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* Add an HyperPlane class in the Geometry module
with its respective unit-test. Feel free to discuss the API on the ML. * Some bugfix in unitOrthogonal found by the hyperplane unit test.
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@ -22,15 +22,16 @@ namespace Eigen {
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* \endcode
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*/
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// the Geometry module use cwiseCos and cwiseSin which are defined in the Array module
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#include "src/Array/CwiseOperators.h"
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#include "src/Array/Functors.h"
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#include "src/Geometry/OrthoMethods.h"
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#include "src/Geometry/Quaternion.h"
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#include "src/Geometry/AngleAxis.h"
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#include "src/Geometry/Rotation.h"
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#include "src/Geometry/Transform.h"
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// the Geometry module use cwiseCos and cwiseSin which are defined in the Array module
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#include "src/Array/CwiseOperators.h"
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#include "src/Array/Functors.h"
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#include "src/Geometry/HyperPlane.h"
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} // namespace Eigen
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166
Eigen/src/Geometry/HyperPlane.h
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166
Eigen/src/Geometry/HyperPlane.h
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@ -0,0 +1,166 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_HYPERPLANE_H
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#define EIGEN_HYPERPLANE_H
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/** \geometry_module \ingroup GeometryModule
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*
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* \class HyperPlane
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*
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* \brief Represents an hyper plane in any dimensions
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*
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* \param _Scalar the scalar type, i.e., the type of the coefficients
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* \param _Dim the dimension of the space, can be a compile time value or Dynamic
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*
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* This class represents an hyper-plane as the zero set of the implicit equation
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* \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is the normal of the plane (linear part)
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* and \f$ d \f$ is the distance (offset) to the origin.
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*
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*/
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// FIXME default to 3 (because plane => dim=3, or default to Dynamic ?)
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template <typename _Scalar, int _Dim = 3>
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class HyperPlane
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{
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public:
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enum { DimAtCompileTime = _Dim };
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typedef _Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef Matrix<Scalar,DimAtCompileTime,1> VectorType;
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HyperPlane(int _dim = DimAtCompileTime)
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: m_normal(_dim)
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{}
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/** Construct a plane from its normal \a normal and a point \a e onto the plane.
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* \warning the vector normal is assumed to be normalized.
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*/
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HyperPlane(const VectorType& normal, const VectorType e)
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: m_normal(normal), m_offset(-e.dot(normal))
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{}
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/** Constructs a plane from its normal \a normal and distance to the origin \a d.
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* \warning the vector normal is assumed to be normalized.
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*/
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HyperPlane(const VectorType& normal, Scalar d)
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: m_normal(normal), m_offset(d)
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{}
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~HyperPlane() {}
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/** \returns the dimension in which the plane holds */
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int dim() const { return m_normal.size(); }
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/** normalizes \c *this */
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void normalize(void)
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{
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RealScalar l = Scalar(1)/m_normal.norm();
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m_normal *= l;
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m_offset *= l;
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}
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/** \returns the signed distance between the plane \c *this and a point \a p.
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*/
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inline Scalar distanceTo(const VectorType& p) const
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{
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return p.dot(m_normal) + m_offset;
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}
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/** \returns the projection of a point \a p onto the plane \c *this.
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*/
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inline VectorType project(const VectorType& p) const
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{
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return p - distanceTo(p) * m_normal;
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}
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/** \returns the normal of the plane, which corresponds to the linear part of the implicit equation. */
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inline const VectorType& normal(void) const { return m_normal; }
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/** \returns the distance to the origin, which is also the constant part
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* of the implicit equation */
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inline Scalar offset(void) const { return m_offset; }
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/** Set the normal of the plane.
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* \warning the vector normal is assumed to be normalized. */
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inline void setNormal(const VectorType& normal) { m_normal = normal; }
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/** Set the distance to origin */
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inline void setOffset(Scalar d) { m_offset = d; }
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/** \returns a pointer the coefficients c_i of the plane equation:
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* c_0*x_0 + ... + c_d-1*x_d-1 + offset = 0
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* \warning this is only for fixed size dimensions !
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*/
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inline const Scalar* equation(void) const { return m_normal.data(); }
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/** \brief Plane/ray intersection.
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Returns the parameter value of the intersection between the plane \a *this
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and the parametric ray of origin \a rayOrigin and axis \a rayDir
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*/
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Scalar rayIntersection(const VectorType& rayOrigin, const VectorType& rayDir)
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{
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return -(m_offset+rayOrigin.dot(m_normal))/(rayDir.dot(m_normal));
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}
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// TODO some convenient functions to fit a 3D plane on 3 points etc...
