1475 lines
56 KiB
C++
1475 lines
56 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_TRANSFORM_H
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#define EIGEN_TRANSFORM_H
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namespace Eigen {
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namespace internal {
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template<typename Transform>
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struct transform_traits
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{
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enum
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{
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Dim = Transform::Dim,
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HDim = Transform::HDim,
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Mode = Transform::Mode,
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IsProjective = (int(Mode)==int(Projective))
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};
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};
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template< typename TransformType,
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typename MatrixType,
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int Case = transform_traits<TransformType>::IsProjective ? 0
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: int(MatrixType::RowsAtCompileTime) == int(transform_traits<TransformType>::HDim) ? 1
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: 2>
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struct transform_right_product_impl;
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template< typename Other,
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int Mode,
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int Options,
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int Dim,
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int HDim,
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int OtherRows=Other::RowsAtCompileTime,
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int OtherCols=Other::ColsAtCompileTime>
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struct transform_left_product_impl;
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template< typename Lhs,
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typename Rhs,
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bool AnyProjective =
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transform_traits<Lhs>::IsProjective ||
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transform_traits<Rhs>::IsProjective>
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struct transform_transform_product_impl;
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template< typename Other,
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int Mode,
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int Options,
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int Dim,
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int HDim,
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int OtherRows=Other::RowsAtCompileTime,
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int OtherCols=Other::ColsAtCompileTime>
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struct transform_construct_from_matrix;
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template<typename TransformType> struct transform_take_affine_part;
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template<int Mode> struct transform_make_affine;
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} // end namespace internal
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/** \geometry_module \ingroup Geometry_Module
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*
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* \class Transform
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*
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* \brief Represents an homogeneous transformation in a N dimensional space
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*
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* \tparam _Scalar the scalar type, i.e., the type of the coefficients
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* \tparam _Dim the dimension of the space
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* \tparam _Mode the type of the transformation. Can be:
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* - #Affine: the transformation is stored as a (Dim+1)^2 matrix,
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* where the last row is assumed to be [0 ... 0 1].
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* - #AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix.
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* - #Projective: the transformation is stored as a (Dim+1)^2 matrix
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* without any assumption.
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* \tparam _Options has the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor.
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* These Options are passed directly to the underlying matrix type.
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*
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* The homography is internally represented and stored by a matrix which
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* is available through the matrix() method. To understand the behavior of
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* this class you have to think a Transform object as its internal
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* matrix representation. The chosen convention is right multiply:
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*
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* \code v' = T * v \endcode
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*
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* Therefore, an affine transformation matrix M is shaped like this:
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*
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* \f$ \left( \begin{array}{cc}
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* linear & translation\\
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* 0 ... 0 & 1
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* \end{array} \right) \f$
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*
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* Note that for a projective transformation the last row can be anything,
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* and then the interpretation of different parts might be sightly different.
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*
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* However, unlike a plain matrix, the Transform class provides many features
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* simplifying both its assembly and usage. In particular, it can be composed
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* with any other transformations (Transform,Translation,RotationBase,DiagonalMatrix)
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* and can be directly used to transform implicit homogeneous vectors. All these
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* operations are handled via the operator*. For the composition of transformations,
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* its principle consists to first convert the right/left hand sides of the product
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* to a compatible (Dim+1)^2 matrix and then perform a pure matrix product.
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* Of course, internally, operator* tries to perform the minimal number of operations
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* according to the nature of each terms. Likewise, when applying the transform
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* to points, the latters are automatically promoted to homogeneous vectors
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* before doing the matrix product. The conventions to homogeneous representations
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* are performed as follow:
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*
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* \b Translation t (Dim)x(1):
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* \f$ \left( \begin{array}{cc}
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* I & t \\
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* 0\,...\,0 & 1
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* \end{array} \right) \f$
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*
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* \b Rotation R (Dim)x(Dim):
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* \f$ \left( \begin{array}{cc}
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* R & 0\\
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* 0\,...\,0 & 1
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* \end{array} \right) \f$
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*<!--
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* \b Linear \b Matrix L (Dim)x(Dim):
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* \f$ \left( \begin{array}{cc}
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* L & 0\\
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* 0\,...\,0 & 1
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* \end{array} \right) \f$
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*
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* \b Affine \b Matrix A (Dim)x(Dim+1):
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* \f$ \left( \begin{array}{c}
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* A\\
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* 0\,...\,0\,1
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* \end{array} \right) \f$
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*-->
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* \b Scaling \b DiagonalMatrix S (Dim)x(Dim):
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* \f$ \left( \begin{array}{cc}
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* S & 0\\
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* 0\,...\,0 & 1
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* \end{array} \right) \f$
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*
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* \b Column \b point v (Dim)x(1):
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* \f$ \left( \begin{array}{c}
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* v\\
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* 1
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* \end{array} \right) \f$
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*
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* \b Set \b of \b column \b points V1...Vn (Dim)x(n):
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* \f$ \left( \begin{array}{ccc}
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* v_1 & ... & v_n\\
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* 1 & ... & 1
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* \end{array} \right) \f$
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*
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* The concatenation of a Transform object with any kind of other transformation
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* always returns a Transform object.
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*
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* A little exception to the "as pure matrix product" rule is the case of the
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* transformation of non homogeneous vectors by an affine transformation. In
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* that case the last matrix row can be ignored, and the product returns non
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* homogeneous vectors.
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*
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* Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation,
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* it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix.
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* The solution is either to use a Dim x Dynamic matrix or explicitly request a
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* vector transformation by making the vector homogeneous:
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* \code
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* m' = T * m.colwise().homogeneous();
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* \endcode
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* Note that there is zero overhead.
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*
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* Conversion methods from/to Qt's QMatrix and QTransform are available if the
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* preprocessor token EIGEN_QT_SUPPORT is defined.
