Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 1 | // This file is part of Eigen, a lightweight C++ template library |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 2 | // for linear algebra. |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 3 | // |
| 4 | // Copyright (C) 2008 Gael Guennebaud <g.gael@free.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 | // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway |
| 12 | |
| 13 | namespace Eigen { |
| 14 | |
| 15 | /** \geometry_module \ingroup Geometry_Module |
| 16 | * |
| 17 | * \class Hyperplane |
| 18 | * |
| 19 | * \brief A hyperplane |
| 20 | * |
| 21 | * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n. |
| 22 | * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane. |
| 23 | * |
| 24 | * \param _Scalar the scalar type, i.e., the type of the coefficients |
| 25 | * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. |
| 26 | * Notice that the dimension of the hyperplane is _AmbientDim-1. |
| 27 | * |
| 28 | * This class represents an hyperplane as the zero set of the implicit equation |
| 29 | * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part) |
| 30 | * and \f$ d \f$ is the distance (offset) to the origin. |
| 31 | */ |
| 32 | template <typename _Scalar, int _AmbientDim> |
| 33 | class Hyperplane |
| 34 | { |
| 35 | public: |
| 36 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1) |
| 37 | enum { AmbientDimAtCompileTime = _AmbientDim }; |
| 38 | typedef _Scalar Scalar; |
| 39 | typedef typename NumTraits<Scalar>::Real RealScalar; |
| 40 | typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; |
| 41 | typedef Matrix<Scalar,int(AmbientDimAtCompileTime)==Dynamic |
| 42 | ? Dynamic |
| 43 | : int(AmbientDimAtCompileTime)+1,1> Coefficients; |
| 44 | typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType; |
| 45 | |
| 46 | /** Default constructor without initialization */ |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 47 | inline Hyperplane() {} |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 48 | |
| 49 | /** Constructs a dynamic-size hyperplane with \a _dim the dimension |
| 50 | * of the ambient space */ |
| 51 | inline explicit Hyperplane(int _dim) : m_coeffs(_dim+1) {} |
| 52 | |
| 53 | /** Construct a plane from its normal \a n and a point \a e onto the plane. |
| 54 | * \warning the vector normal is assumed to be normalized. |
| 55 | */ |
| 56 | inline Hyperplane(const VectorType& n, const VectorType& e) |
| 57 | : m_coeffs(n.size()+1) |
| 58 | { |
| 59 | normal() = n; |
| 60 | offset() = -e.eigen2_dot(n); |
| 61 | } |
| 62 | |
| 63 | /** Constructs a plane from its normal \a n and distance to the origin \a d |
| 64 | * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$. |
| 65 | * \warning the vector normal is assumed to be normalized. |
| 66 | */ |
| 67 | inline Hyperplane(const VectorType& n, Scalar d) |
| 68 | : m_coeffs(n.size()+1) |
| 69 | { |
| 70 | normal() = n; |
| 71 | offset() = d; |
| 72 | } |
| 73 | |
| 74 | /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space |
| 75 | * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made. |
| 76 | */ |
| 77 | static inline Hyperplane Through(const VectorType& p0, const VectorType& p1) |
| 78 | { |
| 79 | Hyperplane result(p0.size()); |
| 80 | result.normal() = (p1 - p0).unitOrthogonal(); |
| 81 | result.offset() = -result.normal().eigen2_dot(p0); |
| 82 | return result; |
| 83 | } |
| 84 | |
| 85 | /** Constructs a hyperplane passing through the three points. The dimension of the ambient space |
| 86 | * is required to be exactly 3. |
| 87 | */ |
| 88 | static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2) |
| 89 | { |
| 90 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3) |
| 91 | Hyperplane result(p0.size()); |
| 92 | result.normal() = (p2 - p0).cross(p1 - p0).normalized(); |
| 93 | result.offset() = -result.normal().eigen2_dot(p0); |
| 94 | return result; |
| 95 | } |
| 96 | |
| 97 | /** Constructs a hyperplane passing through the parametrized line \a parametrized. |
| 98 | * If the dimension of the ambient space is greater than 2, then there isn't uniqueness, |
| 99 | * so an arbitrary choice is made. |
| 100 | */ |
| 101 | // FIXME to be consitent with the rest this could be implemented as a static Through function ?? |
| 102 | explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized) |
| 103 | { |
| 104 | normal() = parametrized.direction().unitOrthogonal(); |
| 105 | offset() = -normal().eigen2_dot(parametrized.origin()); |
| 106 | } |
| 107 | |
| 108 | ~Hyperplane() {} |
| 109 | |
| 110 | /** \returns the dimension in which the plane holds */ |
| 111 | inline int dim() const { return int(AmbientDimAtCompileTime)==Dynamic ? m_coeffs.size()-1 : int(AmbientDimAtCompileTime); } |
| 112 | |
| 113 | /** normalizes \c *this */ |
| 114 | void normalize(void) |
| 115 | { |
| 116 | m_coeffs /= normal().norm(); |
| 117 | } |
| 118 | |
| 119 | /** \returns the signed distance between the plane \c *this and a point \a p. |
| 120 | * \sa absDistance() |
| 121 | */ |
| 122 | inline Scalar signedDistance(const VectorType& p) const { return p.eigen2_dot(normal()) + offset(); } |
| 123 | |
| 124 | /** \returns the absolute distance between the plane \c *this and a point \a p. |
| 125 | * \sa signedDistance() |
| 126 | */ |
| 127 | inline Scalar absDistance(const VectorType& p) const { return ei_abs(signedDistance(p)); } |
| 128 | |
| 129 | /** \returns the projection of a point \a p onto the plane \c *this. |
| 130 | */ |
| 131 | inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); } |
