devtools/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2026-04-10 11:34:33 +08:00
Code Issues Packages Projects Releases Wiki Activity

The discussed changes to Hyperplane, the ParametrizedLine class, and the

Browse Source 
API update in Regression...
This commit is contained in:
Benoit Jacob
2008-08-31 04:25:30 +00:00
parent 5c8c09e021
commit 5c34d8e20a
8 changed files with 255 additions and 119 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
Eigen/src/Core/util/ForwardDeclarations.h
View File

@@ -106,6 +106,8 @@ template<typename Scalar> class Quaternion;
template<typename Scalar> class Rotation2D;
template<typename Scalar> class AngleAxis;
template<typename Scalar,int Dim> class Transform;
template <typename _Scalar, int _AmbientDim> class ParametrizedLine;
template <typename _Scalar, int _AmbientDim> class Hyperplane;
template<typename Scalar,int Dim> class Translation;
template<typename Scalar,int Dim> class Scaling;

252
Eigen/src/Geometry/Hyperplane.h
View File

@@ -2,6 +2,7 @@
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2008 Benoit Jacob <jacob@math.jussieu.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
@@ -27,36 +28,76 @@
/** \geometry_module \ingroup GeometryModule
*
* \class Hyperplane
* \class ParametrizedLine
*
* \brief Represents an hyper plane in any dimensions
* \brief A parametrized line
*
* \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.
*
* \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
* Notice that the dimension of the hyperplane is _AmbientDim-1.
*/
template <typename _Scalar, int _Dim>
class Hyperplane
template <typename _Scalar, int _AmbientDim>
class ParametrizedLine
{
public:
enum { DimAtCompileTime = _Dim };
enum { AmbientDimAtCompileTime = _AmbientDim };
typedef _Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar,DimAtCompileTime,1> VectorType;
typedef Matrix<Scalar,DimAtCompileTime==Dynamic
typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
ParametrizedLine(const VectorType& origin, const VectorType& direction)
: m_origin(origin), m_direction(direction) {}
ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
~ParametrizedLine() {}
const VectorType& origin() const { return m_origin; }
VectorType& origin() { return m_origin; }
const VectorType& direction() const { return m_direction; }
VectorType& direction() { return m_direction; }
Scalar intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
protected:
VectorType m_origin, m_direction;
};
/** \geometry_module \ingroup GeometryModule
*
* \class Hyperplane
*
* \brief A hyperplane
*
* A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
* For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
*
* \param _Scalar the scalar type, i.e., the type of the coefficients
* \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
* Notice that the dimension of the hyperplane is _AmbientDim-1.
*
* This class represents an hyperplane as the zero set of the implicit equation
* \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
* and \f$ d \f$ is the distance (offset) to the origin.
*/
template <typename _Scalar, int _AmbientDim>
class Hyperplane
{
public:
enum { AmbientDimAtCompileTime = _AmbientDim };
typedef _Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
typedef Matrix<Scalar,AmbientDimAtCompileTime==Dynamic
? Dynamic
: DimAtCompileTime+1,1> Coefficients;
typedef Block<Coefficients,DimAtCompileTime,1> NormalReturnType;
: AmbientDimAtCompileTime+1,1> Coefficients;
typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;
/** Default constructor without initialization */
inline Hyperplane(int _dim = DimAtCompileTime) : m_coeffs(_dim+1) {}
inline Hyperplane(int _dim = AmbientDimAtCompileTime) : m_coeffs(_dim+1) {}
/** Construct a plane from its normal \a n and a point \a e onto the plane.
* \warning the vector normal is assumed to be normalized.
@@ -64,8 +105,8 @@ class Hyperplane
inline Hyperplane(const VectorType& n, const VectorType e)
: m_coeffs(n.size()+1)
{
_normal() = n;
_offset() = -e.dot(n);
normal() = n;
offset() = -e.dot(n);
}
/** Constructs a plane from its normal \a n and distance to the origin \a d.
@@ -74,85 +115,152 @@ class Hyperplane
inline Hyperplane(const VectorType& n, Scalar d)
: m_coeffs(n.size()+1)
{
_normal() = n;
_offset() = d;
normal() = n;
offset() = d;
}
/** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
* is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
*/
static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
{
Hyperplane result(p0.size());
result.normal() = (p1 - p0).unitOrthogonal();
result.offset() = -result.normal().dot(p0);
return result;
}
/** Constructs a hyperplane passing through the three points. The dimension of the ambient space
* is required to be exactly 3.
*/
static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3);
Hyperplane result(p0.size());
result.normal() = (p2 - p0).cross(p1 - p0).normalized();
result.offset() = -result.normal().dot(p0);
return result;
}
Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
{
normal() = parametrized.direction().unitOrthogonal();
offset() = -normal().dot(parametrized.origin());
}
~Hyperplane() {}
/** \returns the dimension in which the plane holds */
inline int dim() const { return DimAtCompileTime==Dynamic ? m_coeffs.size()-1 : DimAtCompileTime; }
void normalize(void);
inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_coeffs.size()-1 : AmbientDimAtCompileTime; }
/** normalizes \c *this */
void normalize(void)
{
m_coeffs /= normal().norm();
}
/** \returns the signed distance between the plane \c *this and a point \a p.
*/
