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//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef EIGEN_SCALING_H
11#define EIGEN_SCALING_H
12
13namespace Eigen {
14
15/** \geometry_module \ingroup Geometry_Module
16 *
17 * \class Scaling
18 *
19 * \brief Represents a generic uniform scaling transformation
20 *
21 * \tparam _Scalar the scalar type, i.e., the type of the coefficients.
22 *
23 * This class represent a uniform scaling transformation. It is the return
24 * type of Scaling(Scalar), and most of the time this is the only way it
25 * is used. In particular, this class is not aimed to be used to store a scaling transformation,
26 * but rather to make easier the constructions and updates of Transform objects.
27 *
28 * To represent an axis aligned scaling, use the DiagonalMatrix class.
29 *
30 * \sa Scaling(), class DiagonalMatrix, MatrixBase::asDiagonal(), class Translation, class Transform
31 */
32template<typename _Scalar>
33class UniformScaling
34{
35public:
36 /** the scalar type of the coefficients */
37 typedef _Scalar Scalar;
38
39protected:
40
41 Scalar m_factor;
42
43public:
44
45 /** Default constructor without initialization. */
46 UniformScaling() {}
47 /** Constructs and initialize a uniform scaling transformation */
48 explicit inline UniformScaling(const Scalar& s) : m_factor(s) {}
49
50 inline const Scalar& factor() const { return m_factor; }
51 inline Scalar& factor() { return m_factor; }
52
53 /** Concatenates two uniform scaling */
54 inline UniformScaling operator* (const UniformScaling& other) const
55 { return UniformScaling(m_factor * other.factor()); }
56
57 /** Concatenates a uniform scaling and a translation */
58 template<int Dim>
59 inline Transform<Scalar,Dim,Affine> operator* (const Translation<Scalar,Dim>& t) const;
60
61 /** Concatenates a uniform scaling and an affine transformation */
62 template<int Dim, int Mode, int Options>
63 inline Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Mode)> operator* (const Transform<Scalar,Dim, Mode, Options>& t) const
64 {
65 Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Mode)> res = t;
66 res.prescale(factor());
67 return res;
68 }
69
70 /** Concatenates a uniform scaling and a linear transformation matrix */
71 // TODO returns an expression
72 template<typename Derived>
73 inline typename internal::plain_matrix_type<Derived>::type operator* (const MatrixBase<Derived>& other) const
74 { return other * m_factor; }
75
76 template<typename Derived,int Dim>
77 inline Matrix<Scalar,Dim,Dim> operator*(const RotationBase<Derived,Dim>& r) const
78 { return r.toRotationMatrix() * m_factor; }
79
80 /** \returns the inverse scaling */
81 inline UniformScaling inverse() const
82 { return UniformScaling(Scalar(1)/m_factor); }
83
84 /** \returns \c *this with scalar type casted to \a NewScalarType
85 *
86 * Note that if \a NewScalarType is equal to the current scalar type of \c *this
87 * then this function smartly returns a const reference to \c *this.
88 */
89 template<typename NewScalarType>
90 inline UniformScaling<NewScalarType> cast() const
91 { return UniformScaling<NewScalarType>(NewScalarType(m_factor)); }
92
93 /** Copy constructor with scalar type conversion */
94 template<typename OtherScalarType>
95 inline explicit UniformScaling(const UniformScaling<OtherScalarType>& other)
96 { m_factor = Scalar(other.factor()); }
97
98 /** \returns \c true if \c *this is approximately equal to \a other, within the precision
99 * determined by \a prec.
100 *
101 * \sa MatrixBase::isApprox() */
102 bool isApprox(const UniformScaling& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
103 { return internal::isApprox(m_factor, other.factor(), prec); }
104
105};
106
107/** \addtogroup Geometry_Module */
108//@{
109
110/** Concatenates a linear transformation matrix and a uniform scaling
111 * \relates UniformScaling
112 */
113// NOTE this operator is defiend in MatrixBase and not as a friend function
114// of UniformScaling to fix an internal crash of Intel's ICC
115template<typename Derived,typename Scalar>
116EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,Scalar,product)
117operator*(const MatrixBase<Derived>& matrix, const UniformScaling<Scalar>& s)
118{ return matrix.derived() * s.factor(); }
119
120/** Constructs a uniform scaling from scale factor \a s */
121inline UniformScaling<float> Scaling(float s) { return UniformScaling<float>(s); }
122/** Constructs a uniform scaling from scale factor \a s */
123inline UniformScaling<double> Scaling(double s) { return UniformScaling<double>(s); }
124/** Constructs a uniform scaling from scale factor \a s */
125template<typename RealScalar>
126inline UniformScaling<std::complex<RealScalar> > Scaling(const std::complex<RealScalar>& s)
127{ return UniformScaling<std::complex<RealScalar> >(s); }
128
129/** Constructs a 2D axis aligned scaling */
130template<typename Scalar>
131inline DiagonalMatrix<Scalar,2> Scaling(const Scalar& sx, const Scalar& sy)
132{ return DiagonalMatrix<Scalar,2>(sx, sy); }
133/** Constructs a 3D axis aligned scaling */
134template<typename Scalar>
135inline DiagonalMatrix<Scalar,3> Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz)
136{ return DiagonalMatrix<Scalar,3>(sx, sy, sz); }
137
138/** Constructs an axis aligned scaling expression from vector expression \a coeffs
139 * This is an alias for coeffs.asDiagonal()
140 */
141template<typename Derived>
142inline const DiagonalWrapper<const Derived> Scaling(const MatrixBase<Derived>& coeffs)
143{ return coeffs.asDiagonal(); }
144
145/** \deprecated */
146typedef DiagonalMatrix<float, 2> AlignedScaling2f;
147/** \deprecated */
148typedef DiagonalMatrix<double,2> AlignedScaling2d;
149/** \deprecated */
150typedef DiagonalMatrix<float, 3> AlignedScaling3f;
151/** \deprecated */
152typedef DiagonalMatrix<double,3> AlignedScaling3d;
153//@}
154
155template<typename Scalar>
156template<int Dim>
157inline Transform<Scalar,Dim,Affine>
158UniformScaling<Scalar>::operator* (const Translation<Scalar,Dim>& t) const
159{
160 Transform<Scalar,Dim,Affine> res;
161 res.matrix().setZero();
162 res.linear().diagonal().fill(factor());
163 res.translation() = factor() * t.vector();
164 res(Dim,Dim) = Scalar(1);
165 return res;
166}
167
168} // end namespace Eigen
169
170#endif // EIGEN_SCALING_H
171