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*
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* This class can be extended with the help of the plugin mechanism described on the page
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* \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_TRANSFORM_PLUGIN.
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*
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* \sa class Matrix, class Quaternion
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*/
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template<typename _Scalar, int _Dim, int _Mode, int _Options>
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class Transform
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{
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public:
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
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enum {
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Mode = _Mode,
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Options = _Options,
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Dim = _Dim, ///< space dimension in which the transformation holds
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HDim = _Dim+1, ///< size of a respective homogeneous vector
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Rows = int(Mode)==(AffineCompact) ? Dim : HDim
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};
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/** the scalar type of the coefficients */
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typedef _Scalar Scalar;
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typedef DenseIndex Index;
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/** type of the matrix used to represent the transformation */
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typedef typename internal::make_proper_matrix_type<Scalar,Rows,HDim,Options>::type MatrixType;
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/** constified MatrixType */
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typedef const MatrixType ConstMatrixType;
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/** type of the matrix used to represent the linear part of the transformation */
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typedef Matrix<Scalar,Dim,Dim,Options> LinearMatrixType;
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/** type of read/write reference to the linear part of the transformation */
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typedef Block<MatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> LinearPart;
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/** type of read reference to the linear part of the transformation */
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typedef const Block<ConstMatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> ConstLinearPart;
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/** type of read/write reference to the affine part of the transformation */
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typedef typename internal::conditional<int(Mode)==int(AffineCompact),
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MatrixType&,
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Block<MatrixType,Dim,HDim> >::type AffinePart;
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/** type of read reference to the affine part of the transformation */
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typedef typename internal::conditional<int(Mode)==int(AffineCompact),
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const MatrixType&,
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const Block<const MatrixType,Dim,HDim> >::type ConstAffinePart;
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/** type of a vector */
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typedef Matrix<Scalar,Dim,1> VectorType;
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/** type of a read/write reference to the translation part of the rotation */
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typedef Block<MatrixType,Dim,1,int(Mode)==(AffineCompact)> TranslationPart;
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/** type of a read reference to the translation part of the rotation */
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typedef const Block<ConstMatrixType,Dim,1,int(Mode)==(AffineCompact)> ConstTranslationPart;
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/** corresponding translation type */
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typedef Translation<Scalar,Dim> TranslationType;
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// this intermediate enum is needed to avoid an ICE with gcc 3.4 and 4.0
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enum { TransformTimeDiagonalMode = ((Mode==int(Isometry))?Affine:int(Mode)) };
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/** The return type of the product between a diagonal matrix and a transform */
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typedef Transform<Scalar,Dim,TransformTimeDiagonalMode> TransformTimeDiagonalReturnType;
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protected:
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MatrixType m_matrix;
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public:
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/** Default constructor without initialization of the meaningful coefficients.
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* If Mode==Affine, then the last row is set to [0 ... 0 1] */
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inline Transform()
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{
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check_template_params();
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internal::transform_make_affine<(int(Mode)==Affine) ? Affine : AffineCompact>::run(m_matrix);
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}
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inline Transform(const Transform& other)
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{
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check_template_params();
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m_matrix = other.m_matrix;
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}
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inline explicit Transform(const TranslationType& t)
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{
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check_template_params();
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*this = t;
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}
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inline explicit Transform(const UniformScaling<Scalar>& s)
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{
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check_template_params();
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*this = s;
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}
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template<typename Derived>
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inline explicit Transform(const RotationBase<Derived, Dim>& r)
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{
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check_template_params();
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*this = r;
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}
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inline Transform& operator=(const Transform& other)
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{ m_matrix = other.m_matrix; return *this; }
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typedef internal::transform_take_affine_part<Transform> take_affine_part;
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/** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
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template<typename OtherDerived>
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inline explicit Transform(const EigenBase<OtherDerived>& other)
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{
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EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
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YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
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check_template_params();
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internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
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}
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/** Set \c *this from a Dim^2 or (Dim+1)^2 matrix. */
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template<typename OtherDerived>
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inline Transform& operator=(const EigenBase<OtherDerived>& other)
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{
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EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
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YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
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internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
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return *this;
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}
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template<int OtherOptions>
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inline Transform(const Transform<Scalar,Dim,Mode,OtherOptions>& other)
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{
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check_template_params();
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// only the options change, we can directly copy the matrices
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m_matrix = other.matrix();
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}
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template<int OtherMode,int OtherOptions>
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inline Transform(const Transform<Scalar,Dim,OtherMode,OtherOptions>& other)
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{
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check_template_params();
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// prevent conversions as:
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// Affine | AffineCompact | Isometry = Projective
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EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Projective), Mode==int(Projective)),
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YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
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// prevent conversions as:
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// Isometry = Affine | AffineCompact
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EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Affine)||OtherMode==int(AffineCompact), Mode!=int(Isometry)),
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YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
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enum { ModeIsAffineCompact = Mode == int(AffineCompact),
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OtherModeIsAffineCompact = OtherMode == int(AffineCompact)
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};
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if(ModeIsAffineCompact == OtherModeIsAffineCompact)
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{
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// We need the block expression because the code is compiled for all
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// combinations of transformations and will trigger a compile time error
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// if one tries to assign the matrices directly
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m_matrix.template block<Dim,Dim+1>(0,0) = other.matrix().template block<Dim,Dim+1>(0,0);
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makeAffine();
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}
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else if(OtherModeIsAffineCompact)
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{
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typedef typename Transform<Scalar,Dim,OtherMode,OtherOptions>::MatrixType OtherMatrixType;
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internal::transform_construct_from_matrix<OtherMatrixType,Mode,Options,Dim,HDim>::run(this, other.matrix());
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}
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else
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{
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// here we know that Mode == AffineCompact and OtherMode != AffineCompact.
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// if OtherMode were Projective, the static assert above would already have caught it.
