1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
#include <Eigen/Geometry>
template<typename Scalar,int Size> void homogeneous(void)
{
/* this test covers the following files:
Homogeneous.h
*/
typedef Matrix<Scalar,Size,Size> MatrixType;
typedef Matrix<Scalar,Size,1, ColMajor> VectorType;
typedef Matrix<Scalar,Size+1,Size> HMatrixType;
typedef Matrix<Scalar,Size+1,1> HVectorType;
typedef Matrix<Scalar,Size,Size+1> T1MatrixType;
typedef Matrix<Scalar,Size+1,Size+1> T2MatrixType;
typedef Matrix<Scalar,Size+1,Size> T3MatrixType;
VectorType v0 = VectorType::Random(),
ones = VectorType::Ones();
HVectorType hv0 = HVectorType::Random();
MatrixType m0 = MatrixType::Random();
HMatrixType hm0 = HMatrixType::Random();
hv0 << v0, 1;
VERIFY_IS_APPROX(v0.homogeneous(), hv0);
VERIFY_IS_APPROX(v0, hv0.hnormalized());
VERIFY_IS_APPROX(v0.homogeneous().sum(), hv0.sum());
VERIFY_IS_APPROX(v0.homogeneous().minCoeff(), hv0.minCoeff());
VERIFY_IS_APPROX(v0.homogeneous().maxCoeff(), hv0.maxCoeff());
hm0 << m0, ones.transpose();
VERIFY_IS_APPROX(m0.colwise().homogeneous(), hm0);
VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
hm0.row(Size-1).setRandom();
for(int j=0; j<Size; ++j)
m0.col(j) = hm0.col(j).head(Size) / hm0(Size,j);
VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
T1MatrixType t1 = T1MatrixType::Random();
VERIFY_IS_APPROX(t1 * (v0.homogeneous().eval()), t1 * v0.homogeneous());
VERIFY_IS_APPROX(t1 * (m0.colwise().homogeneous().eval()), t1 * m0.colwise().homogeneous());
T2MatrixType t2 = T2MatrixType::Random();
VERIFY_IS_APPROX(t2 * (v0.homogeneous().eval()), t2 * v0.homogeneous());
VERIFY_IS_APPROX(t2 * (m0.colwise().homogeneous().eval()), t2 * m0.colwise().homogeneous());
VERIFY_IS_APPROX(t2 * (v0.homogeneous().asDiagonal()), t2 * hv0.asDiagonal());
VERIFY_IS_APPROX((v0.homogeneous().asDiagonal()) * t2, hv0.asDiagonal() * t2);
VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t2,
v0.transpose().rowwise().homogeneous() * t2);
VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t2,
m0.transpose().rowwise().homogeneous() * t2);
T3MatrixType t3 = T3MatrixType::Random();
VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t3,
v0.transpose().rowwise().homogeneous() * t3);
VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t3,
m0.transpose().rowwise().homogeneous() * t3);
// test product with a Transform object
Transform<Scalar, Size, Affine> aff;
Transform<Scalar, Size, AffineCompact> caff;
Transform<Scalar, Size, Projective> proj;
Matrix<Scalar, Size, Dynamic> pts;
Matrix<Scalar, Size+1, Dynamic> pts1, pts2;
aff.affine().setRandom();
proj = caff = aff;
pts.setRandom(Size,internal::random<int>(1,20));
pts1 = pts.colwise().homogeneous();
VERIFY_IS_APPROX(aff * pts.colwise().homogeneous(), (aff * pts1).colwise().hnormalized());
VERIFY_IS_APPROX(caff * pts.colwise().homogeneous(), (caff * pts1).colwise().hnormalized());
VERIFY_IS_APPROX(proj * pts.colwise().homogeneous(), (proj * pts1));
VERIFY_IS_APPROX((aff * pts1).colwise().hnormalized(), aff * pts);
VERIFY_IS_APPROX((caff * pts1).colwise().hnormalized(), caff * pts);
pts2 = pts1;
pts2.row(Size).setRandom();
VERIFY_IS_APPROX((aff * pts2).colwise().hnormalized(), aff * pts2.colwise().hnormalized());
VERIFY_IS_APPROX((caff * pts2).colwise().hnormalized(), caff * pts2.colwise().hnormalized());
VERIFY_IS_APPROX((proj * pts2).colwise().hnormalized(), (proj * pts2.colwise().hnormalized().colwise().homogeneous()).colwise().hnormalized());
// Test combination of homogeneous
VERIFY_IS_APPROX( (t2 * v0.homogeneous()).hnormalized(),
(t2.template topLeftCorner<Size,Size>() * v0 + t2.template topRightCorner<Size,1>())
/ ((t2.template bottomLeftCorner<1,Size>()*v0).value() + t2(Size,Size)) );
VERIFY_IS_APPROX( (t2 * pts.colwise().homogeneous()).colwise().hnormalized(),
(Matrix<Scalar, Size+1, Dynamic>(t2 * pts1).colwise().hnormalized()) );
VERIFY_IS_APPROX( (t2 .lazyProduct( v0.homogeneous() )).hnormalized(), (t2 * v0.homogeneous()).hnormalized() );
VERIFY_IS_APPROX( (t2 .lazyProduct ( pts.colwise().homogeneous() )).colwise().hnormalized(), (t2 * pts1).colwise().hnormalized() );
VERIFY_IS_APPROX( (v0.transpose().homogeneous() .lazyProduct( t2 )).hnormalized(), (v0.transpose().homogeneous()*t2).hnormalized() );
VERIFY_IS_APPROX( (pts.transpose().rowwise().homogeneous() .lazyProduct( t2 )).rowwise().hnormalized(), (pts1.transpose()*t2).rowwise().hnormalized() );
VERIFY_IS_APPROX( (t2.template triangularView<Lower>() * v0.homogeneous()).eval(), (t2.template triangularView<Lower>()*hv0) );
}
EIGEN_DECLARE_TEST(geo_homogeneous)
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(( homogeneous<float,1>() ));
CALL_SUBTEST_2(( homogeneous<double,3>() ));
CALL_SUBTEST_3(( homogeneous<double,8>() ));
}
}
|
