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src/Geometry/OrthoMethods.h@1:3b8049da21b8, 2019-09-24 (annotated)

Committer:
jsoh91
Date:
Tue Sep 24 00:18:23 2019 +0000
Revision:
1:3b8049da21b8
Parent:
0:13a5d365ba16 
ignore and revise some of error parts

Who changed what in which revision?

UserRevisionLine numberNew contents of line
ykuroda 0:13a5d365ba16 1 // This file is part of Eigen, a lightweight C++ template library
ykuroda 0:13a5d365ba16 2 // for linear algebra.
ykuroda 0:13a5d365ba16 3 //
ykuroda 0:13a5d365ba16 4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
ykuroda 0:13a5d365ba16 5 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
ykuroda 0:13a5d365ba16 6 //
ykuroda 0:13a5d365ba16 7 // This Source Code Form is subject to the terms of the Mozilla
ykuroda 0:13a5d365ba16 8 // Public License v. 2.0. If a copy of the MPL was not distributed
ykuroda 0:13a5d365ba16 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
ykuroda 0:13a5d365ba16 10
ykuroda 0:13a5d365ba16 11 #ifndef EIGEN_ORTHOMETHODS_H
ykuroda 0:13a5d365ba16 12 #define EIGEN_ORTHOMETHODS_H
ykuroda 0:13a5d365ba16 13
ykuroda 0:13a5d365ba16 14 namespace Eigen {
ykuroda 0:13a5d365ba16 15
ykuroda 0:13a5d365ba16 16 /** \geometry_module
ykuroda 0:13a5d365ba16 17 *
ykuroda 0:13a5d365ba16 18 * \returns the cross product of \c *this and \a other
ykuroda 0:13a5d365ba16 19 *
ykuroda 0:13a5d365ba16 20 * Here is a very good explanation of cross-product: http://xkcd.com/199/
ykuroda 0:13a5d365ba16 21 * \sa MatrixBase::cross3()
ykuroda 0:13a5d365ba16 22 */
ykuroda 0:13a5d365ba16 23 template<typename Derived>
ykuroda 0:13a5d365ba16 24 template<typename OtherDerived>
ykuroda 0:13a5d365ba16 25 inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
ykuroda 0:13a5d365ba16 26 MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
ykuroda 0:13a5d365ba16 27 {
ykuroda 0:13a5d365ba16 28 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
ykuroda 0:13a5d365ba16 29 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
ykuroda 0:13a5d365ba16 30
ykuroda 0:13a5d365ba16 31 // Note that there is no need for an expression here since the compiler
ykuroda 0:13a5d365ba16 32 // optimize such a small temporary very well (even within a complex expression)
ykuroda 0:13a5d365ba16 33 typename internal::nested<Derived,2>::type lhs(derived());
ykuroda 0:13a5d365ba16 34 typename internal::nested<OtherDerived,2>::type rhs(other.derived());
ykuroda 0:13a5d365ba16 35 return typename cross_product_return_type<OtherDerived>::type(
ykuroda 0:13a5d365ba16 36 numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
ykuroda 0:13a5d365ba16 37 numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
ykuroda 0:13a5d365ba16 38 numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
ykuroda 0:13a5d365ba16 39 );
ykuroda 0:13a5d365ba16 40 }
ykuroda 0:13a5d365ba16 41
ykuroda 0:13a5d365ba16 42 namespace internal {
ykuroda 0:13a5d365ba16 43
ykuroda 0:13a5d365ba16 44 template< int Arch,typename VectorLhs,typename VectorRhs,
ykuroda 0:13a5d365ba16 45 typename Scalar = typename VectorLhs::Scalar,
ykuroda 0:13a5d365ba16 46 bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
ykuroda 0:13a5d365ba16 47 struct cross3_impl {
ykuroda 0:13a5d365ba16 48 static inline typename internal::plain_matrix_type<VectorLhs>::type
ykuroda 0:13a5d365ba16 49 run(const VectorLhs& lhs, const VectorRhs& rhs)
ykuroda 0:13a5d365ba16 50 {