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// So the only possibility is that OtherMode == Affine
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linear() = other.linear();
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translation() = other.translation();
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}
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}
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template<typename OtherDerived>
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Transform(const ReturnByValue<OtherDerived>& other)
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{
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check_template_params();
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other.evalTo(*this);
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}
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template<typename OtherDerived>
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Transform& operator=(const ReturnByValue<OtherDerived>& other)
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{
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other.evalTo(*this);
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return *this;
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}
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#ifdef EIGEN_QT_SUPPORT
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inline Transform(const QMatrix& other);
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inline Transform& operator=(const QMatrix& other);
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inline QMatrix toQMatrix(void) const;
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inline Transform(const QTransform& other);
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inline Transform& operator=(const QTransform& other);
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inline QTransform toQTransform(void) const;
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#endif
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/** shortcut for m_matrix(row,col);
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* \sa MatrixBase::operator(Index,Index) const */
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inline Scalar operator() (Index row, Index col) const { return m_matrix(row,col); }
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/** shortcut for m_matrix(row,col);
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* \sa MatrixBase::operator(Index,Index) */
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inline Scalar& operator() (Index row, Index col) { return m_matrix(row,col); }
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/** \returns a read-only expression of the transformation matrix */
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inline const MatrixType& matrix() const { return m_matrix; }
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/** \returns a writable expression of the transformation matrix */
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inline MatrixType& matrix() { return m_matrix; }
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/** \returns a read-only expression of the linear part of the transformation */
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inline ConstLinearPart linear() const { return ConstLinearPart(m_matrix,0,0); }
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/** \returns a writable expression of the linear part of the transformation */
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inline LinearPart linear() { return LinearPart(m_matrix,0,0); }
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/** \returns a read-only expression of the Dim x HDim affine part of the transformation */
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inline ConstAffinePart affine() const { return take_affine_part::run(m_matrix); }
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/** \returns a writable expression of the Dim x HDim affine part of the transformation */
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inline AffinePart affine() { return take_affine_part::run(m_matrix); }
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/** \returns a read-only expression of the translation vector of the transformation */
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inline ConstTranslationPart translation() const { return ConstTranslationPart(m_matrix,0,Dim); }
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/** \returns a writable expression of the translation vector of the transformation */
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inline TranslationPart translation() { return TranslationPart(m_matrix,0,Dim); }
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/** \returns an expression of the product between the transform \c *this and a matrix expression \a other.
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*
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* The right-hand-side \a other can be either:
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* \li an homogeneous vector of size Dim+1,
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* \li a set of homogeneous vectors of size Dim+1 x N,
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* \li a transformation matrix of size Dim+1 x Dim+1.
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*
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* Moreover, if \c *this represents an affine transformation (i.e., Mode!=Projective), then \a other can also be:
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* \li a point of size Dim (computes: \code this->linear() * other + this->translation()\endcode),
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* \li a set of N points as a Dim x N matrix (computes: \code (this->linear() * other).colwise() + this->translation()\endcode),
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*
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* In all cases, the return type is a matrix or vector of same sizes as the right-hand-side \a other.
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*
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* If you want to interpret \a other as a linear or affine transformation, then first convert it to a Transform<> type,
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* or do your own cooking.
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*
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* Finally, if you want to apply Affine transformations to vectors, then explicitly apply the linear part only:
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* \code
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* Affine3f A;
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* Vector3f v1, v2;
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* v2 = A.linear() * v1;
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* \endcode
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*
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*/
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// note: this function is defined here because some compilers cannot find the respective declaration
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template<typename OtherDerived>
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EIGEN_STRONG_INLINE const typename OtherDerived::PlainObject
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operator * (const EigenBase<OtherDerived> &other) const
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{ return internal::transform_right_product_impl<Transform, OtherDerived>::run(*this,other.derived()); }
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/** \returns the product expression of a transformation matrix \a a times a transform \a b
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*
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* The left hand side \a other can be either:
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* \li a linear transformation matrix of size Dim x Dim,
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* \li an affine transformation matrix of size Dim x Dim+1,
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* \li a general transformation matrix of size Dim+1 x Dim+1.
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*/
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template<typename OtherDerived> friend
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inline const typename internal::transform_left_product_impl<OtherDerived,Mode,Options,_Dim,_Dim+1>::ResultType
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operator * (const EigenBase<OtherDerived> &a, const Transform &b)
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{ return internal::transform_left_product_impl<OtherDerived,Mode,Options,Dim,HDim>::run(a.derived(),b); }
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/** \returns The product expression of a transform \a a times a diagonal matrix \a b
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*
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* The rhs diagonal matrix is interpreted as an affine scaling transformation. The
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* product results in a Transform of the same type (mode) as the lhs only if the lhs
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* mode is no isometry. In that case, the returned transform is an affinity.
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*/
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template<typename DiagonalDerived>
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inline const TransformTimeDiagonalReturnType
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operator * (const DiagonalBase<DiagonalDerived> &b) const
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{
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TransformTimeDiagonalReturnType res(*this);
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res.linearExt() *= b;
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return res;
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}
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/** \returns The product expression of a diagonal matrix \a a times a transform \a b
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*
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* The lhs diagonal matrix is interpreted as an affine scaling transformation. The
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* product results in a Transform of the same type (mode) as the lhs only if the lhs
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* mode is no isometry. In that case, the returned transform is an affinity.
