBase<Derived>::end(Index size)
|
||||
|
||||
/** \deprecated use DenseMase::tail(Index) */
|
||||
template<typename Derived>
|
||||
inline const VectorBlock<Derived>
|
||||
inline const VectorBlock<const Derived>
|
||||
MatrixBase<Derived>::end(Index size) const
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
|
||||
return VectorBlock<Derived>(derived(), this->size() - size, size);
|
||||
return VectorBlock<const Derived>(derived(), this->size() - size, size);
|
||||
}
|
||||
|
||||
/** \deprecated use DenseMase::head() */
|
||||
@ -75,11 +75,11 @@ MatrixBase<Derived>::start()
|
||||
/** \deprecated use DenseMase::head() */
|
||||
template<typename Derived>
|
||||
template<int Size>
|
||||
inline const VectorBlock<Derived,Size>
|
||||
inline const VectorBlock<const Derived,Size>
|
||||
MatrixBase<Derived>::start() const
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
|
||||
return VectorBlock<Derived,Size>(derived(), 0);
|
||||
return VectorBlock<const Derived,Size>(derived(), 0);
|
||||
}
|
||||
|
||||
/** \deprecated use DenseMase::tail() */
|
||||
@ -95,11 +95,11 @@ MatrixBase<Derived>::end()
|
||||
/** \deprecated use DenseMase::tail() */
|
||||
template<typename Derived>
|
||||
template<int Size>
|
||||
inline const VectorBlock<Derived,Size>
|
||||
inline const VectorBlock<const Derived,Size>
|
||||
MatrixBase<Derived>::end() const
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
|
||||
return VectorBlock<Derived, Size>(derived(), size() - Size);
|
||||
return VectorBlock<const Derived, Size>(derived(), size() - Size);
|
||||
}
|
||||
|
||||
#endif // EIGEN_VECTORBLOCK2_H
|
||||
#endif // EIGEN2_VECTORBLOCK_H
|
||||
|
||||
@ -141,7 +141,7 @@ static inline DiagonalMatrix<Scalar,3> Scaling(Scalar sx, Scalar sy, Scalar sz)
|
||||
* This is an alias for coeffs.asDiagonal()
|
||||
*/
|
||||
template<typename Derived>
|
||||
static inline const DiagonalWrapper<Derived> Scaling(const MatrixBase<Derived>& coeffs)
|
||||
static inline const DiagonalWrapper<const Derived> Scaling(const MatrixBase<Derived>& coeffs)
|
||||
{ return coeffs.asDiagonal(); }
|
||||
|
||||
/** \addtogroup Geometry_Module */
|
||||
|
||||
@ -607,10 +607,6 @@ typedef Transform<double,2,Projective> Projective2d;
|
||||
/** \ingroup Geometry_Module */
|
||||
typedef Transform<double,3,Projective> Projective3d;
|
||||
|
||||
#ifdef EIGEN2_SUPPORT
|
||||
#include "../Eigen2Support/Transform.h"
|
||||
#endif
|
||||
|
||||
/**************************
|
||||
*** Optional QT support ***
|
||||
**************************/
|
||||
|
||||
Loading…
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Reference in New Issue
Block a user