inline Scalar distanceTo(const VectorType& p) const { return p.dot(normal()) + offset(); }
inline Scalar signedDistance(const VectorType& p) const { return p.dot(normal()) + offset(); }
/** \returns the absolute distance between the plane \c *this and a point \a p.
*/
inline Scalar absDistance(const VectorType& p) const { return ei_abs(signedDistance(p)); }
/** \returns the projection of a point \a p onto the plane \c *this.
*/
inline VectorType project(const VectorType& p) const { return p - distanceTo(p) * normal(); }
/** \returns the normal of the plane, which corresponds to the linear part of the implicit equation. */
inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }
/** \returns a constant reference to the unit normal vector of the plane, which corresponds
* to the linear part of the implicit equation.
*/
inline const NormalReturnType normal() const { return NormalReturnType(m_coeffs,0,0,dim(),1); }
/** \returns the distance to the origin, which is also the constant part
/** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
* to the linear part of the implicit equation.
*/
inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
/** \returns the distance to the origin, which is also the "constant term" of the implicit equation
* \warning the vector normal is assumed to be normalized.
*/
inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }
/** \returns a non-constant reference to the distance to the origin, which is also the constant part
* of the implicit equation */
inline Scalar offset() const { return m_coeffs(dim()); }
inline Scalar& offset() { return m_coeffs(dim()); }
/** Set the normal of the plane.
* \warning the vector normal is assumed to be normalized. */
inline void setNormal(const VectorType& normal) { _normal() = normal; }
/** Set the distance to origin */
inline void setOffset(Scalar d) { _offset() = d; }
/** \returns the coefficients c_i of the plane equation:
/** \returns a constant reference to the coefficients c_i of the plane equation:
* \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
*/
// FIXME name: equation vs coeffs vs coefficients ???
inline Coefficients equation(void) const { return m_coeffs; }
/** \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
*/
inline Scalar rayIntersection(const VectorType& rayOrigin, const VectorType& rayDir)
inline const Coefficients& coeffs() const { return m_coeffs; }
/** \returns a non-constant reference to the coefficients c_i of the plane equation:
* \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
*/
inline Coefficients& coeffs() { return m_coeffs; }
/** \returns the intersection of *this with \a other.
*
* \warning The ambient space must be a plane, i.e. have dimension 2, so that *this and \a other are lines.
*
* \note If \a other is approximately parallel to *this, this method will return any point on *this.
*/
VectorType intersection(const Hyperplane& other)
{
return -(_offset()+rayOrigin.dot(_normal()))/(rayDir.dot(_normal()));
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2);
Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
// since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
// whether the two lines are approximately parallel.
if(ei_isMuchSmallerThan(det, Scalar(1)))
{ // special case where the two lines are approximately parallel. Pick any point on the first line.
if(ei_abs(coeffs().coeff(1))>ei_abs(coeffs().coeff(0)))
return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
else
return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));
}
else
{ // general case
Scalar invdet = Scalar(1) / det;
return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),
invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));
}
}
#if 0
template<typename XprType>
inline Hyperplane operator* (const MatrixBase<XprType>& mat) const
{ return Hyperplane(mat.inverse().transpose() * _normal(), _offset()); }
{ return Hyperplane(mat.inverse().transpose() * normal(), offset()); }
template<typename XprType>
inline Hyperplane& operator*= (const MatrixBase<XprType>& mat) const
{ _normal() = mat.inverse().transpose() * _normal(); return *this; }
// 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);
// }
{ normal() = mat.inverse().transpose() * normal(); return *this; }
#endif
protected:
inline NormalReturnType _normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
inline Scalar& _offset() { return m_coeffs(dim()); }
Coefficients m_coeffs;
};
template <typename _Scalar, int _AmbientDim>
ParametrizedLine<_Scalar, _AmbientDim>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
{
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2);
direction() = hyperplane.normal().unitOrthogonal();
origin() = -hyperplane.normal()*hyperplane.offset();
}
/** \returns the parameter value of the intersection between *this and the given hyperplane
*/
template <typename _Scalar, int _AmbientDim>
inline _Scalar ParametrizedLine<_Scalar, _AmbientDim>::intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
{
return -(hyperplane.offset()+origin().dot(hyperplane.normal()))
/(direction().dot(hyperplane.normal()));
}
#if 0
/** \addtogroup GeometryModule */
//@{
typedef Hyperplane<float, 2> Hyperplane2f;
@@ -166,14 +274,6 @@ typedef Hyperplane<double,3> Planed;
typedef Hyperplane<float, Dynamic> HyperplaneXf;
typedef Hyperplane<double,Dynamic> HyperplaneXd;
//@}
/** normalizes \c *this */
template <typename _Scalar, int _Dim>
void Hyperplane<_Scalar,_Dim>::normalize(void)
{
RealScalar l = Scalar(1)/_normal().norm();
_normal() *= l;
_offset() *= l;
}
#endif
#endif // EIGEN_Hyperplane_H

