Transform.h
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00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
00005 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
00006 //
00007 // This Source Code Form is subject to the terms of the Mozilla
00008 // Public License v. 2.0. If a copy of the MPL was not distributed
00009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00010 
00011 // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
00012 
00013 namespace Eigen { 
00014 
00015 // Note that we have to pass Dim and HDim because it is not allowed to use a template
00016 // parameter to define a template specialization. To be more precise, in the following
00017 // specializations, it is not allowed to use Dim+1 instead of HDim.
00018 template< typename Other,
00019           int Dim,
00020           int HDim,
00021           int OtherRows=Other::RowsAtCompileTime,
00022           int OtherCols=Other::ColsAtCompileTime>
00023 struct ei_transform_product_impl;
00024 
00042 template<typename _Scalar, int _Dim>
00043 class Transform
00044 {
00045 public:
00046   EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
00047   enum {
00048     Dim = _Dim,     
00049     HDim = _Dim+1   
00050   };
00052   typedef _Scalar Scalar;
00054   typedef Matrix<Scalar,HDim,HDim> MatrixType;
00056   typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
00058   typedef Block<MatrixType,Dim,Dim> LinearPart;
00060   typedef const Block<const MatrixType,Dim,Dim> ConstLinearPart;
00062   typedef Matrix<Scalar,Dim,1> VectorType;
00064   typedef Block<MatrixType,Dim,1> TranslationPart;
00066   typedef const Block<const MatrixType,Dim,1> ConstTranslationPart;
00068   typedef Translation<Scalar,Dim> TranslationType;
00070   typedef Scaling<Scalar,Dim> ScalingType;
00071 
00072 protected:
00073 
00074   MatrixType m_matrix;
00075 
00076 public:
00077 
00079   inline Transform() { }
00080 
00081   inline Transform(const Transform& other)
00082   {
00083     m_matrix = other.m_matrix;
00084   }
00085 
00086   inline explicit Transform(const TranslationType& t) { *this = t; }
00087   inline explicit Transform(const ScalingType& s) { *this = s; }
00088   template<typename Derived>
00089   inline explicit Transform(const RotationBase<Derived, Dim>& r) { *this = r; }
00090 
00091   inline Transform& operator=(const Transform& other)
00092   { m_matrix = other.m_matrix; return *this; }
00093 
00094   template<typename OtherDerived, bool BigMatrix> // MSVC 2005 will commit suicide if BigMatrix has a default value
00095   struct construct_from_matrix
00096   {
00097     static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
00098     {
00099       transform->matrix() = other;
00100     }
00101   };
00102 
00103   template<typename OtherDerived> struct construct_from_matrix<OtherDerived, true>
00104   {
00105     static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
00106     {
00107       transform->linear() = other;
00108       transform->translation().setZero();
00109       transform->matrix()(Dim,Dim) = Scalar(1);
00110       transform->matrix().template block<1,Dim>(Dim,0).setZero();
00111     }
00112   };
00113 
00115   template<typename OtherDerived>
00116   inline explicit Transform(const MatrixBase<OtherDerived>& other)
00117   {
00118     construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other);
00119   }
00120 
00122   template<typename OtherDerived>
00123   inline Transform& operator=(const MatrixBase<OtherDerived>& other)
00124   { m_matrix = other; return *this; }
00125 
00126   #ifdef EIGEN_QT_SUPPORT
00127   inline Transform(const QMatrix& other);
00128   inline Transform& operator=(const QMatrix& other);
00129   inline QMatrix toQMatrix(void) const;
00130   inline Transform(const QTransform& other);
00131   inline Transform& operator=(const QTransform& other);
00132   inline QTransform toQTransform(void) const;
00133   #endif
00134 
00137   inline Scalar operator() (int row, int col) const { return m_matrix(row,col); }
00140   inline Scalar& operator() (int row, int col) { return m_matrix(row,col); }
00141 
00143   inline const MatrixType& matrix() const { return m_matrix; }
00145   inline MatrixType& matrix() { return m_matrix; }
00146 
00148   inline ConstLinearPart linear() const { return m_matrix.template block<Dim,Dim>(0,0); }
00150   inline LinearPart linear() { return m_matrix.template block<Dim,Dim>(0,0); }
00151 
