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Integrated spline class and simple spline fitting
This commit is contained in:
Hauke Heibel
@@ -1,6 +1,6 @@
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set(Eigen_HEADERS AdolcForward BVH IterativeSolvers MatrixFunctions MoreVectorization AutoDiff AlignedVector3 Polynomials
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FFT NonLinearOptimization SparseExtra IterativeSolvers
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NumericalDiff Skyline MPRealSupport OpenGLSupport KroneckerProduct
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NumericalDiff Skyline MPRealSupport OpenGLSupport KroneckerProduct Splines
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)
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install(FILES
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52
unsupported/Eigen/Splines
Normal file
52
unsupported/Eigen/Splines
Normal file
@@ -0,0 +1,52 @@
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// 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) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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||||
// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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||||
// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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||||
// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_SPLINES_MODULE_H
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#define EIGEN_SPLINES_MODULE_H
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namespace Eigen
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{
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/** \ingroup Unsupported_modules
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* \defgroup Splines_Module Spline and spline fitting module
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*
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* This module provides a simple multi-dimensional spline class while
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* offering most basic functionality to fit a spline to point sets.
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*
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* \code
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* #include <unsupported/Eigen/Splines>
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* \endcode
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*/
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//@{
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}
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#include "src/Splines/SplineFwd.h"
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#include "src/Splines/Spline.h"
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#include "src/Splines/SplineFitting.h"
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namespace Eigen
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{
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//@}
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}
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#endif // EIGEN_SPLINES_MODULE_H
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@@ -9,4 +9,5 @@ ADD_SUBDIRECTORY(NumericalDiff)
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ADD_SUBDIRECTORY(Polynomials)
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ADD_SUBDIRECTORY(Skyline)
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ADD_SUBDIRECTORY(SparseExtra)
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ADD_SUBDIRECTORY(KroneckerProduct)
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ADD_SUBDIRECTORY(KroneckerProduct)
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ADD_SUBDIRECTORY(Splines)
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407
unsupported/Eigen/src/Splines/Spline.h
Normal file
407
unsupported/Eigen/src/Splines/Spline.h
Normal file
@@ -0,0 +1,407 @@
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// 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) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>
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//
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// Eigen is free software; you can redistribute it and/or
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||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
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//
|
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// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
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||||
//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
|
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_SPLINE_H
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#define EIGEN_SPLINE_H
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#include "SplineFwd.h"
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namespace Eigen
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{
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/**
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* \class Spline class
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* \brief A class representing N-D spline curves.
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* \tparam _Scalar The underlying data type (typically float or double)
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* \tparam _Dim The curve dimension (e.g. 2 or 3)
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* \tparam _Degree Per default set to Dynamic; could be set to the actual desired
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* degree for optimization purposes (would result in stack allocation
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* of several temporary variables).
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**/
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template <typename _Scalar, int _Dim, int _Degree>
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class Spline
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{
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public:
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typedef _Scalar Scalar;
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enum { Dimension = _Dim };
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enum { Degree = _Degree };
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typedef typename SplineTraits<Spline>::PointType PointType;
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typedef typename SplineTraits<Spline>::KnotVectorType KnotVectorType;
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typedef typename SplineTraits<Spline>::BasisVectorType BasisVectorType;
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typedef typename SplineTraits<Spline>::ControlPointVectorType ControlPointVectorType;
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/**
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* \brief Creates a spline from a knot vector and control points.
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**/
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template <typename OtherVectorType, typename OtherArrayType>
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Spline(const OtherVectorType& knots, const OtherArrayType& ctrls) : m_knots(knots), m_ctrls(ctrls) {}
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template <int OtherDegree>
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Spline(const Spline<Scalar, Dimension, OtherDegree>& spline) :
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m_knots(spline.knots()), m_ctrls(spline.ctrls()) {}
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/* Const access methods for knots and control points. */
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const KnotVectorType& knots() const { return m_knots; }
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const ControlPointVectorType& ctrls() const { return m_ctrls; }
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/* Spline evaluation. */
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PointType operator()(Scalar u) const;
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/* Evaluation of spline derivatives of up-to given order.