ykuroda 0:13a5d365ba16 51 return typename internal::plain_matrix_type<VectorLhs>::type(
ykuroda 0:13a5d365ba16 52 numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
ykuroda 0:13a5d365ba16 53 numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
ykuroda 0:13a5d365ba16 54 numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
ykuroda 0:13a5d365ba16 55 0
ykuroda 0:13a5d365ba16 56 );
ykuroda 0:13a5d365ba16 57 }
ykuroda 0:13a5d365ba16 58 };
ykuroda 0:13a5d365ba16 59
ykuroda 0:13a5d365ba16 60 }
ykuroda 0:13a5d365ba16 61
ykuroda 0:13a5d365ba16 62 /** \geometry_module
ykuroda 0:13a5d365ba16 63 *
ykuroda 0:13a5d365ba16 64 * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
ykuroda 0:13a5d365ba16 65 *
ykuroda 0:13a5d365ba16 66 * The size of \c *this and \a other must be four. This function is especially useful
ykuroda 0:13a5d365ba16 67 * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
ykuroda 0:13a5d365ba16 68 *
ykuroda 0:13a5d365ba16 69 * \sa MatrixBase::cross()
ykuroda 0:13a5d365ba16 70 */
ykuroda 0:13a5d365ba16 71 template<typename Derived>
ykuroda 0:13a5d365ba16 72 template<typename OtherDerived>
ykuroda 0:13a5d365ba16 73 inline typename MatrixBase<Derived>::PlainObject
ykuroda 0:13a5d365ba16 74 MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
ykuroda 0:13a5d365ba16 75 {
ykuroda 0:13a5d365ba16 76 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
ykuroda 0:13a5d365ba16 77 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
ykuroda 0:13a5d365ba16 78
ykuroda 0:13a5d365ba16 79 typedef typename internal::nested<Derived,2>::type DerivedNested;
ykuroda 0:13a5d365ba16 80 typedef typename internal::nested<OtherDerived,2>::type OtherDerivedNested;
ykuroda 0:13a5d365ba16 81 DerivedNested lhs(derived());
ykuroda 0:13a5d365ba16 82 OtherDerivedNested rhs(other.derived());
ykuroda 0:13a5d365ba16 83
ykuroda 0:13a5d365ba16 84 return internal::cross3_impl<Architecture::Target,
ykuroda 0:13a5d365ba16 85 typename internal::remove_all<DerivedNested>::type,
ykuroda 0:13a5d365ba16 86 typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
ykuroda 0:13a5d365ba16 87 }
ykuroda 0:13a5d365ba16 88
ykuroda 0:13a5d365ba16 89 /** \returns a matrix expression of the cross product of each column or row
ykuroda 0:13a5d365ba16 90 * of the referenced expression with the \a other vector.
ykuroda 0:13a5d365ba16 91 *
ykuroda 0:13a5d365ba16 92 * The referenced matrix must have one dimension equal to 3.
ykuroda 0:13a5d365ba16 93 * The result matrix has the same dimensions than the referenced one.
ykuroda 0:13a5d365ba16 94 *
ykuroda 0:13a5d365ba16 95 * \geometry_module
ykuroda 0:13a5d365ba16 96 *
ykuroda 0:13a5d365ba16 97 * \sa MatrixBase::cross() */
ykuroda 0:13a5d365ba16 98 template<typename ExpressionType, int Direction>
ykuroda 0:13a5d365ba16 99 template<typename OtherDerived>
ykuroda 0:13a5d365ba16 100 const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
ykuroda 0:13a5d365ba16 101 VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
ykuroda 0:13a5d365ba16 102 {
ykuroda 0:13a5d365ba16 103 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
ykuroda 0:13a5d365ba16 104 EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
ykuroda 0:13a5d365ba16 105 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
ykuroda 0:13a5d365ba16 106
ykuroda 0:13a5d365ba16 107 CrossReturnType res(_expression().rows(),_expression().cols());