00153   inline ConstTranslationPart translation() const { return m_matrix.template block<Dim,1>(0,Dim); }
00155   inline TranslationPart translation() { return m_matrix.template block<Dim,1>(0,Dim); }
00156 
00164   // note: this function is defined here because some compilers cannot find the respective declaration
00165   template<typename OtherDerived>
00166   inline const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
00167   operator * (const MatrixBase<OtherDerived> &other) const
00168   { return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); }
00169 
00172   template<typename OtherDerived>
00173   friend inline const typename ProductReturnType<OtherDerived,MatrixType>::Type
00174   operator * (const MatrixBase<OtherDerived> &a, const Transform &b)
00175   { return a.derived() * b.matrix(); }
00176 
00178   inline const Transform
00179   operator * (const Transform& other) const
00180   { return Transform(m_matrix * other.matrix()); }
00181 
00183   void setIdentity() { m_matrix.setIdentity(); }
00184   static const typename MatrixType::IdentityReturnType Identity()
00185   {
00186     return MatrixType::Identity();
00187   }
00188 
00189   template<typename OtherDerived>
00190   inline Transform& scale(const MatrixBase<OtherDerived> &other);
00191 
00192   template<typename OtherDerived>
00193   inline Transform& prescale(const MatrixBase<OtherDerived> &other);
00194 
00195   inline Transform& scale(Scalar s);
00196   inline Transform& prescale(Scalar s);
00197 
00198   template<typename OtherDerived>
00199   inline Transform& translate(const MatrixBase<OtherDerived> &other);
00200 
00201   template<typename OtherDerived>
00202   inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
00203 
00204   template<typename RotationType>
00205   inline Transform& rotate(const RotationType& rotation);
00206 
00207   template<typename RotationType>
00208   inline Transform& prerotate(const RotationType& rotation);
00209 
00210   Transform& shear(Scalar sx, Scalar sy);
00211   Transform& preshear(Scalar sx, Scalar sy);
00212 
00213   inline Transform& operator=(const TranslationType& t);
00214   inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
00215   inline Transform operator*(const TranslationType& t) const;
00216 
00217   inline Transform& operator=(const ScalingType& t);
00218   inline Transform& operator*=(const ScalingType& s) { return scale(s.coeffs()); }
00219   inline Transform operator*(const ScalingType& s) const;
00220   friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t)
00221   {
00222     Transform res = t;
00223     res.matrix().row(Dim) = t.matrix().row(Dim);
00224     res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy();
00225     return res;
00226   }
00227 
00228   template<typename Derived>
00229   inline Transform& operator=(const RotationBase<Derived,Dim>& r);
00230   template<typename Derived>
00231   inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
00232   template<typename Derived>
00233   inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
00234 
00235   LinearMatrixType rotation() const;
00236   template<typename RotationMatrixType, typename ScalingMatrixType>
00237   void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
00238   template<typename ScalingMatrixType, typename RotationMatrixType>
00239   void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
00240 
00241   template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
00242   Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
00243     const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
00244 
00245   inline const MatrixType inverse(TransformTraits traits = Affine) const;
00246 
00248   const Scalar* data() const { return m_matrix.data(); }
00250   Scalar* data() { return m_matrix.data(); }
00251 
00257   template<typename NewScalarType>
00258   inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type cast() const
00259   { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type(*this); }
00260 
00262   template<typename OtherScalarType>
00263   inline explicit Transform(const Transform<OtherScalarType,Dim>& other)
00264   { m_matrix = other.matrix().template cast<Scalar>(); }
00265 
00270   bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
00271   { return m_matrix.isApprox(other.m_matrix, prec); }
00272 
00273   #ifdef EIGEN_TRANSFORM_PLUGIN
00274   #include EIGEN_TRANSFORM_PLUGIN
00275   #endif
00276 
