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Eigen  3.4.0
 
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Hyperplane.h
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11#ifndef EIGEN_HYPERPLANE_H
12#define EIGEN_HYPERPLANE_H
13
14namespace Eigen {
15
33template <typename _Scalar, int _AmbientDim, int _Options>
35{
36public:
37 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
38 enum {
39 AmbientDimAtCompileTime = _AmbientDim,
40 Options = _Options
41 };
42 typedef _Scalar Scalar;
43 typedef typename NumTraits<Scalar>::Real RealScalar;
46 typedef Matrix<Scalar,Index(AmbientDimAtCompileTime)==Dynamic
47 ? Dynamic
48 : Index(AmbientDimAtCompileTime)+1,1,Options> Coefficients;
51
53 EIGEN_DEVICE_FUNC inline Hyperplane() {}
54
55 template<int OtherOptions>
57 : m_coeffs(other.coeffs())
58 {}
59
62 EIGEN_DEVICE_FUNC inline explicit Hyperplane(Index _dim) : m_coeffs(_dim+1) {}
63
67 EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const VectorType& e)
68 : m_coeffs(n.size()+1)
69 {
70 normal() = n;
71 offset() = -n.dot(e);
72 }
73
78 EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const Scalar& d)
79 : m_coeffs(n.size()+1)
80 {
81 normal() = n;
82 offset() = d;
83 }
84
88 EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
89 {
90 Hyperplane result(p0.size());
91 result.normal() = (p1 - p0).unitOrthogonal();
92 result.offset() = -p0.dot(result.normal());
93 return result;
94 }
95
99 EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
100 {
101 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
102 Hyperplane result(p0.size());
103 VectorType v0(p2 - p0), v1(p1 - p0);
104 result.normal() = v0.cross(v1);
105 RealScalar norm = result.normal().norm();
106 if(norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon())
107 {
108 Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
110 result.normal() = svd.matrixV().col(2);
111 }
112 else
113 result.normal() /= norm;
114 result.offset() = -p0.dot(result.normal());
115 return result;
116 }
117
122 // FIXME to be consistent with the rest this could be implemented as a static Through function ??
123 EIGEN_DEVICE_FUNC explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
124 {
125 normal() = parametrized.direction().unitOrthogonal();
126 offset() = -parametrized.origin().dot(normal());
127 }
128
129 EIGEN_DEVICE_FUNC ~Hyperplane() {}
130
132 EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_coeffs.size()-1 : Index(AmbientDimAtCompileTime); }
133
135 EIGEN_DEVICE_FUNC void normalize(void)
136 {
137 m_coeffs /= normal().norm();
138 }
139
143 EIGEN_DEVICE_FUNC inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }
144
148 EIGEN_DEVICE_FUNC inline Scalar absDistance(const VectorType& p) const { return numext::abs(signedDistance(p)); }
149
152 EIGEN_DEVICE_FUNC inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }
153
157 EIGEN_DEVICE_FUNC inline ConstNormalReturnType normal() const { return ConstNormalReturnType(m_coeffs,0,0,dim(),1); }
158
162 EIGEN_DEVICE_FUNC inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
163
167 EIGEN_DEVICE_FUNC inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }
168
171 EIGEN_DEVICE_FUNC inline Scalar& offset() { return m_coeffs(dim()); }
172
176 EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }
177
181 EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }
182
189 EIGEN_DEVICE_FUNC VectorType intersection(const Hyperplane& other) const
190 {
191 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
192 Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
193 // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
194 // whether the two lines are approximately parallel.
195 if(internal::isMuchSmallerThan(det, Scalar(1)))
196 { // special case where the two lines are approximately parallel. Pick any point on the first line.
