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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.
This commit is contained in:
Gael Guennebaud 2008-08-28 17:44:27 +00:00
parent ee2df6026a
commit 9b4d46c82e
5 changed files with 248 additions and 9 deletions

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@ -22,15 +22,16 @@ namespace Eigen {
* \endcode
*/
// the Geometry module use cwiseCos and cwiseSin which are defined in the Array module
#include "src/Array/CwiseOperators.h"
#include "src/Array/Functors.h"
#include "src/Geometry/OrthoMethods.h"
#include "src/Geometry/Quaternion.h"
#include "src/Geometry/AngleAxis.h"
#include "src/Geometry/Rotation.h"
#include "src/Geometry/Transform.h"
// the Geometry module use cwiseCos and cwiseSin which are defined in the Array module
#include "src/Array/CwiseOperators.h"
#include "src/Array/Functors.h"
#include "src/Geometry/HyperPlane.h"
} // namespace Eigen

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@ -0,0 +1,166 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_HYPERPLANE_H
#define EIGEN_HYPERPLANE_H
/** \geometry_module \ingroup GeometryModule
*
* \class HyperPlane
*
* \brief Represents an hyper plane in any dimensions
*
* \param _Scalar the scalar type, i.e., the type of the coefficients
* \param _Dim the dimension of the space, can be a compile time value or Dynamic
*
* This class represents an hyper-plane as the zero set of the implicit equation
* \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is the normal of the plane (linear part)
* and \f$ d \f$ is the distance (offset) to the origin.
*
*/
// FIXME default to 3 (because plane => dim=3, or default to Dynamic ?)
template <typename _Scalar, int _Dim = 3>
class HyperPlane
{
public:
enum { DimAtCompileTime = _Dim };
typedef _Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar,DimAtCompileTime,1> VectorType;
HyperPlane(int _dim = DimAtCompileTime)
: m_normal(_dim)
{}
/** Construct a plane from its normal \a normal and a point \a e onto the plane.
* \warning the vector normal is assumed to be normalized.
*/
HyperPlane(const VectorType& normal, const VectorType e)
: m_normal(normal), m_offset(-e.dot(normal))
{}
/** Constructs a plane from its normal \a normal and distance to the origin \a d.
* \warning the vector normal is assumed to be normalized.
*/
HyperPlane(const VectorType& normal, Scalar d)
: m_normal(normal), m_offset(d)
{}
~HyperPlane() {}
/** \returns the dimension in which the plane holds */
int dim() const { return m_normal.size(); }
/** normalizes \c *this */
void normalize(void)
{
RealScalar l = Scalar(1)/m_normal.norm();
m_normal *= l;
m_offset *= l;
}
/** \returns the signed distance between the plane \c *this and a point \a p.
*/
inline Scalar distanceTo(const VectorType& p) const
{
return p.dot(m_normal) + m_offset;
}
/** \returns the projection of a point \a p onto the plane \c *this.
*/
inline VectorType project(const VectorType& p) const
{
return p - distanceTo(p) * m_normal;
}
/** \returns the normal of the plane, which corresponds to the linear part of the implicit equation. */
inline const VectorType& normal(void) const { return m_normal; }
/** \returns the distance to the origin, which is also the constant part
* of the implicit equation */
inline Scalar offset(void) const { return m_offset; }
/** Set the normal of the plane.
* \warning the vector normal is assumed to be normalized. */
inline void setNormal(const VectorType& normal) { m_normal = normal; }
/** Set the distance to origin */
inline void setOffset(Scalar d) { m_offset = d; }
/** \returns a pointer the coefficients c_i of the plane equation:
* c_0*x_0 + ... + c_d-1*x_d-1 + offset = 0
* \warning this is only for fixed size dimensions !
*/
inline const Scalar* equation(void) const { return m_normal.data(); }
/** \brief Plane/ray intersection.
Returns the parameter value of the intersection between the plane \a *this
and the parametric ray of origin \a rayOrigin and axis \a rayDir
*/
Scalar rayIntersection(const VectorType& rayOrigin, const VectorType& rayDir)
{
return -(m_offset+rayOrigin.dot(m_normal))/(rayDir.dot(m_normal));
}
// TODO some convenient functions to fit a 3D plane on 3 points etc...
// void makePassBy(const VectorType& p0, const VectorType& p1, const VectorType& p2)
// {
// EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(3);
// m_normal = (p2 - p0).cross(p1 - p0).normalized();
// m_offset = -m_normal.dot(p0);
// }
//
// void makePassBy(const VectorType& p0, const VectorType& p1)
// {
// EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(2);
// m_normal = (p2 - p0).cross(p1 - p0).normalized();
// m_offset = -m_normal.dot(p0);
// }
protected:
VectorType m_normal;
Scalar m_offset;
};
/** \addtogroup GeometryModule */
//@{
typedef HyperPlane<float, 2> HyperPlane2f;
typedef HyperPlane<double,2> HyperPlane2d;
typedef HyperPlane<float, 3> HyperPlane3f;
typedef HyperPlane<double,3> HyperPlane3d;
typedef HyperPlane<float, 2> Linef;
typedef HyperPlane<double,2> Lined;
typedef HyperPlane<float, 3> Planef;
typedef HyperPlane<double,3> Planed;
typedef HyperPlane<float, Dynamic> HyperPlaneXf;
typedef HyperPlane<double,Dynamic> HyperPlaneXd;
//@}
#endif // EIGEN_HYPERPLANE_H