00277 protected:
00278 
00279 };
00280 
00282 typedef Transform<float,2> Transform2f;
00284 typedef Transform<float,3> Transform3f;
00286 typedef Transform<double,2> Transform2d;
00288 typedef Transform<double,3> Transform3d;
00289 
00290 /**************************
00291 *** Optional QT support ***
00292 **************************/
00293 
00294 #ifdef EIGEN_QT_SUPPORT
00295 
00299 template<typename Scalar, int Dim>
00300 Transform<Scalar,Dim>::Transform(const QMatrix& other)
00301 {
00302   *this = other;
00303 }
00304 
00309 template<typename Scalar, int Dim>
00310 Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QMatrix& other)
00311 {
00312   EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
00313   m_matrix << other.m11(), other.m21(), other.dx(),
00314               other.m12(), other.m22(), other.dy(),
00315               0, 0, 1;
00316    return *this;
00317 }
00318 
00325 template<typename Scalar, int Dim>
00326 QMatrix Transform<Scalar,Dim>::toQMatrix(void) const
00327 {
00328   EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
00329   return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
00330                  m_matrix.coeff(0,1), m_matrix.coeff(1,1),
00331                  m_matrix.coeff(0,2), m_matrix.coeff(1,2));
00332 }
00333 
00338 template<typename Scalar, int Dim>
00339 Transform<Scalar,Dim>::Transform(const QTransform& other)
00340 {
00341   *this = other;
00342 }
00343 
00348 template<typename Scalar, int Dim>
00349 Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QTransform& other)
00350 {
00351   EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
00352   m_matrix << other.m11(), other.m21(), other.dx(),
00353               other.m12(), other.m22(), other.dy(),
00354               other.m13(), other.m23(), other.m33();
00355    return *this;
00356 }
00357 
00362 template<typename Scalar, int Dim>
00363 QTransform Transform<Scalar,Dim>::toQTransform(void) const
00364 {
00365   EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
00366   return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0),
00367                     m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1),
00368                     m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2));
00369 }
00370 #endif
00371 
00372 /*********************
00373 *** Procedural API ***
00374 *********************/
00375 
00380 template<typename Scalar, int Dim>
00381 template<typename OtherDerived>
00382 Transform<Scalar,Dim>&
00383 Transform<Scalar,Dim>::scale(const MatrixBase<OtherDerived> &other)
00384 {
00385   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
00386   linear() = (linear() * other.asDiagonal()).lazy();
00387   return *this;
00388 }
00389 
00394 template<typename Scalar, int Dim>
00395 inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::scale(Scalar s)
00396 {
00397   linear() *= s;
00398   return *this;
00399 }
00400 
00405 template<typename Scalar, int Dim>
00406 template<typename OtherDerived>
00407 Transform<Scalar,Dim>&
00408 Transform<Scalar,Dim>::prescale(const MatrixBase<OtherDerived> &other)
00409 {
00410   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
00411   m_matrix.template block<Dim,HDim>(0,0) = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0)).lazy();
00412   return *this;
00413 }
00414 
00419 template<typename Scalar, int Dim>
00420 inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::prescale(Scalar s)
00421 {
00422   m_matrix.template corner<Dim,HDim>(TopLeft) *= s;
00423   return *this;
00424 }
00425 
00430 template<typename Scalar, int Dim>
00431 template<typename OtherDerived>
00432 Transform<Scalar,Dim>&
00433 Transform<Scalar,Dim>::translate(const MatrixBase<OtherDerived> &other)
00434 {
00435   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
00436   translation() += linear() * other;
00437   return *this;
00438 }
00439 
00444 template<typename Scalar, int Dim>
00445 template<typename OtherDerived>
00446 Transform<Scalar,Dim>&
00447 Transform<Scalar,Dim>::pretranslate(const MatrixBase<OtherDerived> &other)
00448 {
00449   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
00450   translation() += other;
00451   return *this;
00452 }
00453 
00471 template<typename Scalar, int Dim>
00472 template<typename RotationType>
00473 Transform<Scalar,Dim>&
00474 Transform<Scalar,Dim>::rotate(const RotationType& rotation)
00475 {
00476   linear() *= ei_toRotationMatrix<Scalar,Dim>(rotation);