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* The returned matrix has dimensions Dim-by-(Order+1) containing
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* the 0-th order up-to Order-th order derivatives.
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*/
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typename SplineTraits<Spline>::DerivativeType
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derivatives(Scalar u, DenseIndex order) const;
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/**
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* Evaluation of spline derivatives of up-to given order.
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* The function performs identically to derivatives(Scalar, int) but
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* does not require any heap allocations.
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* \sa derivatives(Scalar, int)
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**/
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template <int DerivativeOrder>
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typename SplineTraits<Spline,DerivativeOrder>::DerivativeType
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derivatives(Scalar u, DenseIndex order = DerivativeOrder) const;
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/* Non-zero spline basis functions. */
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typename SplineTraits<Spline>::BasisVectorType
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basisFunctions(Scalar u) const;
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/* Non-zero spline basis function derivatives up to given order.
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* The order is different from the spline order - it is the order
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* up to which derivatives will be computed.
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* \sa basisFunctions(Scalar)
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*/
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typename SplineTraits<Spline>::BasisDerivativeType
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basisFunctionDerivatives(Scalar u, DenseIndex order) const;
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/**
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* Computes non-zero basis function derivatives up to the given derivative order.
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* As opposed to basisFunctionDerivatives(Scalar, int) this function does not perform
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* any heap allocations.
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* \sa basisFunctionDerivatives(Scalar, int)
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**/
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template <int DerivativeOrder>
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typename SplineTraits<Spline,DerivativeOrder>::BasisDerivativeType
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basisFunctionDerivatives(Scalar u, DenseIndex order = DerivativeOrder) const;
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/**
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* \brief The current spline degree. It's a function of knot size and number
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* of controls and thus does not require a dedicated member.
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*/
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DenseIndex degree() const;
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/** Computes the span within the knot vector in which u falls. */
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DenseIndex span(Scalar u) const;
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static DenseIndex Span(typename SplineTraits<Spline>::Scalar u, DenseIndex degree, const typename SplineTraits<Spline>::KnotVectorType& knots);
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static BasisVectorType BasisFunctions(Scalar u, DenseIndex degree, const KnotVectorType& knots);
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private:
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KnotVectorType m_knots; /* Knot vector. */
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ControlPointVectorType m_ctrls; /* Control points. */
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};
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template <typename _Scalar, int _Dim, int _Degree>
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DenseIndex Spline<_Scalar, _Dim, _Degree>::Span(
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typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::Scalar u,
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DenseIndex degree,
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const typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::KnotVectorType& knots)
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{
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// Piegl & Tiller, "The NURBS Book", A2.1 (p. 68)
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if (u <= knots(0)) return degree;
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const Scalar* pos = std::upper_bound(knots.data()+degree-1, knots.data()+knots.size()-degree-1, u);
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return static_cast<DenseIndex>( std::distance(knots.data(), pos) - 1 );
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}
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template <typename _Scalar, int _Dim, int _Degree>
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typename Spline<_Scalar, _Dim, _Degree>::BasisVectorType
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Spline<_Scalar, _Dim, _Degree>::BasisFunctions(
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typename Spline<_Scalar, _Dim, _Degree>::Scalar u,
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DenseIndex degree,
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const typename Spline<_Scalar, _Dim, _Degree>::KnotVectorType& knots)
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{
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typedef typename Spline<_Scalar, _Dim, _Degree>::BasisVectorType BasisVectorType;
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const DenseIndex p = degree;
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const DenseIndex i = Spline::Span(u, degree, knots);
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const KnotVectorType& U = knots;
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BasisVectorType left(p+1); left(0) = Scalar(0);
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BasisVectorType right(p+1); right(0) = Scalar(0);
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VectorBlock<BasisVectorType,Degree>(left,1,p) = u - VectorBlock<const KnotVectorType,Degree>(U,i+1-p,p).reverse();
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VectorBlock<BasisVectorType,Degree>(right,1,p) = VectorBlock<const KnotVectorType,Degree>(U,i+1,p) - u;
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BasisVectorType N(1,p+1);
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N(0) = Scalar(1);
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for (DenseIndex j=1; j<=p; ++j)
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{
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Scalar saved = Scalar(0);
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for (DenseIndex r=0; r<j; r++)
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{
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const Scalar tmp = N(r)/(right(r+1)+left(j-r));
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N[r] = saved + right(r+1)*tmp;
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saved = left(j-r)*tmp;
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}
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N(j) = saved;
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}
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return N;
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}
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template <typename _Scalar, int _Dim, int _Degree>
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DenseIndex Spline<_Scalar, _Dim, _Degree>::degree() const
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{
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if (_Degree == Dynamic)
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return m_knots.size() - m_ctrls.cols() - 1;
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else
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return _Degree;
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}
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template <typename _Scalar, int _Dim, int _Degree>
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DenseIndex Spline<_Scalar, _Dim, _Degree>::span(Scalar u) const
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{
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return Spline::Span(u, degree(), knots());
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}
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/**
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* \brief A functor for the computation of a spline point.