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@ -54,7 +54,7 @@ struct ei_unitOrthogonal_selector
typedef typename NumTraits<Scalar>::Real RealScalar;
inline static VectorType run(const Derived& src)
{
VectorType perp;
VectorType perp(src.size());
/* Let us compute the crossed product of *this with a vector
* that is not too close to being colinear to *this.
*/
@ -65,7 +65,7 @@ struct ei_unitOrthogonal_selector
if((!ei_isMuchSmallerThan(src.x(), src.z()))
|| (!ei_isMuchSmallerThan(src.y(), src.z())))
{
RealScalar invnm = Scalar(1)/src.template start<2>().norm();
RealScalar invnm = RealScalar(1)/src.template start<2>().norm();
perp.coeffRef(0) = -ei_conj(src.y())*invnm;
perp.coeffRef(1) = ei_conj(src.x())*invnm;
perp.coeffRef(2) = 0;
@ -76,7 +76,7 @@ struct ei_unitOrthogonal_selector
*/
else
{
RealScalar invnm = Scalar(1)/src.template end<2>().norm();
RealScalar invnm = RealScalar(1)/src.template end<2>().norm();
perp.coeffRef(0) = 0;
perp.coeffRef(1) = -ei_conj(src.z())*invnm;
perp.coeffRef(2) = ei_conj(src.y())*invnm;

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@ -116,9 +116,10 @@ EI_ADD_TEST(determinant)
EI_ADD_TEST(inverse)
EI_ADD_TEST(qr)
EI_ADD_TEST(eigensolver)
EI_ADD_TEST(geometry)
EI_ADD_TEST(regression)
EI_ADD_TEST(svd)
EI_ADD_TEST(geometry)
EI_ADD_TEST(hyperplane)
EI_ADD_TEST(regression)
EI_ADD_TEST(sparse)
ENDIF(BUILD_TESTS)

71
test/hyperplane.cpp Normal file
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@ -0,0 +1,71 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <Eigen/Geometry>
#include <Eigen/LU>
template<typename PlaneType> void hyperplane(const PlaneType& _plane)
{
/* this test covers the following files:
HyperPlane.h
*/
const int dim = _plane.dim();
typedef typename PlaneType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, PlaneType::DimAtCompileTime, 1> VectorType;
VectorType p0 = VectorType::Random(dim);
VectorType p1 = VectorType::Random(dim);
VectorType n0 = VectorType::Random(dim).normalized();
VectorType n1 = VectorType::Random(dim).normalized();
PlaneType pl0(n0, p0);
PlaneType pl1(n1, p1);
Scalar s0 = ei_random<Scalar>();
Scalar s1 = ei_random<Scalar>();
VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
VERIFY_IS_MUCH_SMALLER_THAN( pl0.distanceTo(p0), Scalar(1) );
VERIFY_IS_APPROX( pl1.distanceTo(p1 + n1 * s0), s0 );
VERIFY_IS_MUCH_SMALLER_THAN( pl1.distanceTo(pl1.project(p0)), Scalar(1) );
VERIFY_IS_MUCH_SMALLER_THAN( pl1.distanceTo(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) );
}
void test_hyperplane()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( hyperplane(HyperPlane<float,2>()) );
CALL_SUBTEST( hyperplane(HyperPlane<float,3>()) );
CALL_SUBTEST( hyperplane(HyperPlane<double,4>()) );
CALL_SUBTEST( hyperplane(HyperPlane<std::complex<double>,5>()) );
CALL_SUBTEST( hyperplane(HyperPlane<double,Dynamic>(13)) );
}
}