3
Eigen/src/Geometry/Transform.h
View File

@@ -539,8 +539,9 @@ Transform<Scalar,Dim>::extractRotation(TransformTraits traits) const
}
else if (traits == NoScaling) // though that's stupid let's handle it !
return linear();
else
else {
ei_assert("invalid traits value in Transform::inverse()");
}
return LinearMatrixType();
}

13
Eigen/src/Regression/Regression.h
View File

@@ -155,21 +155,20 @@ void linearRegression(int numPoints,
*
* \sa linearRegression()
*/
template<typename VectorType, typename BigVectorType>
template<typename VectorType, typename HyperplaneType>
void fitHyperplane(int numPoints,
VectorType **points,
BigVectorType *result,
HyperplaneType *result,
typename NumTraits<typename VectorType::Scalar>::Real* soundness = 0)
{
typedef typename VectorType::Scalar Scalar;
typedef Matrix<Scalar,VectorType::SizeAtCompileTime,VectorType::SizeAtCompileTime> CovMatrixType;
EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(BigVectorType)
ei_assert(numPoints >= 1);
int size = points[0]->size();
ei_assert(size+1 == result->size());
ei_assert(size+1 == result->coeffs().size());
// compue the mean of the data
// compute the mean of the data
VectorType mean = VectorType::Zero(size);
for(int i = 0; i < numPoints; i++)
mean += *(points[i]);
@@ -186,13 +185,13 @@ void fitHyperplane(int numPoints,
// now we just have to pick the eigen vector with smallest eigen value
SelfAdjointEigenSolver<CovMatrixType> eig(covMat);
result->start(size) = eig.eigenvectors().col(0);
result->normal() = eig.eigenvectors().col(0);
if (soundness)
*soundness = eig.eigenvalues().coeff(0)/eig.eigenvalues().coeff(1);
// let's compute the constant coefficient such that the
// plane pass trough the mean point:
result->coeffRef(size) = - (result->start(size).cwise()* mean).sum();
result->offset() = - (result->normal().cwise()* mean).sum();
}