00477   return *this;
00478 }
00479 
00487 template<typename Scalar, int Dim>
00488 template<typename RotationType>
00489 Transform<Scalar,Dim>&
00490 Transform<Scalar,Dim>::prerotate(const RotationType& rotation)
00491 {
00492   m_matrix.template block<Dim,HDim>(0,0) = ei_toRotationMatrix<Scalar,Dim>(rotation)
00493                                          * m_matrix.template block<Dim,HDim>(0,0);
00494   return *this;
00495 }
00496 
00502 template<typename Scalar, int Dim>
00503 Transform<Scalar,Dim>&
00504 Transform<Scalar,Dim>::shear(Scalar sx, Scalar sy)
00505 {
00506   EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
00507   VectorType tmp = linear().col(0)*sy + linear().col(1);
00508   linear() << linear().col(0) + linear().col(1)*sx, tmp;
00509   return *this;
00510 }
00511 
00517 template<typename Scalar, int Dim>
00518 Transform<Scalar,Dim>&
00519 Transform<Scalar,Dim>::preshear(Scalar sx, Scalar sy)
00520 {
00521   EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
00522   m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0);
00523   return *this;
00524 }
00525 
00526 /******************************************************
00527 *** Scaling, Translation and Rotation compatibility ***
00528 ******************************************************/
00529 
00530 template<typename Scalar, int Dim>
00531 inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const TranslationType& t)
00532 {
00533   linear().setIdentity();
00534   translation() = t.vector();
00535   m_matrix.template block<1,Dim>(Dim,0).setZero();
00536   m_matrix(Dim,Dim) = Scalar(1);
00537   return *this;
00538 }
00539 
00540 template<typename Scalar, int Dim>
00541 inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const TranslationType& t) const
00542 {
00543   Transform res = *this;
00544   res.translate(t.vector());
00545   return res;
00546 }
00547 
00548 template<typename Scalar, int Dim>
00549 inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const ScalingType& s)
00550 {
00551   m_matrix.setZero();
00552   linear().diagonal() = s.coeffs();
00553   m_matrix.coeffRef(Dim,Dim) = Scalar(1);
00554   return *this;
00555 }
00556 
00557 template<typename Scalar, int Dim>
00558 inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const ScalingType& s) const
00559 {
00560   Transform res = *this;
00561   res.scale(s.coeffs());
00562   return res;
00563 }
00564 
00565 template<typename Scalar, int Dim>
00566 template<typename Derived>
00567 inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const RotationBase<Derived,Dim>& r)
00568 {
00569   linear() = ei_toRotationMatrix<Scalar,Dim>(r);
00570   translation().setZero();
00571   m_matrix.template block<1,Dim>(Dim,0).setZero();
00572   m_matrix.coeffRef(Dim,Dim) = Scalar(1);
00573   return *this;
00574 }
00575 
00576 template<typename Scalar, int Dim>
00577 template<typename Derived>
00578 inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const RotationBase<Derived,Dim>& r) const
00579 {
00580   Transform res = *this;
00581   res.rotate(r.derived());
00582   return res;
00583 }
00584 
00585 /************************
00586 *** Special functions ***
00587 ************************/
00588 
00596 template<typename Scalar, int Dim>
00597 typename Transform<Scalar,Dim>::LinearMatrixType
00598 Transform<Scalar,Dim>::rotation() const
00599 {
00600   LinearMatrixType result;
00601   computeRotationScaling(&result, (LinearMatrixType*)0);
00602   return result;
00603 }
00604 
00605 
00617 template<typename Scalar, int Dim>
00618 template<typename RotationMatrixType, typename ScalingMatrixType>
00619 void Transform<Scalar,Dim>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const
00620 {
00621   JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
00622   Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
00623   Matrix<Scalar, Dim, 1> sv(svd.singularValues());
00624   sv.coeffRef(0) *= x;
00625   if(scaling)
00626   {
00627     scaling->noalias() = svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint();
00628   }
00629   if(rotation)
00630   {
00631     LinearMatrixType m(svd.matrixU());
00632     m.col(0) /= x;
00633     rotation->noalias() = m * svd.matrixV().adjoint();
00634   }
00635 }
00636 
00648 template<typename Scalar, int Dim>
00649 template<typename ScalingMatrixType, typename RotationMatrixType>
00650 void Transform<Scalar,Dim>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const