ykuroda 0:13a5d365ba16 108 if(Direction==Vertical)
ykuroda 0:13a5d365ba16 109 {
ykuroda 0:13a5d365ba16 110 eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
ykuroda 0:13a5d365ba16 111 res.row(0) = (_expression().row(1) * other.coeff(2) - _expression().row(2) * other.coeff(1)).conjugate();
ykuroda 0:13a5d365ba16 112 res.row(1) = (_expression().row(2) * other.coeff(0) - _expression().row(0) * other.coeff(2)).conjugate();
ykuroda 0:13a5d365ba16 113 res.row(2) = (_expression().row(0) * other.coeff(1) - _expression().row(1) * other.coeff(0)).conjugate();
ykuroda 0:13a5d365ba16 114 }
ykuroda 0:13a5d365ba16 115 else
ykuroda 0:13a5d365ba16 116 {
ykuroda 0:13a5d365ba16 117 eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
ykuroda 0:13a5d365ba16 118 res.col(0) = (_expression().col(1) * other.coeff(2) - _expression().col(2) * other.coeff(1)).conjugate();
ykuroda 0:13a5d365ba16 119 res.col(1) = (_expression().col(2) * other.coeff(0) - _expression().col(0) * other.coeff(2)).conjugate();
ykuroda 0:13a5d365ba16 120 res.col(2) = (_expression().col(0) * other.coeff(1) - _expression().col(1) * other.coeff(0)).conjugate();
ykuroda 0:13a5d365ba16 121 }
ykuroda 0:13a5d365ba16 122 return res;
ykuroda 0:13a5d365ba16 123 }
ykuroda 0:13a5d365ba16 124
ykuroda 0:13a5d365ba16 125 namespace internal {
ykuroda 0:13a5d365ba16 126
ykuroda 0:13a5d365ba16 127 template<typename Derived, int Size = Derived::SizeAtCompileTime>
ykuroda 0:13a5d365ba16 128 struct unitOrthogonal_selector
ykuroda 0:13a5d365ba16 129 {
ykuroda 0:13a5d365ba16 130 typedef typename plain_matrix_type<Derived>::type VectorType;
ykuroda 0:13a5d365ba16 131 typedef typename traits<Derived>::Scalar Scalar;
ykuroda 0:13a5d365ba16 132 typedef typename NumTraits<Scalar>::Real RealScalar;
ykuroda 0:13a5d365ba16 133 typedef typename Derived::Index Index;
ykuroda 0:13a5d365ba16 134 typedef Matrix<Scalar,2,1> Vector2;
ykuroda 0:13a5d365ba16 135 static inline VectorType run(const Derived& src)
ykuroda 0:13a5d365ba16 136 {
ykuroda 0:13a5d365ba16 137 VectorType perp = VectorType::Zero(src.size());
ykuroda 0:13a5d365ba16 138 Index maxi = 0;
ykuroda 0:13a5d365ba16 139 Index sndi = 0;
ykuroda 0:13a5d365ba16 140 src.cwiseAbs().maxCoeff(&maxi);
ykuroda 0:13a5d365ba16 141 if (maxi==0)
ykuroda 0:13a5d365ba16 142 sndi = 1;
ykuroda 0:13a5d365ba16 143 RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
ykuroda 0:13a5d365ba16 144 perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
ykuroda 0:13a5d365ba16 145 perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
ykuroda 0:13a5d365ba16 146
ykuroda 0:13a5d365ba16 147 return perp;
ykuroda 0:13a5d365ba16 148 }
ykuroda 0:13a5d365ba16 149 };
ykuroda 0:13a5d365ba16 150
ykuroda 0:13a5d365ba16 151 template<typename Derived>
ykuroda 0:13a5d365ba16 152 struct unitOrthogonal_selector<Derived,3>
ykuroda 0:13a5d365ba16 153 {
ykuroda 0:13a5d365ba16 154 typedef typename plain_matrix_type<Derived>::type VectorType;
ykuroda 0:13a5d365ba16 155 typedef typename traits<Derived>::Scalar Scalar;
ykuroda 0:13a5d365ba16 156 typedef typename NumTraits<Scalar>::Real RealScalar;
ykuroda 0:13a5d365ba16 157 static inline VectorType run(const Derived& src)
ykuroda 0:13a5d365ba16 158 {
ykuroda 0:13a5d365ba16 159 VectorType perp;
ykuroda 0:13a5d365ba16 160 /* Let us compute the crossed product of *this with a vector
ykuroda 0:13a5d365ba16 161 * that is not too close to being colinear to *this.