197 if(numext::abs(coeffs().coeff(1))>numext::abs(coeffs().coeff(0)))
198 return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
199 else
200 return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));
201 }
202 else
203 { // general case
204 Scalar invdet = Scalar(1) / det;
205 return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),
206 invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));
207 }
208 }
209
216 template<typename XprType>
217 EIGEN_DEVICE_FUNC inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
218 {
219 if (traits==Affine)
220 {
221 normal() = mat.inverse().transpose() * normal();
222 m_coeffs /= normal().norm();
223 }
224 else if (traits==Isometry)
225 normal() = mat * normal();
226 else
227 {
228 eigen_assert(0 && "invalid traits value in Hyperplane::transform()");
229 }
230 return *this;
231 }
232
240 template<int TrOptions>
242 TransformTraits traits = Affine)
243 {
244 transform(t.linear(), traits);
245 offset() -= normal().dot(t.translation());
246 return *this;
247 }
248
254 template<typename NewScalarType>
255 EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Hyperplane,
257 {
258 return typename internal::cast_return_type<Hyperplane,
260 }
261
263 template<typename OtherScalarType,int OtherOptions>
265 { m_coeffs = other.coeffs().template cast<Scalar>(); }
266
271 template<int OtherOptions>
272 EIGEN_DEVICE_FUNC bool isApprox(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
273 { return m_coeffs.isApprox(other.m_coeffs, prec); }
274
275protected:
276
277 Coefficients m_coeffs;
278};
279
280} // end namespace Eigen
281
282#endif // EIGEN_HYPERPLANE_H
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:105
A hyperplane.
Definition: Hyperplane.h:35
Scalar & offset()
Definition: Hyperplane.h:171
Hyperplane(const VectorType &n, const VectorType &e)
Definition: Hyperplane.h:67
Index dim() const
Definition: Hyperplane.h:132
static Hyperplane Through(const VectorType &p0, const VectorType &p1, const VectorType &p2)
Definition: Hyperplane.h:99
Scalar absDistance(const VectorType &p) const
Definition: Hyperplane.h:148
VectorType intersection(const Hyperplane &other) const
Definition: Hyperplane.h:189
Hyperplane & transform(const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &t, TransformTraits traits=Affine)
Definition: Hyperplane.h:241
NormalReturnType normal()
Definition: Hyperplane.h:162
Eigen::Index Index
Definition: Hyperplane.h:44
const Coefficients & coeffs() const
Definition: Hyperplane.h:176
Hyperplane(Index _dim)
Definition: Hyperplane.h:62
Hyperplane(const VectorType &n, const Scalar &d)
Definition: Hyperplane.h:78
static Hyperplane Through(const VectorType &p0, const VectorType &p1)
Definition: Hyperplane.h:88
VectorType projection(const VectorType &p) const
Definition: Hyperplane.h:152
Hyperplane()
Definition: Hyperplane.h:53
Hyperplane & transform(const MatrixBase< XprType > &mat, TransformTraits traits=Affine)
Definition: Hyperplane.h:217
Scalar signedDistance(const VectorType &p) const
Definition: Hyperplane.h:143
ConstNormalReturnType normal() const
Definition: Hyperplane.h:157
Coefficients & coeffs()
Definition: Hyperplane.h:181
Hyperplane(const ParametrizedLine< Scalar, AmbientDimAtCompileTime > &parametrized)
Definition: Hyperplane.h:123
internal::cast_return_type< Hyperplane, Hyperplane< NewScalarType, AmbientDimAtCompileTime, Options > >::type cast() const
Definition: Hyperplane.h:256
bool isApprox(const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Hyperplane.h:272
Hyperplane(const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)
Definition: Hyperplane.h:264
void normalize(void)
Definition: Hyperplane.h:135
const Scalar & offset() const
Definition: Hyperplane.h:167
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition: JacobiSVD.h:490
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
const Inverse< Derived > inverse() const
Definition: InverseImpl.h:348
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:180
A parametrized line.
Definition: ParametrizedLine.h:31
const Scalar & coeff(Index rowId, Index colId) const
Definition: PlainObjectBase.h:152
const MatrixVType & matrixV() const
Definition: SVDBase.h:117
Represents an homogeneous transformation in a N dimensional space.
Definition: Transform.h:205
ConstTranslationPart translation() const
Definition: Transform.h:404
ConstLinearPart linear() const
Definition: Transform.h:394
TransformTraits
Definition: Constants.h:455
@ ComputeFullV
Definition: Constants.h:397
@ Affine
Definition: Constants.h:460
@ Isometry
Definition: Constants.h:457
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
const int Dynamic
Definition: Constants.h:22
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:233