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*/
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template<typename DiagonalDerived>
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friend inline TransformTimeDiagonalReturnType
|
|
operator * (const DiagonalBase<DiagonalDerived> &a, const Transform &b)
|
|
{
|
|
TransformTimeDiagonalReturnType res;
|
|
res.linear().noalias() = a*b.linear();
|
|
res.translation().noalias() = a*b.translation();
|
|
if (Mode!=int(AffineCompact))
|
|
res.matrix().row(Dim) = b.matrix().row(Dim);
|
|
return res;
|
|
}
|
|
|
|
template<typename OtherDerived>
|
|
inline Transform& operator*=(const EigenBase<OtherDerived>& other) { return *this = *this * other; }
|
|
|
|
/** Concatenates two transformations */
|
|
inline const Transform operator * (const Transform& other) const
|
|
{
|
|
return internal::transform_transform_product_impl<Transform,Transform>::run(*this,other);
|
|
}
|
|
|
|
#ifdef __INTEL_COMPILER
|
|
private:
|
|
// this intermediate structure permits to workaround a bug in ICC 11:
|
|
// error: template instantiation resulted in unexpected function type of "Eigen::Transform<double, 3, 32, 0>
|
|
// (const Eigen::Transform<double, 3, 2, 0> &) const"
|
|
// (the meaning of a name may have changed since the template declaration -- the type of the template is:
|
|
// "Eigen::internal::transform_transform_product_impl<Eigen::Transform<double, 3, 32, 0>,
|
|
// Eigen::Transform<double, 3, Mode, Options>, <expression>>::ResultType (const Eigen::Transform<double, 3, Mode, Options> &) const")
|
|
//
|
|
template<int OtherMode,int OtherOptions> struct icc_11_workaround
|
|
{
|
|
typedef internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> > ProductType;
|
|
typedef typename ProductType::ResultType ResultType;
|
|
};
|
|
|
|
public:
|
|
/** Concatenates two different transformations */
|
|
template<int OtherMode,int OtherOptions>
|
|
inline typename icc_11_workaround<OtherMode,OtherOptions>::ResultType
|
|
operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
|
|
{
|
|
typedef typename icc_11_workaround<OtherMode,OtherOptions>::ProductType ProductType;
|
|
return ProductType::run(*this,other);
|
|
}
|
|
#else
|
|
/** Concatenates two different transformations */
|
|
template<int OtherMode,int OtherOptions>
|
|
inline typename internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::ResultType
|
|
operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
|
|
{
|
|
return internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::run(*this,other);
|
|
}
|
|
#endif
|
|
|
|
/** \sa MatrixBase::setIdentity() */
|
|
void setIdentity() { m_matrix.setIdentity(); }
|
|
|
|
/**
|
|
* \brief Returns an identity transformation.
|
|
* \todo In the future this function should be returning a Transform expression.
|
|
*/
|
|
static const Transform Identity()
|
|
{
|
|
return Transform(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(const Scalar& s);
|
|
inline Transform& prescale(const 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(const Scalar& sx, const Scalar& sy);
|
|
Transform& preshear(const Scalar& sx, const 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 UniformScaling<Scalar>& t);
|
|
inline Transform& operator*=(const UniformScaling<Scalar>& s) { return scale(s.factor()); }
|
|
inline Transform<Scalar,Dim,(int(Mode)==int(Isometry)?int(Affine):int(Mode))> operator*(const UniformScaling<Scalar>& s) const
|
|
{
|
|
Transform<Scalar,Dim,(int(Mode)==int(Isometry)?int(Affine):int(Mode)),Options> res = *this;
|
|
res.scale(s.factor());
|
|
return res;
|
|
}
|
|
|
|
inline Transform& operator*=(const DiagonalMatrix<Scalar,Dim>& s) { linearExt() *= s; return *this; }
|
|
|
|
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;
|
|
|
|
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 Transform inverse(TransformTraits traits = (TransformTraits)Mode) 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,Mode,Options> >::type cast() const
|
|
{ return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type(*this); }
|
|
|
|
/** Copy constructor with scalar type conversion */
|
|
template<typename OtherScalarType>
|
|
inline explicit Transform(const Transform<OtherScalarType,Dim,Mode,Options>& other)
|
|
{
|
|
check_template_params();
|
|
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, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
|
|
{ return m_matrix.isApprox(other.m_matrix, prec); }
|
|
|
|
/** Sets the last row to [0 ... 0 1]
|
|
*/
|
|
void makeAffine()
|
|
{
|
|
internal::transform_make_affine<int(Mode)>::run(m_matrix);
|
|
}
|
|
|
|
/** \internal
|
|
* \returns the Dim x Dim linear part if the transformation is affine,
|
|
* and the HDim x Dim part for projective transformations.
|
|
*/
|
|
inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt()
|
|
{ return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
|
|
/** \internal
|
|
* \returns the Dim x Dim linear part if the transformation is affine,
|
|
* and the HDim x Dim part for projective transformations.
|
|
*/
|
|
inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt() const
|
|
{ return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
|
|
|
|
/** \internal
|
|
* \returns the translation part if the transformation is affine,
|
|
* and the last column for projective transformations.
|
|
*/
|
|
inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt()
|
|
{ return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
|
|
/** \internal
|
|
* \returns the translation part if the transformation is affine,
|
|
* and the last column for projective transformations.