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// void makePassBy(const VectorType& p0, const VectorType& p1, const VectorType& p2)
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// {
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// EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(3);
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// m_normal = (p2 - p0).cross(p1 - p0).normalized();
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// m_offset = -m_normal.dot(p0);
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// }
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//
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// void makePassBy(const VectorType& p0, const VectorType& p1)
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// {
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// EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(2);
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// m_normal = (p2 - p0).cross(p1 - p0).normalized();
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// m_offset = -m_normal.dot(p0);
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// }
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protected:
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VectorType m_normal;
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Scalar m_offset;
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};
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/** \addtogroup GeometryModule */
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//@{
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typedef HyperPlane<float, 2> HyperPlane2f;
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typedef HyperPlane<double,2> HyperPlane2d;
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typedef HyperPlane<float, 3> HyperPlane3f;
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typedef HyperPlane<double,3> HyperPlane3d;
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typedef HyperPlane<float, 2> Linef;
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typedef HyperPlane<double,2> Lined;
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typedef HyperPlane<float, 3> Planef;
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typedef HyperPlane<double,3> Planed;
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typedef HyperPlane<float, Dynamic> HyperPlaneXf;
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typedef HyperPlane<double,Dynamic> HyperPlaneXd;
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//@}
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#endif // EIGEN_HYPERPLANE_H
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@ -54,7 +54,7 @@ struct ei_unitOrthogonal_selector
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typedef typename NumTraits<Scalar>::Real RealScalar;
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inline static VectorType run(const Derived& src)
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{
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VectorType perp;
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VectorType perp(src.size());
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/* Let us compute the crossed product of *this with a vector
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* that is not too close to being colinear to *this.
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*/
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@ -65,7 +65,7 @@ struct ei_unitOrthogonal_selector
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if((!ei_isMuchSmallerThan(src.x(), src.z()))
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|| (!ei_isMuchSmallerThan(src.y(), src.z())))
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{
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RealScalar invnm = Scalar(1)/src.template start<2>().norm();
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RealScalar invnm = RealScalar(1)/src.template start<2>().norm();
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perp.coeffRef(0) = -ei_conj(src.y())*invnm;
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perp.coeffRef(1) = ei_conj(src.x())*invnm;
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perp.coeffRef(2) = 0;
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@ -76,7 +76,7 @@ struct ei_unitOrthogonal_selector
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*/
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else
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{
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RealScalar invnm = Scalar(1)/src.template end<2>().norm();
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RealScalar invnm = RealScalar(1)/src.template end<2>().norm();
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perp.coeffRef(0) = 0;
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perp.coeffRef(1) = -ei_conj(src.z())*invnm;
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perp.coeffRef(2) = ei_conj(src.y())*invnm;
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@ -116,9 +116,10 @@ EI_ADD_TEST(determinant)
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EI_ADD_TEST(inverse)
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EI_ADD_TEST(qr)
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EI_ADD_TEST(eigensolver)
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EI_ADD_TEST(geometry)
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EI_ADD_TEST(regression)
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EI_ADD_TEST(svd)
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EI_ADD_TEST(geometry)
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EI_ADD_TEST(hyperplane)
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EI_ADD_TEST(regression)
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EI_ADD_TEST(sparse)
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ENDIF(BUILD_TESTS)
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71
test/hyperplane.cpp
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71
test/hyperplane.cpp
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#include "main.h"
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#include <Eigen/Geometry>
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#include <Eigen/LU>
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template<typename PlaneType> void hyperplane(const PlaneType& _plane)
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{
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/* this test covers the following files:
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HyperPlane.h
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*/
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const int dim = _plane.dim();
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typedef typename PlaneType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef Matrix<Scalar, PlaneType::DimAtCompileTime, 1> VectorType;
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VectorType p0 = VectorType::Random(dim);
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VectorType p1 = VectorType::Random(dim);
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VectorType n0 = VectorType::Random(dim).normalized();
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VectorType n1 = VectorType::Random(dim).normalized();
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PlaneType pl0(n0, p0);
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PlaneType pl1(n1, p1);
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Scalar s0 = ei_random<Scalar>();
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Scalar s1 = ei_random<Scalar>();
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VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
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VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
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VERIFY_IS_MUCH_SMALLER_THAN( pl0.distanceTo(p0), Scalar(1) );
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VERIFY_IS_APPROX( pl1.distanceTo(p1 + n1 * s0), s0 );
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VERIFY_IS_MUCH_SMALLER_THAN( pl1.distanceTo(pl1.project(p0)), Scalar(1) );
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VERIFY_IS_MUCH_SMALLER_THAN( pl1.distanceTo(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) );
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}
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void test_hyperplane()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST( hyperplane(HyperPlane<float,2>()) );
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CALL_SUBTEST( hyperplane(HyperPlane<float,3>()) );
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CALL_SUBTEST( hyperplane(HyperPlane<double,4>()) );
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CALL_SUBTEST( hyperplane(HyperPlane<std::complex<double>,5>()) );
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CALL_SUBTEST( hyperplane(HyperPlane<double,Dynamic>(13)) );
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}
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}
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