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* \sa Piegl & Tiller, "The NURBS Book", A4.1 (p. 124)
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**/
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template <typename _Scalar, int _Dim, int _Degree>
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typename Spline<_Scalar, _Dim, _Degree>::PointType Spline<_Scalar, _Dim, _Degree>::operator()(Scalar u) const
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{
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enum { Order = SplineTraits<Spline>::OrderAtCompileTime };
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const DenseIndex span = this->span(u);
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const DenseIndex p = degree();
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const BasisVectorType basis_funcs = basisFunctions(u);
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const Replicate<BasisVectorType,Dimension,1> ctrl_weights(basis_funcs);
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const Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(ctrls(),0,span-p,Dimension,p+1);
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return (ctrl_weights * ctrl_pts).rowwise().sum();
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}
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/* --------------------------------------------------------------------------------------------- */
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template <typename SplineType, typename DerivativeType>
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void derivativesImpl(const SplineType& spline, typename SplineType::Scalar u, DenseIndex order, DerivativeType& der)
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{
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enum { Dimension = SplineTraits<SplineType>::Dimension };
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enum { Order = SplineTraits<SplineType>::OrderAtCompileTime };
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enum { DerivativeOrder = DerivativeType::ColsAtCompileTime };
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typedef typename SplineTraits<SplineType>::Scalar Scalar;
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typedef typename SplineTraits<SplineType>::BasisVectorType BasisVectorType;
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typedef typename SplineTraits<SplineType>::ControlPointVectorType ControlPointVectorType;
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typedef typename SplineTraits<SplineType,DerivativeOrder>::BasisDerivativeType BasisDerivativeType;
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typedef typename BasisDerivativeType::ConstRowXpr BasisDerivativeRowXpr;
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const DenseIndex p = spline.degree();
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const DenseIndex span = spline.span(u);
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const DenseIndex n = (std::min)(p, order);
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der.resize(Dimension,n+1);
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// Retrieve the basis function derivatives up to the desired order...
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const BasisDerivativeType basis_func_ders = spline.template basisFunctionDerivatives<DerivativeOrder>(u, n+1);
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// ... and perform the linear combinations of the control points.
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for (DenseIndex der_order=0; der_order<n+1; ++der_order)
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{
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const Replicate<BasisDerivativeRowXpr,Dimension,1> ctrl_weights( basis_func_ders.row(der_order) );
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const Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(spline.ctrls(),0,span-p,Dimension,p+1);
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der.col(der_order) = (ctrl_weights * ctrl_pts).rowwise().sum();
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}
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}
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/**
|
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* \brief A functor for the computation of a spline point.