|
|
*/
|
|
inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt() const
|
|
{ return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
|
|
|
|
|
|
#ifdef EIGEN_TRANSFORM_PLUGIN
|
|
#include EIGEN_TRANSFORM_PLUGIN
|
|
#endif
|
|
|
|
protected:
|
|
#ifndef EIGEN_PARSED_BY_DOXYGEN
|
|
static EIGEN_STRONG_INLINE void check_template_params()
|
|
{
|
|
EIGEN_STATIC_ASSERT((Options & (DontAlign|RowMajor)) == Options, INVALID_MATRIX_TEMPLATE_PARAMETERS)
|
|
}
|
|
#endif
|
|
|
|
};
|
|
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<float,2,Isometry> Isometry2f;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<float,3,Isometry> Isometry3f;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<double,2,Isometry> Isometry2d;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<double,3,Isometry> Isometry3d;
|
|
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<float,2,Affine> Affine2f;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<float,3,Affine> Affine3f;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<double,2,Affine> Affine2d;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<double,3,Affine> Affine3d;
|
|
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<float,2,AffineCompact> AffineCompact2f;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<float,3,AffineCompact> AffineCompact3f;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<double,2,AffineCompact> AffineCompact2d;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<double,3,AffineCompact> AffineCompact3d;
|
|
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<float,2,Projective> Projective2f;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<float,3,Projective> Projective3f;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<double,2,Projective> Projective2d;
|
|
/** \ingroup Geometry_Module */
|
|
typedef Transform<double,3,Projective> Projective3d;
|
|
|
|
/**************************
|
|
*** Optional QT support ***
|
|
**************************/
|
|
|
|
#ifdef EIGEN_QT_SUPPORT
|
|
/** Initializes \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, int Mode,int Options>
|
|
Transform<Scalar,Dim,Mode,Options>::Transform(const QMatrix& other)
|
|
{
|
|
check_template_params();
|
|
*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, int Mode,int Options>
|
|
Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::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 conversion 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, int Mode, int Options>
|
|
QMatrix Transform<Scalar,Dim,Mode,Options>::toQMatrix(void) const
|
|
{
|
|
check_template_params();
|
|
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));
|
|
}
|
|
|
|
/** Initializes \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, int Mode,int Options>
|
|
Transform<Scalar,Dim,Mode,Options>::Transform(const QTransform& other)
|
|
{
|
|
check_template_params();
|
|
*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, int Mode, int Options>
|
|
Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QTransform& other)
|
|
{
|
|
check_template_params();
|
|
EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
|
|
if (Mode == int(AffineCompact))
|
|
m_matrix << other.m11(), other.m21(), other.dx(),
|
|
other.m12(), other.m22(), other.dy();
|
|
else
|
|
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, int Mode, int Options>
|
|
QTransform Transform<Scalar,Dim,Mode,Options>::toQTransform(void) const
|
|
{
|
|
EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
|
|
if (Mode == int(AffineCompact))
|
|
return QTransform(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));
|
|
else
|
|
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, int Mode, int Options>
|
|
template<typename OtherDerived>
|
|
Transform<Scalar,Dim,Mode,Options>&
|
|
Transform<Scalar,Dim,Mode,Options>::scale(const MatrixBase<OtherDerived> &other)
|
|
{
|
|
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
|
|
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
|
|
linearExt().noalias() = (linearExt() * other.asDiagonal());
|
|
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, int Mode, int Options>
|
|
inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::scale(const Scalar& s)
|
|
{
|
|
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
|
|
linearExt() *= 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, int Mode, int Options>
|
|
template<typename OtherDerived>
|
|
Transform<Scalar,Dim,Mode,Options>&
|
|
Transform<Scalar,Dim,Mode,Options>::prescale(const MatrixBase<OtherDerived> &other)
|
|
{
|
|
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
|
|
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
|
|
affine().noalias() = (other.asDiagonal() * affine());
|
|
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, int Mode, int Options>
|
|
inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::prescale(const Scalar& s)
|
|
{
|
|
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
|
|
m_matrix.template topRows<Dim>() *= 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, int Mode, int Options>
|
|
template<typename OtherDerived>
|
|
Transform<Scalar,Dim,Mode,Options>&
|
|
Transform<Scalar,Dim,Mode,Options>::translate(const MatrixBase<OtherDerived> &other)
|
|
{
|
|
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
|
|
translationExt() += linearExt() * 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, int Mode, int Options>
|
|
template<typename OtherDerived>
|
|
Transform<Scalar,Dim,Mode,Options>&
|
|
Transform<Scalar,Dim,Mode,Options>::pretranslate(const MatrixBase<OtherDerived> &other)
|
|
{
|
|
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
|
|
if(int(Mode)==int(Projective))
|
|
affine() += other * m_matrix.row(Dim);
|
|
else
|
|
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 internal::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, int Mode, int Options>
|
|
template<typename RotationType>
|
|
Transform<Scalar,Dim,Mode,Options>&
|
|
Transform<Scalar,Dim,Mode,Options>::rotate(const RotationType& rotation)
|
|
{
|
|
linearExt() *= internal::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, int Mode, int Options>
|
|
template<typename RotationType>
|
|
Transform<Scalar,Dim,Mode,Options>&
|
|
Transform<Scalar,Dim,Mode,Options>::prerotate(const RotationType& rotation)
|
|
{
|
|
m_matrix.template block<Dim,HDim>(0,0) = internal::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, int Mode, int Options>
|
|
Transform<Scalar,Dim,Mode,Options>&
|
|
Transform<Scalar,Dim,Mode,Options>::shear(const Scalar& sx, const Scalar& sy)
|
|
{
|
|
EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
|
|
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
|
|
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, int Mode, int Options>
|
|
Transform<Scalar,Dim,Mode,Options>&
|
|
Transform<Scalar,Dim,Mode,Options>::preshear(const Scalar& sx, const Scalar& sy)
|
|
{
|
|
EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
|
|
EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
|
|
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, int Mode, int Options>
|
|
inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const TranslationType& t)
|
|
{
|
|
linear().setIdentity();
|
|
translation() = t.vector();
|
|
makeAffine();
|
|
return *this;
|
|
}
|
|
|
|
template<typename Scalar, int Dim, int Mode, int Options>
|
|
inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const TranslationType& t) const
|
|
{
|
|
Transform res = *this;
|
|
res.translate(t.vector());
|
|
return res;
|
|
}
|
|
|
|
template<typename Scalar, int Dim, int Mode, int Options>
|
|
inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const UniformScaling<Scalar>& s)
|
|
{
|
|
m_matrix.setZero();
|
|
linear().diagonal().fill(s.factor());
|
|
makeAffine();
|
|
return *this;
|
|
}
|
|
|
|
template<typename Scalar, int Dim, int Mode, int Options>
|
|
template<typename Derived>
|
|
inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const RotationBase<Derived,Dim>& r)
|
|
{
|
|
linear() = internal::toRotationMatrix<Scalar,Dim>(r);
|
|
translation().setZero();
|
|
makeAffine();
|
|
return *this;
|
|
}
|
|
|
|
template<typename Scalar, int Dim, int Mode, int Options>
|
|
template<typename Derived>
|
|
inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::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
|
|
*
|
|
*
|
|
* \svd_module
|
|
*
|
|
* \sa computeRotationScaling(), computeScalingRotation(), class SVD
|
|
*/
|
|
template<typename Scalar, int Dim, int Mode, int Options>
|
|
const typename Transform<Scalar,Dim,Mode,Options>::LinearMatrixType
|
|
Transform<Scalar,Dim,Mode,Options>::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.
