1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2009 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 #include "main.h"
11 #include <Eigen/Geometry>
12
homogeneous(void)13 template<typename Scalar,int Size> void homogeneous(void)
14 {
15 /* this test covers the following files:
16 Homogeneous.h
17 */
18
19 typedef Matrix<Scalar,Size,Size> MatrixType;
20 typedef Matrix<Scalar,Size,1, ColMajor> VectorType;
21
22 typedef Matrix<Scalar,Size+1,Size> HMatrixType;
23 typedef Matrix<Scalar,Size+1,1> HVectorType;
24
25 typedef Matrix<Scalar,Size,Size+1> T1MatrixType;
26 typedef Matrix<Scalar,Size+1,Size+1> T2MatrixType;
27 typedef Matrix<Scalar,Size+1,Size> T3MatrixType;
28
29 VectorType v0 = VectorType::Random(),
30 ones = VectorType::Ones();
31
32 HVectorType hv0 = HVectorType::Random();
33
34 MatrixType m0 = MatrixType::Random();
35
36 HMatrixType hm0 = HMatrixType::Random();
37
38 hv0 << v0, 1;
39 VERIFY_IS_APPROX(v0.homogeneous(), hv0);
40 VERIFY_IS_APPROX(v0, hv0.hnormalized());
41
42 VERIFY_IS_APPROX(v0.homogeneous().sum(), hv0.sum());
43 VERIFY_IS_APPROX(v0.homogeneous().minCoeff(), hv0.minCoeff());
44 VERIFY_IS_APPROX(v0.homogeneous().maxCoeff(), hv0.maxCoeff());
45
46 hm0 << m0, ones.transpose();
47 VERIFY_IS_APPROX(m0.colwise().homogeneous(), hm0);
48 VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
49 hm0.row(Size-1).setRandom();
50 for(int j=0; j<Size; ++j)
51 m0.col(j) = hm0.col(j).head(Size) / hm0(Size,j);
52 VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
53
54 T1MatrixType t1 = T1MatrixType::Random();
55 VERIFY_IS_APPROX(t1 * (v0.homogeneous().eval()), t1 * v0.homogeneous());
56 VERIFY_IS_APPROX(t1 * (m0.colwise().homogeneous().eval()), t1 * m0.colwise().homogeneous());
57
58 T2MatrixType t2 = T2MatrixType::Random();
59 VERIFY_IS_APPROX(t2 * (v0.homogeneous().eval()), t2 * v0.homogeneous());
60 VERIFY_IS_APPROX(t2 * (m0.colwise().homogeneous().eval()), t2 * m0.colwise().homogeneous());
61 VERIFY_IS_APPROX(t2 * (v0.homogeneous().asDiagonal()), t2 * hv0.asDiagonal());
62 VERIFY_IS_APPROX((v0.homogeneous().asDiagonal()) * t2, hv0.asDiagonal() * t2);
63
64 VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t2,
65 v0.transpose().rowwise().homogeneous() * t2);
66 VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t2,
67 m0.transpose().rowwise().homogeneous() * t2);
68
69 T3MatrixType t3 = T3MatrixType::Random();
70 VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t3,
71 v0.transpose().rowwise().homogeneous() * t3);
72 VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t3,
73 m0.transpose().rowwise().homogeneous() * t3);
74
75 // test product with a Transform object
76 Transform<Scalar, Size, Affine> aff;
77 Transform<Scalar, Size, AffineCompact> caff;
78 Transform<Scalar, Size, Projective> proj;
79 Matrix<Scalar, Size, Dynamic> pts;
80 Matrix<Scalar, Size+1, Dynamic> pts1, pts2;
81
82 aff.affine().setRandom();
83 proj = caff = aff;
84 pts.setRandom(Size,internal::random<int>(1,20));
85
86 pts1 = pts.colwise().homogeneous();
87 VERIFY_IS_APPROX(aff * pts.colwise().homogeneous(), (aff * pts1).colwise().hnormalized());
88 VERIFY_IS_APPROX(caff * pts.colwise().homogeneous(), (caff * pts1).colwise().hnormalized());
89 VERIFY_IS_APPROX(proj * pts.colwise().homogeneous(), (proj * pts1));
90
91 VERIFY_IS_APPROX((aff * pts1).colwise().hnormalized(), aff * pts);
92 VERIFY_IS_APPROX((caff * pts1).colwise().hnormalized(), caff * pts);
93
94 pts2 = pts1;
95 pts2.row(Size).setRandom();
96 VERIFY_IS_APPROX((aff * pts2).colwise().hnormalized(), aff * pts2.colwise().hnormalized());
97 VERIFY_IS_APPROX((caff * pts2).colwise().hnormalized(), caff * pts2.colwise().hnormalized());
98 VERIFY_IS_APPROX((proj * pts2).colwise().hnormalized(), (proj * pts2.colwise().hnormalized().colwise().homogeneous()).colwise().hnormalized());
99
100 // Test combination of homogeneous
101
102 VERIFY_IS_APPROX( (t2 * v0.homogeneous()).hnormalized(),
103 (t2.template topLeftCorner<Size,Size>() * v0 + t2.template topRightCorner<Size,1>())
104 / ((t2.template bottomLeftCorner<1,Size>()*v0).value() + t2(Size,Size)) );
105
106 VERIFY_IS_APPROX( (t2 * pts.colwise().homogeneous()).colwise().hnormalized(),
107 (Matrix<Scalar, Size+1, Dynamic>(t2 * pts1).colwise().hnormalized()) );
108
109 VERIFY_IS_APPROX( (t2 .lazyProduct( v0.homogeneous() )).hnormalized(), (t2 * v0.homogeneous()).hnormalized() );
110 VERIFY_IS_APPROX( (t2 .lazyProduct ( pts.colwise().homogeneous() )).colwise().hnormalized(), (t2 * pts1).colwise().hnormalized() );
111
112 VERIFY_IS_APPROX( (v0.transpose().homogeneous() .lazyProduct( t2 )).hnormalized(), (v0.transpose().homogeneous()*t2).hnormalized() );
113 VERIFY_IS_APPROX( (pts.transpose().rowwise().homogeneous() .lazyProduct( t2 )).rowwise().hnormalized(), (pts1.transpose()*t2).rowwise().hnormalized() );
114
115 VERIFY_IS_APPROX( (t2.template triangularView<Lower>() * v0.homogeneous()).eval(), (t2.template triangularView<Lower>()*hv0) );
116 }
117
test_geo_homogeneous()118 void test_geo_homogeneous()
119 {
120 for(int i = 0; i < g_repeat; i++) {
121 CALL_SUBTEST_1(( homogeneous<float,1>() ));
122 CALL_SUBTEST_2(( homogeneous<double,3>() ));
123 CALL_SUBTEST_3(( homogeneous<double,8>() ));
124 }
125 }
126