| 132 | |
| 133 | /** \returns a constant reference to the unit normal vector of the plane, which corresponds |
| 134 | * to the linear part of the implicit equation. |
| 135 | */ |
| 136 | inline const NormalReturnType normal() const { return NormalReturnType(*const_cast<Coefficients*>(&m_coeffs),0,0,dim(),1); } |
| 137 | |
| 138 | /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds |
| 139 | * to the linear part of the implicit equation. |
| 140 | */ |
| 141 | inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); } |
| 142 | |
| 143 | /** \returns the distance to the origin, which is also the "constant term" of the implicit equation |
| 144 | * \warning the vector normal is assumed to be normalized. |
| 145 | */ |
| 146 | inline const Scalar& offset() const { return m_coeffs.coeff(dim()); } |
| 147 | |
| 148 | /** \returns a non-constant reference to the distance to the origin, which is also the constant part |
| 149 | * of the implicit equation */ |
| 150 | inline Scalar& offset() { return m_coeffs(dim()); } |
| 151 | |
| 152 | /** \returns a constant reference to the coefficients c_i of the plane equation: |
| 153 | * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$ |
| 154 | */ |
| 155 | inline const Coefficients& coeffs() const { return m_coeffs; } |
| 156 | |
| 157 | /** \returns a non-constant reference to the coefficients c_i of the plane equation: |
| 158 | * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$ |
| 159 | */ |
| 160 | inline Coefficients& coeffs() { return m_coeffs; } |
| 161 | |
| 162 | /** \returns the intersection of *this with \a other. |
| 163 | * |
| 164 | * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines. |
| 165 | * |
| 166 | * \note If \a other is approximately parallel to *this, this method will return any point on *this. |
| 167 | */ |
| 168 | VectorType intersection(const Hyperplane& other) |
| 169 | { |
| 170 | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2) |
| 171 | Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0); |
| 172 | // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests |
| 173 | // whether the two lines are approximately parallel. |
| 174 | if(ei_isMuchSmallerThan(det, Scalar(1))) |
| 175 | { // special case where the two lines are approximately parallel. Pick any point on the first line. |
| 176 | if(ei_abs(coeffs().coeff(1))>ei_abs(coeffs().coeff(0))) |
| 177 | return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0)); |
| 178 | else |
| 179 | return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0)); |
| 180 | } |
| 181 | else |
| 182 | { // general case |
| 183 | Scalar invdet = Scalar(1) / det; |
| 184 | return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)), |
| 185 | invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2))); |
| 186 | } |
| 187 | } |
| 188 | |
| 189 | /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this. |
| 190 | * |
| 191 | * \param mat the Dim x Dim transformation matrix |
| 192 | * \param traits specifies whether the matrix \a mat represents an Isometry |
| 193 | * or a more generic Affine transformation. The default is Affine. |
| 194 | */ |
| 195 | template<typename XprType> |
| 196 | inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine) |
| 197 | { |
| 198 | if (traits==Affine) |
| 199 | normal() = mat.inverse().transpose() * normal(); |
| 200 | else if (traits==Isometry) |
| 201 | normal() = mat * normal(); |
| 202 | else |
| 203 | { |
| 204 | ei_assert("invalid traits value in Hyperplane::transform()"); |
| 205 | } |
| 206 | return *this; |
| 207 | } |
| 208 | |
| 209 | /** Applies the transformation \a t to \c *this and returns a reference to \c *this. |
| 210 | * |
| 211 | * \param t the transformation of dimension Dim |
| 212 | * \param traits specifies whether the transformation \a t represents an Isometry |
| 213 | * or a more generic Affine transformation. The default is Affine. |
| 214 | * Other kind of transformations are not supported. |
| 215 | */ |
| 216 | inline Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime>& t, |
| 217 | TransformTraits traits = Affine) |
| 218 | { |
| 219 | transform(t.linear(), traits); |
| 220 | offset() -= t.translation().eigen2_dot(normal()); |
| 221 | return *this; |
| 222 | } |
| 223 | |
| 224 | /** \returns \c *this with scalar type casted to \a NewScalarType |
| 225 | * |
| 226 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this |
| 227 | * then this function smartly returns a const reference to \c *this. |
| 228 | */ |
| 229 | template<typename NewScalarType> |
| 230 | inline typename internal::cast_return_type<Hyperplane, |
| 231 | Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type cast() const |
| 232 | { |
| 233 | return typename internal::cast_return_type<Hyperplane, |
| 234 | Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type(*this); |
| 235 | } |
| 236 | |
| 237 | /** Copy constructor with scalar type conversion */ |
| 238 | template<typename OtherScalarType> |
| 239 | inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime>& other) |
| 240 | { m_coeffs = other.coeffs().template cast<Scalar>(); } |
| 241 | |
| 242 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision |
| 243 | * determined by \a prec. |
| 244 | * |
| 245 | * \sa MatrixBase::isApprox() */ |
| 246 | bool isApprox(const Hyperplane& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const |
| 247 | { return m_coeffs.isApprox(other.m_coeffs, prec); } |
| 248 | |
| 249 | protected: |
| 250 | |
| 251 | Coefficients m_coeffs; |
| 252 | }; |
| 253 | |
| 254 | } // end namespace Eigen |