|
|
*
|
|
*
|
|
*
|
|
* \svd_module
|
|
*
|
|
* \sa computeScalingRotation(), rotation(), class SVD
|
|
*/
|
|
template<typename Scalar, int Dim, int Mode, int Options>
|
|
template<typename RotationMatrixType, typename ScalingMatrixType>
|
|
void Transform<Scalar,Dim,Mode,Options>::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
|
|
VectorType sv(svd.singularValues());
|
|
sv.coeffRef(0) *= x;
|
|
if(scaling) scaling->lazyAssign(svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint());
|
|
if(rotation)
|
|
{
|
|
LinearMatrixType m(svd.matrixU());
|
|
m.col(0) /= x;
|
|
rotation->lazyAssign(m * svd.matrixV().adjoint());
|
|
}
|
|
}
|
|
|
|
/** decomposes the linear part of the transformation as a product scaling x rotation, the scaling being
|
|
* not necessarily positive.
|
|
*
|
|
* If either pointer is zero, the corresponding computation is skipped.
|
|
*
|
|
*
|
|
*
|
|
* \svd_module
|
|
*
|
|
* \sa computeRotationScaling(), rotation(), class SVD
|
|
*/
|
|
template<typename Scalar, int Dim, int Mode, int Options>
|
|
template<typename ScalingMatrixType, typename RotationMatrixType>
|
|
void Transform<Scalar,Dim,Mode,Options>::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
|
|
VectorType sv(svd.singularValues());
|
|
sv.coeffRef(0) *= x;
|
|
if(scaling) scaling->lazyAssign(svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint());
|
|
if(rotation)
|
|
{
|
|
LinearMatrixType m(svd.matrixU());
|
|
m.col(0) /= x;
|
|
rotation->lazyAssign(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, int Mode, int Options>
|
|
template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
|
|
Transform<Scalar,Dim,Mode,Options>&
|
|
Transform<Scalar,Dim,Mode,Options>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
|
|
const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
|
|
{
|
|
linear() = internal::toRotationMatrix<Scalar,Dim>(orientation);
|
|
linear() *= scale.asDiagonal();
|
|
translation() = position;
|
|
makeAffine();
|
|
return *this;
|
|
}
|
|
|
|
namespace internal {
|
|
|
|
template<int Mode>
|
|
struct transform_make_affine
|
|
{
|
|
template<typename MatrixType>
|
|
static void run(MatrixType &mat)
|
|
{
|
|
static const int Dim = MatrixType::ColsAtCompileTime-1;
|
|
mat.template block<1,Dim>(Dim,0).setZero();
|
|
mat.coeffRef(Dim,Dim) = typename MatrixType::Scalar(1);
|
|
}
|
|
};
|
|
|
|
template<>
|
|
struct transform_make_affine<AffineCompact>
|
|
{
|
|
template<typename MatrixType> static void run(MatrixType &) { }
|
|
};
|
|
|
|
// selector needed to avoid taking the inverse of a 3x4 matrix
|
|
template<typename TransformType, int Mode=TransformType::Mode>
|
|
struct projective_transform_inverse
|
|
{
|
|
static inline void run(const TransformType&, TransformType&)
|
|
{}
|
|
};
|
|
|
|
template<typename TransformType>
|
|
struct projective_transform_inverse<TransformType, Projective>
|
|
{
|
|
static inline void run(const TransformType& m, TransformType& res)
|
|
{
|
|
res.matrix() = m.matrix().inverse();
|
|
}
|
|
};
|
|
|
|
} // end namespace internal
|
|
|
|
|
|
/**
|
|
*
|
|
* \returns the inverse transformation according to some given knowledge
|
|
* on \c *this.
|
|
*
|
|
* \param hint allows to optimize the inversion process when the transformation
|
|
* is known to be not a general transformation (optional). 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 if the last row can be assumed to be [0 ... 0 1]
|
|
* - #Isometry if the transformation is only a concatenations of translations
|
|
* and rotations.
|
|
* The default is the template class parameter \c Mode.