|
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* \sa Piegl & Tiller, "The NURBS Book", A4.1 (p. 124)
|
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**/
|
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template <typename _Scalar, int _Dim, int _Degree>
|
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typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::DerivativeType
|
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Spline<_Scalar, _Dim, _Degree>::derivatives(Scalar u, DenseIndex order) const
|
||||
{
|
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typename SplineTraits< Spline >::DerivativeType res;
|
||||
derivativesImpl(*this, u, order, res);
|
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return res;
|
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}
|
||||
|
||||
template <typename _Scalar, int _Dim, int _Degree>
|
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template <int DerivativeOrder>
|
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typename SplineTraits< Spline<_Scalar, _Dim, _Degree>, DerivativeOrder >::DerivativeType
|
||||
Spline<_Scalar, _Dim, _Degree>::derivatives(Scalar u, DenseIndex order) const
|
||||
{
|
||||
typename SplineTraits< Spline, DerivativeOrder >::DerivativeType res;
|
||||
derivativesImpl(*this, u, order, res);
|
||||
return res;
|
||||
}
|
||||
|
||||
/**
|
||||
* \brief A functor for the computation of a spline's non-zero basis functions.
|
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* \sa Piegl & Tiller, "The NURBS Book", A2.2 (p. 70)
|
||||
**/
|
||||
template <typename _Scalar, int _Dim, int _Degree>
|
||||
typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::BasisVectorType
|
||||
Spline<_Scalar, _Dim, _Degree>::basisFunctions(Scalar u) const
|
||||
{
|
||||
return Spline::BasisFunctions(u, degree(), knots());
|
||||
}
|
||||
|
||||
/* --------------------------------------------------------------------------------------------- */
|
||||
|
||||
template <typename SplineType, typename DerivativeType>
|
||||
void basisFunctionDerivativesImpl(const SplineType& spline, typename SplineType::Scalar u, DenseIndex order, DerivativeType& N_)
|
||||
{
|
||||
enum { Order = SplineTraits<SplineType>::OrderAtCompileTime };
|
||||
|
||||
typedef typename SplineTraits<SplineType>::Scalar Scalar;
|
||||
typedef typename SplineTraits<SplineType>::BasisVectorType BasisVectorType;
|
||||
typedef typename SplineTraits<SplineType>::KnotVectorType KnotVectorType;
|
||||
typedef typename SplineTraits<SplineType>::ControlPointVectorType ControlPointVectorType;
|
||||
|
||||
const KnotVectorType& U = spline.knots();
|
||||
|
||||
const DenseIndex p = spline.degree();
|
||||
const DenseIndex span = spline.span(u);
|
||||
|
||||
const DenseIndex n = (std::min)(p, order);
|
||||
|
||||
N_.resize(n+1, p+1);
|
||||
|
||||
BasisVectorType left = BasisVectorType::Zero(p+1);
|
||||
BasisVectorType right = BasisVectorType::Zero(p+1);
|
||||
|
||||
Matrix<Scalar,Order,Order> ndu(p+1,p+1);
|
||||
|
||||
double saved, temp;
|
||||
|
||||
ndu(0,0) = 1.0;
|
||||
|
||||
DenseIndex j;
|
||||
for (j=1; j<=p; ++j)
|
||||
{
|
||||
left[j] = u-U[span+1-j];
|
||||
right[j] = U[span+j]-u;
|
||||
saved = 0.0;
|
||||
|
||||
for (DenseIndex r=0; r<j; ++r)
|
||||
{
|
||||
/* Lower triangle */
|
||||
ndu(j,r) = right[r+1]+left[j-r];