00651 {
00652   JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU|ComputeFullV);
00653   Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
00654   Matrix<Scalar, Dim, 1> sv(svd.singularValues());
00655   sv.coeffRef(0) *= x;
00656   if(scaling)
00657   {
00658     scaling->noalias() = svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint();
00659   }
00660   if(rotation)
00661   {
00662     LinearMatrixType m(svd.matrixU());
00663     m.col(0) /= x;
00664     rotation->noalias() = m * svd.matrixV().adjoint();
00665   }
00666 }
00667 
00671 template<typename Scalar, int Dim>
00672 template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
00673 Transform<Scalar,Dim>&
00674 Transform<Scalar,Dim>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
00675   const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
00676 {
00677   linear() = ei_toRotationMatrix<Scalar,Dim>(orientation);
00678   linear() *= scale.asDiagonal();
00679   translation() = position;
00680   m_matrix.template block<1,Dim>(Dim,0).setZero();
00681   m_matrix(Dim,Dim) = Scalar(1);
00682   return *this;
00683 }
00684 
00704 template<typename Scalar, int Dim>
00705 inline const typename Transform<Scalar,Dim>::MatrixType
00706 Transform<Scalar,Dim>::inverse(TransformTraits traits) const
00707 {
00708   if (traits == Projective)
00709   {
00710     return m_matrix.inverse();
00711   }
00712   else
00713   {
00714     MatrixType res;
00715     if (traits == Affine)
00716     {
00717       res.template corner<Dim,Dim>(TopLeft) = linear().inverse();
00718     }
00719     else if (traits == Isometry)
00720     {
00721       res.template corner<Dim,Dim>(TopLeft) = linear().transpose();
00722     }
00723     else
00724     {
00725       ei_assert("invalid traits value in Transform::inverse()");
00726     }
00727     // translation and remaining parts
00728     res.template corner<Dim,1>(TopRight) = - res.template corner<Dim,Dim>(TopLeft) * translation();
00729     res.template corner<1,Dim>(BottomLeft).setZero();
00730     res.coeffRef(Dim,Dim) = Scalar(1);
00731     return res;
00732   }
00733 }
00734 
00735 /*****************************************************
00736 *** Specializations of operator* with a MatrixBase ***
00737 *****************************************************/
00738 
00739 template<typename Other, int Dim, int HDim>
00740 struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim>
00741 {
00742   typedef Transform<typename Other::Scalar,Dim> TransformType;
00743   typedef typename TransformType::MatrixType MatrixType;
00744   typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
00745   static ResultType run(const TransformType& tr, const Other& other)
00746   { return tr.matrix() * other; }
00747 };
00748 
00749 template<typename Other, int Dim, int HDim>
00750 struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim>
00751 {
00752   typedef Transform<typename Other::Scalar,Dim> TransformType;
00753   typedef typename TransformType::MatrixType MatrixType;
00754   typedef TransformType ResultType;
00755   static ResultType run(const TransformType& tr, const Other& other)
00756   {
00757     TransformType res;
00758     res.translation() = tr.translation();
00759     res.matrix().row(Dim) = tr.matrix().row(Dim);
00760     res.linear() = (tr.linear() * other).lazy();
00761     return res;
00762   }
00763 };
00764 
00765 template<typename Other, int Dim, int HDim>
00766 struct ei_transform_product_impl<Other,Dim,HDim, HDim,1>
00767 {
00768   typedef Transform<typename Other::Scalar,Dim> TransformType;
00769   typedef typename TransformType::MatrixType MatrixType;
00770   typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
00771   static ResultType run(const TransformType& tr, const Other& other)
00772   { return tr.matrix() * other; }
00773 };
00774 
00775 template<typename Other, int Dim, int HDim>
00776 struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
00777 {
00778   typedef typename Other::Scalar Scalar;
00779   typedef Transform<Scalar,Dim> TransformType;
00780   typedef Matrix<Scalar,Dim,1> ResultType;
00781   static ResultType run(const TransformType& tr, const Other& other)
00782   { return ((tr.linear() * other) + tr.translation())
00783           * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
00784 };
00785 
00786 } // end namespace Eigen


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Sat Jun 8 2019 19:39:56