|
|
*
|
|
* \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, int Mode, int Options>
|
|
Transform<Scalar,Dim,Mode,Options>
|
|
Transform<Scalar,Dim,Mode,Options>::inverse(TransformTraits hint) const
|
|
{
|
|
Transform res;
|
|
if (hint == Projective)
|
|
{
|
|
internal::projective_transform_inverse<Transform>::run(*this, res);
|
|
}
|
|
else
|
|
{
|
|
if (hint == Isometry)
|
|
{
|
|
res.matrix().template topLeftCorner<Dim,Dim>() = linear().transpose();
|
|
}
|
|
else if(hint&Affine)
|
|
{
|
|
res.matrix().template topLeftCorner<Dim,Dim>() = linear().inverse();
|
|
}
|
|
else
|
|
{
|
|
eigen_assert(false && "Invalid transform traits in Transform::Inverse");
|
|
}
|
|
// translation and remaining parts
|
|
res.matrix().template topRightCorner<Dim,1>()
|
|
= - res.matrix().template topLeftCorner<Dim,Dim>() * translation();
|
|
res.makeAffine(); // we do need this, because in the beginning res is uninitialized
|
|
}
|
|
return res;
|
|
}
|
|
|
|
namespace internal {
|
|
|
|
/*****************************************************
|
|
*** Specializations of take affine part ***
|
|
*****************************************************/
|
|
|
|
template<typename TransformType> struct transform_take_affine_part {
|
|
typedef typename TransformType::MatrixType MatrixType;
|
|
typedef typename TransformType::AffinePart AffinePart;
|
|
typedef typename TransformType::ConstAffinePart ConstAffinePart;
|
|
static inline AffinePart run(MatrixType& m)
|
|
{ return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
|
|
static inline ConstAffinePart run(const MatrixType& m)
|
|
{ return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
|
|
};
|
|
|
|
template<typename Scalar, int Dim, int Options>
|
|
struct transform_take_affine_part<Transform<Scalar,Dim,AffineCompact, Options> > {
|
|
typedef typename Transform<Scalar,Dim,AffineCompact,Options>::MatrixType MatrixType;
|
|
static inline MatrixType& run(MatrixType& m) { return m; }
|
|
static inline const MatrixType& run(const MatrixType& m) { return m; }
|
|
};
|
|
|
|
/*****************************************************
|
|
*** Specializations of construct from matrix ***
|
|
*****************************************************/
|
|
|
|
template<typename Other, int Mode, int Options, int Dim, int HDim>
|
|
struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,Dim>
|
|
{
|
|
static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
|
|
{
|
|
transform->linear() = other;
|
|
transform->translation().setZero();
|
|
transform->makeAffine();
|
|
}
|
|
};
|
|
|
|
template<typename Other, int Mode, int Options, int Dim, int HDim>
|
|
struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,HDim>
|
|
{
|
|
static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
|
|
{
|
|
transform->affine() = other;
|
|
transform->makeAffine();
|
|
}
|
|
};
|
|
|
|
template<typename Other, int Mode, int Options, int Dim, int HDim>
|
|
struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, HDim,HDim>
|
|
{
|
|
static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
|
|
{ transform->matrix() = other; }
|
|
};
|
|
|
|
template<typename Other, int Options, int Dim, int HDim>
|
|
struct transform_construct_from_matrix<Other, AffineCompact,Options,Dim,HDim, HDim,HDim>
|
|
{
|
|
static inline void run(Transform<typename Other::Scalar,Dim,AffineCompact,Options> *transform, const Other& other)
|
|
{ transform->matrix() = other.template block<Dim,HDim>(0,0); }
|
|
};
|
|
|
|
/**********************************************************
|
|
*** Specializations of operator* with rhs EigenBase ***
|
|
**********************************************************/
|
|
|
|
template<int LhsMode,int RhsMode>
|
|
struct transform_product_result
|
|
{
|
|
enum
|
|
{
|
|
Mode =
|
|
(LhsMode == (int)Projective || RhsMode == (int)Projective ) ? Projective :
|
|
(LhsMode == (int)Affine || RhsMode == (int)Affine ) ? Affine :
|
|
(LhsMode == (int)AffineCompact || RhsMode == (int)AffineCompact ) ? AffineCompact :
|
|
(LhsMode == (int)Isometry || RhsMode == (int)Isometry ) ? Isometry : Projective
|
|
};
|
|
};
|
|
|
|
template< typename TransformType, typename MatrixType >
|
|
struct transform_right_product_impl< TransformType, MatrixType, 0 >
|
|
{
|
|
typedef typename MatrixType::PlainObject ResultType;
|
|
|
|
static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
|
|
{
|
|
return T.matrix() * other;
|
|
}
|
|
};
|
|
|
|
template< typename TransformType, typename MatrixType >
|
|
struct transform_right_product_impl< TransformType, MatrixType, 1 >
|
|
{
|
|
enum {
|
|
Dim = TransformType::Dim,
|
|
HDim = TransformType::HDim,
|
|
OtherRows = MatrixType::RowsAtCompileTime,
|
|
OtherCols = MatrixType::ColsAtCompileTime
|
|
};
|
|
|
|
typedef typename MatrixType::PlainObject ResultType;
|
|
|
|
static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
|
|
{
|
|
EIGEN_STATIC_ASSERT(OtherRows==HDim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
|
|
|
|
typedef Block<ResultType, Dim, OtherCols, int(MatrixType::RowsAtCompileTime)==Dim> TopLeftLhs;
|
|
|
|
ResultType res(other.rows(),other.cols());
|
|
TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() = T.affine() * other;
|
|
res.row(OtherRows-1) = other.row(OtherRows-1);
|
|
|
|
return res;
|
|
}
|
|
};
|
|
|
|
template< typename TransformType, typename MatrixType >
|
|
struct transform_right_product_impl< TransformType, MatrixType, 2 >
|
|
{
|
|
enum {
|
|
Dim = TransformType::Dim,
|
|
HDim = TransformType::HDim,
|
|
OtherRows = MatrixType::RowsAtCompileTime,
|
|
OtherCols = MatrixType::ColsAtCompileTime
|
|
};
|
|
|
|
typedef typename MatrixType::PlainObject ResultType;
|
|
|
|
static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
|
|
{
|
|
EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
|
|
|
|
typedef Block<ResultType, Dim, OtherCols, true> TopLeftLhs;
|
|
ResultType res(Replicate<typename TransformType::ConstTranslationPart, 1, OtherCols>(T.translation(),1,other.cols()));