|
||||
temp = ndu(r,j-1)/ndu(j,r);
|
||||
/* Upper triangle */
|
||||
ndu(r,j) = static_cast<Scalar>(saved+right[r+1] * temp);
|
||||
saved = left[j-r] * temp;
|
||||
}
|
||||
|
||||
ndu(j,j) = static_cast<Scalar>(saved);
|
||||
}
|
||||
|
||||
for (j = p; j>=0; --j)
|
||||
N_(0,j) = ndu(j,p);
|
||||
|
||||
// Compute the derivatives
|
||||
DerivativeType a(n+1,p+1);
|
||||
DenseIndex r=0;
|
||||
for (; r<=p; ++r)
|
||||
{
|
||||
DenseIndex s1,s2;
|
||||
s1 = 0; s2 = 1; // alternate rows in array a
|
||||
a(0,0) = 1.0;
|
||||
|
||||
// Compute the k-th derivative
|
||||
for (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k)
|
||||
{
|
||||
double d = 0.0;
|
||||
DenseIndex rk,pk,j1,j2;
|
||||
rk = r-k; pk = p-k;
|
||||
|
||||
if (r>=k)
|
||||
{
|
||||
a(s2,0) = a(s1,0)/ndu(pk+1,rk);
|
||||
d = a(s2,0)*ndu(rk,pk);
|
||||
}
|
||||
|
||||
if (rk>=-1) j1 = 1;
|
||||
else j1 = -rk;
|
||||
|
||||
if (r-1 <= pk) j2 = k-1;
|
||||
else j2 = p-r;
|
||||
|
||||
for (j=j1; j<=j2; ++j)
|
||||
{
|
||||
a(s2,j) = (a(s1,j)-a(s1,j-1))/ndu(pk+1,rk+j);
|
||||
d += a(s2,j)*ndu(rk+j,pk);
|
||||
}
|
||||
|
||||
if (r<=pk)
|
||||
{
|
||||
a(s2,k) = -a(s1,k-1)/ndu(pk+1,r);
|
||||
d += a(s2,k)*ndu(r,pk);
|
||||
}
|
||||
|
||||
N_(k,r) = static_cast<Scalar>(d);
|
||||
j = s1; s1 = s2; s2 = j; // Switch rows
|
||||
}
|
||||
}
|
||||
|
||||
/* Multiply through by the correct factors */
|
||||
/* (Eq. [2.9]) */
|
||||
r = p;
|
||||
for (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k)
|
||||
{
|
||||
for (DenseIndex j=p; j>=0; --j) N_(k,j) *= r;
|
||||
r *= p-k;
|
||||
}
|
||||
}
|
||||
|
||||
template <typename _Scalar, int _Dim, int _Degree>
|
||||
typename SplineTraits< Spline<_Scalar, _Dim, _Degree> >::BasisDerivativeType
|
||||
Spline<_Scalar, _Dim, _Degree>::basisFunctionDerivatives(Scalar u, DenseIndex order) const
|
||||
{
|
||||
typename SplineTraits< Spline >::BasisDerivativeType der;
|
||||
basisFunctionDerivativesImpl(*this, u, order, der);
|
||||
return der;
|
||||
}
|
||||
|
||||
template <typename _Scalar, int _Dim, int _Degree>
|
||||
template <int DerivativeOrder>
|
||||
typename SplineTraits< Spline<_Scalar, _Dim, _Degree>, DerivativeOrder >::BasisDerivativeType
|
||||
Spline<_Scalar, _Dim, _Degree>::basisFunctionDerivatives(Scalar u, DenseIndex order) const
|
||||
{
|
||||
typename SplineTraits< Spline, DerivativeOrder >::BasisDerivativeType der;
|
||||
basisFunctionDerivativesImpl(*this, u, order, der);
|
||||
return der;
|
||||
}
|
||||
}
|
||||
|
||||
#endif // EIGEN_SPLINE_H
|
||||
115
unsupported/Eigen/src/Splines/SplineFitting.h
Normal file
115
unsupported/Eigen/src/Splines/SplineFitting.h
Normal file
@@ -0,0 +1,115 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_SPLINE_FITTING_H
|
||||
#define EIGEN_SPLINE_FITTING_H
|
||||
|
||||
#include <numeric>
|
||||
|
||||
#include "SplineFwd.h"
|
||||
|
||||
#include <Eigen/QR>
|
||||
|
||||
namespace Eigen
|
||||
{
|
||||
template <typename KnotVectorType>
|
||||
void KnotAveraging(const KnotVectorType& parameters, DenseIndex degree, KnotVectorType& knots)
|
||||
{
|
||||
typedef typename KnotVectorType::Scalar Scalar;
|
||||
|
||||
knots.resize(parameters.size()+degree+1);
|
||||
|
||||
for (DenseIndex j=1; j<parameters.size()-degree; ++j)
|
||||
knots(j+degree) = parameters.segment(j,degree).mean();
|
||||
|
||||