ykuroda 0:13a5d365ba16 162 */
ykuroda 0:13a5d365ba16 163
ykuroda 0:13a5d365ba16 164 /* unless the x and y coords are both close to zero, we can
ykuroda 0:13a5d365ba16 165 * simply take ( -y, x, 0 ) and normalize it.
ykuroda 0:13a5d365ba16 166 */
ykuroda 0:13a5d365ba16 167 if((!isMuchSmallerThan(src.x(), src.z()))
ykuroda 0:13a5d365ba16 168 || (!isMuchSmallerThan(src.y(), src.z())))
ykuroda 0:13a5d365ba16 169 {
ykuroda 0:13a5d365ba16 170 RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
ykuroda 0:13a5d365ba16 171 perp.coeffRef(0) = -numext::conj(src.y())*invnm;
ykuroda 0:13a5d365ba16 172 perp.coeffRef(1) = numext::conj(src.x())*invnm;
ykuroda 0:13a5d365ba16 173 perp.coeffRef(2) = 0;
ykuroda 0:13a5d365ba16 174 }
ykuroda 0:13a5d365ba16 175 /* if both x and y are close to zero, then the vector is close
ykuroda 0:13a5d365ba16 176 * to the z-axis, so it's far from colinear to the x-axis for instance.
ykuroda 0:13a5d365ba16 177 * So we take the crossed product with (1,0,0) and normalize it.
ykuroda 0:13a5d365ba16 178 */
ykuroda 0:13a5d365ba16 179 else
ykuroda 0:13a5d365ba16 180 {
ykuroda 0:13a5d365ba16 181 RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
ykuroda 0:13a5d365ba16 182 perp.coeffRef(0) = 0;
ykuroda 0:13a5d365ba16 183 perp.coeffRef(1) = -numext::conj(src.z())*invnm;
ykuroda 0:13a5d365ba16 184 perp.coeffRef(2) = numext::conj(src.y())*invnm;
ykuroda 0:13a5d365ba16 185 }
ykuroda 0:13a5d365ba16 186
ykuroda 0:13a5d365ba16 187 return perp;
ykuroda 0:13a5d365ba16 188 }
ykuroda 0:13a5d365ba16 189 };
ykuroda 0:13a5d365ba16 190
ykuroda 0:13a5d365ba16 191 template<typename Derived>
ykuroda 0:13a5d365ba16 192 struct unitOrthogonal_selector<Derived,2>
ykuroda 0:13a5d365ba16 193 {
ykuroda 0:13a5d365ba16 194 typedef typename plain_matrix_type<Derived>::type VectorType;
ykuroda 0:13a5d365ba16 195 static inline VectorType run(const Derived& src)
ykuroda 0:13a5d365ba16 196 { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
ykuroda 0:13a5d365ba16 197 };
ykuroda 0:13a5d365ba16 198
ykuroda 0:13a5d365ba16 199 } // end namespace internal
ykuroda 0:13a5d365ba16 200
ykuroda 0:13a5d365ba16 201 /** \returns a unit vector which is orthogonal to \c *this
ykuroda 0:13a5d365ba16 202 *
ykuroda 0:13a5d365ba16 203 * The size of \c *this must be at least 2. If the size is exactly 2,
ykuroda 0:13a5d365ba16 204 * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
ykuroda 0:13a5d365ba16 205 *
ykuroda 0:13a5d365ba16 206 * \sa cross()
ykuroda 0:13a5d365ba16 207 */
ykuroda 0:13a5d365ba16 208 template<typename Derived>
ykuroda 0:13a5d365ba16 209 typename MatrixBase<Derived>::PlainObject
ykuroda 0:13a5d365ba16 210 MatrixBase<Derived>::unitOrthogonal() const
ykuroda 0:13a5d365ba16 211 {
ykuroda 0:13a5d365ba16 212 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
ykuroda 0:13a5d365ba16 213 return internal::unitOrthogonal_selector<Derived>::run(derived());
ykuroda 0:13a5d365ba16 214 }
ykuroda 0:13a5d365ba16 215
ykuroda 0:13a5d365ba16 216 } // end namespace Eigen
ykuroda 0:13a5d365ba16 217
ykuroda 0:13a5d365ba16 218 #endif // EIGEN_ORTHOMETHODS_H