|
|
TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() += T.linear() * other;
|
|
|
|
return res;
|
|
}
|
|
};
|
|
|
|
/**********************************************************
|
|
*** Specializations of operator* with lhs EigenBase ***
|
|
**********************************************************/
|
|
|
|
// generic HDim x HDim matrix * T => Projective
|
|
template<typename Other,int Mode, int Options, int Dim, int HDim>
|
|
struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, HDim,HDim>
|
|
{
|
|
typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
|
|
typedef typename TransformType::MatrixType MatrixType;
|
|
typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
|
|
static ResultType run(const Other& other,const TransformType& tr)
|
|
{ return ResultType(other * tr.matrix()); }
|
|
};
|
|
|
|
// generic HDim x HDim matrix * AffineCompact => Projective
|
|
template<typename Other, int Options, int Dim, int HDim>
|
|
struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, HDim,HDim>
|
|
{
|
|
typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
|
|
typedef typename TransformType::MatrixType MatrixType;
|
|
typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
|
|
static ResultType run(const Other& other,const TransformType& tr)
|
|
{
|
|
ResultType res;
|
|
res.matrix().noalias() = other.template block<HDim,Dim>(0,0) * tr.matrix();
|
|
res.matrix().col(Dim) += other.col(Dim);
|
|
return res;
|
|
}
|
|
};
|
|
|
|
// affine matrix * T
|
|
template<typename Other,int Mode, int Options, int Dim, int HDim>
|
|
struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,HDim>
|
|
{
|
|
typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
|
|
typedef typename TransformType::MatrixType MatrixType;
|
|
typedef TransformType ResultType;
|
|
static ResultType run(const Other& other,const TransformType& tr)
|
|
{
|
|
ResultType res;
|
|
res.affine().noalias() = other * tr.matrix();
|
|
res.matrix().row(Dim) = tr.matrix().row(Dim);
|
|
return res;
|
|
}
|
|
};
|
|
|
|
// affine matrix * AffineCompact
|
|
template<typename Other, int Options, int Dim, int HDim>
|
|
struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, Dim,HDim>
|
|
{
|
|
typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
|
|
typedef typename TransformType::MatrixType MatrixType;
|
|
typedef TransformType ResultType;
|
|
static ResultType run(const Other& other,const TransformType& tr)
|
|
{
|
|
ResultType res;
|
|
res.matrix().noalias() = other.template block<Dim,Dim>(0,0) * tr.matrix();
|
|
res.translation() += other.col(Dim);
|
|
return res;
|
|
}
|
|
};
|
|
|
|
// linear matrix * T
|
|
template<typename Other,int Mode, int Options, int Dim, int HDim>
|
|
struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,Dim>
|
|
{
|
|
typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
|
|
typedef typename TransformType::MatrixType MatrixType;
|
|
typedef TransformType ResultType;
|
|
static ResultType run(const Other& other, const TransformType& tr)
|
|
{
|
|
TransformType res;
|
|
if(Mode!=int(AffineCompact))
|
|
res.matrix().row(Dim) = tr.matrix().row(Dim);
|
|
res.matrix().template topRows<Dim>().noalias()
|
|
= other * tr.matrix().template topRows<Dim>();
|
|
return res;
|
|
}
|
|
};
|
|
|
|
/**********************************************************
|
|
*** Specializations of operator* with another Transform ***
|
|
**********************************************************/
|
|
|
|
template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
|
|
struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,false >
|
|
{
|
|
enum { ResultMode = transform_product_result<LhsMode,RhsMode>::Mode };
|
|
typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
|
|
typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
|
|
typedef Transform<Scalar,Dim,ResultMode,LhsOptions> ResultType;
|
|
static ResultType run(const Lhs& lhs, const Rhs& rhs)
|
|
{
|
|
ResultType res;
|
|
res.linear() = lhs.linear() * rhs.linear();
|
|
res.translation() = lhs.linear() * rhs.translation() + lhs.translation();
|
|
res.makeAffine();
|
|
return res;
|
|
}
|
|
};
|
|
|
|
template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
|
|
struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,true >
|
|
{
|
|
typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
|
|
typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
|
|
typedef Transform<Scalar,Dim,Projective> ResultType;
|
|
static ResultType run(const Lhs& lhs, const Rhs& rhs)
|
|
{
|
|
return ResultType( lhs.matrix() * rhs.matrix() );
|
|
}
|
|
};
|
|
|
|
template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
|
|
struct transform_transform_product_impl<Transform<Scalar,Dim,AffineCompact,LhsOptions>,Transform<Scalar,Dim,Projective,RhsOptions>,true >
|
|
{
|
|
typedef Transform<Scalar,Dim,AffineCompact,LhsOptions> Lhs;
|
|
typedef Transform<Scalar,Dim,Projective,RhsOptions> Rhs;
|
|
typedef Transform<Scalar,Dim,Projective> ResultType;
|
|
static ResultType run(const Lhs& lhs, const Rhs& rhs)
|
|
{
|
|
ResultType res;
|
|
res.matrix().template topRows<Dim>() = lhs.matrix() * rhs.matrix();
|
|
res.matrix().row(Dim) = rhs.matrix().row(Dim);
|
|
return res;
|
|
}
|
|
};
|
|
|
|
template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
|
|
struct transform_transform_product_impl<Transform<Scalar,Dim,Projective,LhsOptions>,Transform<Scalar,Dim,AffineCompact,RhsOptions>,true >
|
|
{
|
|
typedef Transform<Scalar,Dim,Projective,LhsOptions> Lhs;
|
|
typedef Transform<Scalar,Dim,AffineCompact,RhsOptions> Rhs;
|
|
typedef Transform<Scalar,Dim,Projective> ResultType;
|
|
static ResultType run(const Lhs& lhs, const Rhs& rhs)
|
|
{
|
|
ResultType res(lhs.matrix().template leftCols<Dim>() * rhs.matrix());
|
|
res.matrix().col(Dim) += lhs.matrix().col(Dim);
|
|
return res;
|
|
}
|
|
};
|
|
|
|
} // end namespace internal
|
|
|
|
} // end namespace Eigen
|
|
|
|
#endif // EIGEN_TRANSFORM_H
|