knots.segment(0,degree+1) = KnotVectorType::Zero(degree+1);
|
||||
knots.segment(knots.size()-degree-1,degree+1) = KnotVectorType::Ones(degree+1);
|
||||
}
|
||||
|
||||
template <typename PointArrayType, typename KnotVectorType>
|
||||
void ChordLengths(const PointArrayType& pts, KnotVectorType& chord_lengths)
|
||||
{
|
||||
typedef typename KnotVectorType::Scalar Scalar;
|
||||
|
||||
const DenseIndex n = pts.cols();
|
||||
|
||||
// 1. compute the column-wise norms
|
||||
chord_lengths.resize(pts.cols());
|
||||
chord_lengths[0] = 0;
|
||||
chord_lengths.rightCols(n-1) = (pts.array().leftCols(n-1) - pts.array().rightCols(n-1)).matrix().colwise().norm();
|
||||
|
||||
// 2. compute the partial sums
|
||||
std::partial_sum(chord_lengths.data(), chord_lengths.data()+n, chord_lengths.data());
|
||||
|
||||
// 3. normalize the data
|
||||
chord_lengths /= chord_lengths(n-1);
|
||||
chord_lengths(n-1) = Scalar(1);
|
||||
}
|
||||
|
||||
template <typename SplineType>
|
||||
struct SplineFitting
|
||||
{
|
||||
template <typename PointArrayType>
|
||||
static SplineType Interpolate(const PointArrayType& pts, DenseIndex degree);
|
||||
};
|
||||
|
||||
template <typename SplineType>
|
||||
template <typename PointArrayType>
|
||||
SplineType SplineFitting<SplineType>::Interpolate(const PointArrayType& pts, DenseIndex degree)
|
||||
{
|
||||
typedef typename SplineType::KnotVectorType::Scalar Scalar;
|
||||
typedef typename SplineType::KnotVectorType KnotVectorType;
|
||||
typedef typename SplineType::BasisVectorType BasisVectorType;
|
||||
typedef typename SplineType::ControlPointVectorType ControlPointVectorType;
|
||||
|
||||
typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
|
||||
|
||||
KnotVectorType chord_lengths; // knot parameters
|
||||
ChordLengths(pts, chord_lengths);
|
||||
|
||||
KnotVectorType knots;
|
||||
KnotAveraging(chord_lengths, degree, knots);
|
||||
|
||||
DenseIndex n = pts.cols();
|
||||
MatrixType A = MatrixType::Zero(n,n);
|
||||
for (DenseIndex i=1; i<n-1; ++i)
|
||||
{
|
||||
const DenseIndex span = SplineType::Span(chord_lengths[i], degree, knots);
|
||||
|
||||
// The segment call should somehow be told the spline order at compile time.
|
||||
A.row(i).segment(span-degree, degree+1) = SplineType::BasisFunctions(chord_lengths[i], degree, knots);
|
||||
}
|
||||
A(0,0) = 1.0;
|
||||
A(n-1,n-1) = 1.0;
|
||||
|
||||
HouseholderQR<MatrixType> qr(A);
|
||||
|
||||
// Here, we are creating a temporary due to an Eigen issue.
|
||||
ControlPointVectorType ctrls = qr.solve(MatrixType(pts.transpose())).transpose();
|
||||
|
||||
return SplineType(knots, ctrls);
|
||||
}
|
||||
}
|
||||
|
||||
#endif // EIGEN_SPLINE_FITTING_H
|
||||
78
unsupported/Eigen/src/Splines/SplineFwd.h
Normal file
78
unsupported/Eigen/src/Splines/SplineFwd.h
Normal file
@@ -0,0 +1,78 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>
|
||||
//
|
||||
// Eigen is free software; you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public
|
||||
// License as published by the Free Software Foundation; either
|
||||
// version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Alternatively, you can redistribute it and/or
|
||||
// modify it under the terms of the GNU General Public License as
|
||||
// published by the Free Software Foundation; either version 2 of
|
||||
// the License, or (at your option) any later version.
|
||||
//
|
||||
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
|
||||
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
|
||||
// GNU General Public License for more details.
|
||||
//
|
||||
// You should have received a copy of the GNU Lesser General Public
|
||||
// License and a copy of the GNU General Public License along with
|
||||
// Eigen. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
#ifndef EIGEN_SPLINES_FWD_H
|
||||
#define EIGEN_SPLINES_FWD_H
|
||||
|
||||
#include <Eigen/Core>
|
||||
|
||||
namespace Eigen
|
||||
{
|
||||
template <typename Scalar, int Dim, int Degree = Dynamic> class Spline;
|
||||
|
||||
template < typename SplineType, int _DerivativeOrder = Dynamic > struct SplineTraits {};
|
||||
|
||||
// hide specializations from doxygen
|
||||
#ifndef DOXYGEN_SHOULD_SKIP_THIS
|
||||
|
||||
template <typename _Scalar, int _Dim, int _Degree>
|
||||
struct SplineTraits< Spline<_Scalar, _Dim, _Degree>, Dynamic >
|
||||
{
|
||||
typedef _Scalar Scalar; /* The underlying scalar value. */
|
||||
enum { Dimension = _Dim }; /* The spline curve's dimension. */
|
||||
enum { Degree = _Degree }; /* The spline curve's degree. */
|
||||
|
||||
enum { OrderAtCompileTime = _Degree==Dynamic ? Dynamic : _Degree+1 };
|
||||
enum { NumOfDerivativesAtCompileTime = OrderAtCompileTime };
|
||||
|
||||
typedef Array<Scalar,1,OrderAtCompileTime> BasisVectorType;
|
||||
|
||||
typedef Array<Scalar,Dynamic,Dynamic,RowMajor,NumOfDerivativesAtCompileTime,OrderAtCompileTime> BasisDerivativeType;
|
||||
typedef Array<Scalar,Dimension,Dynamic,ColMajor,Dimension,NumOfDerivativesAtCompileTime> DerivativeType;
|
||||
|
||||
typedef Array<Scalar,Dimension,1> PointType;
|
||||
typedef Array<Scalar,1,Dynamic> KnotVectorType;
|
||||
typedef Array<Scalar,Dimension,Dynamic> ControlPointVectorType;
|
||||
};
|
||||
|
||||
template < typename _Scalar, int _Dim, int _Degree, int _DerivativeOrder >
|
||||
struct SplineTraits< Spline<_Scalar, _Dim, _Degree>, _DerivativeOrder > : public SplineTraits< Spline<_Scalar, _Dim, _Degree> >
|
||||
{
|
||||
enum { OrderAtCompileTime = _Degree==Dynamic ? Dynamic : _Degree+1 };
|
||||
enum { NumOfDerivativesAtCompileTime = _DerivativeOrder==Dynamic ? Dynamic : _DerivativeOrder+1 };
|
||||
|
||||
typedef Array<_Scalar,Dynamic,Dynamic,RowMajor,NumOfDerivativesAtCompileTime,OrderAtCompileTime> BasisDerivativeType;
|
||||
typedef Array<_Scalar,_Dim,Dynamic,ColMajor,_Dim,NumOfDerivativesAtCompileTime> DerivativeType;
|
||||
};
|
||||
|
||||
#endif
|
||||
|
||||
typedef Spline<float,2> Spline2f;
|
||||
typedef Spline<float,3> Spline3f;
|
||||
|
||||
typedef Spline<double,2> Spline2d;
|
||||
typedef Spline<double,3> Spline3d;
|
||||
}
|
||||
|
||||
#endif // EIGEN_SPLINES_FWD_H
|
||||
Reference in New Issue
Block a user