1*bf2c3715SXin Li // This file is part of Eigen, a lightweight C++ template library
2*bf2c3715SXin Li // for linear algebra.
3*bf2c3715SXin Li //
4*bf2c3715SXin Li // Copyright (C) 2008 Gael Guennebaud <[email protected]>
5*bf2c3715SXin Li // Copyright (C) 2008 Benoit Jacob <[email protected]>
6*bf2c3715SXin Li //
7*bf2c3715SXin Li // This Source Code Form is subject to the terms of the Mozilla
8*bf2c3715SXin Li // Public License v. 2.0. If a copy of the MPL was not distributed
9*bf2c3715SXin Li // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10*bf2c3715SXin Li
11*bf2c3715SXin Li #include "main.h"
12*bf2c3715SXin Li #include <Eigen/Geometry>
13*bf2c3715SXin Li #include <Eigen/LU>
14*bf2c3715SXin Li #include <Eigen/QR>
15*bf2c3715SXin Li
hyperplane(const HyperplaneType & _plane)16*bf2c3715SXin Li template<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane)
17*bf2c3715SXin Li {
18*bf2c3715SXin Li /* this test covers the following files:
19*bf2c3715SXin Li Hyperplane.h
20*bf2c3715SXin Li */
21*bf2c3715SXin Li using std::abs;
22*bf2c3715SXin Li const Index dim = _plane.dim();
23*bf2c3715SXin Li enum { Options = HyperplaneType::Options };
24*bf2c3715SXin Li typedef typename HyperplaneType::Scalar Scalar;
25*bf2c3715SXin Li typedef typename HyperplaneType::RealScalar RealScalar;
26*bf2c3715SXin Li typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
27*bf2c3715SXin Li typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,
28*bf2c3715SXin Li HyperplaneType::AmbientDimAtCompileTime> MatrixType;
29*bf2c3715SXin Li
30*bf2c3715SXin Li VectorType p0 = VectorType::Random(dim);
31*bf2c3715SXin Li VectorType p1 = VectorType::Random(dim);
32*bf2c3715SXin Li
33*bf2c3715SXin Li VectorType n0 = VectorType::Random(dim).normalized();
34*bf2c3715SXin Li VectorType n1 = VectorType::Random(dim).normalized();
35*bf2c3715SXin Li
36*bf2c3715SXin Li HyperplaneType pl0(n0, p0);
37*bf2c3715SXin Li HyperplaneType pl1(n1, p1);
38*bf2c3715SXin Li HyperplaneType pl2 = pl1;
39*bf2c3715SXin Li
40*bf2c3715SXin Li Scalar s0 = internal::random<Scalar>();
41*bf2c3715SXin Li Scalar s1 = internal::random<Scalar>();
42*bf2c3715SXin Li
43*bf2c3715SXin Li VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
44*bf2c3715SXin Li
45*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) );
46*bf2c3715SXin Li if(numext::abs2(s0)>RealScalar(1e-6))
47*bf2c3715SXin Li VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0);
48*bf2c3715SXin Li else
49*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1) );
50*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) );
51*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) );
52*bf2c3715SXin Li
53*bf2c3715SXin Li // transform
54*bf2c3715SXin Li if (!NumTraits<Scalar>::IsComplex)
55*bf2c3715SXin Li {
56*bf2c3715SXin Li MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ();
57*bf2c3715SXin Li DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
58*bf2c3715SXin Li Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
59*bf2c3715SXin Li
60*bf2c3715SXin Li while(scaling.diagonal().cwiseAbs().minCoeff()<RealScalar(1e-4)) scaling.diagonal() = VectorType::Random();
61*bf2c3715SXin Li
62*bf2c3715SXin Li pl2 = pl1;
63*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) );
64*bf2c3715SXin Li pl2 = pl1;
65*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );
66*bf2c3715SXin Li pl2 = pl1;
67*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );
68*bf2c3715SXin Li VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
69*bf2c3715SXin Li pl2 = pl1;
70*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation)
71*bf2c3715SXin Li .absDistance((rot*scaling*translation) * p1), Scalar(1) );
72*bf2c3715SXin Li VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
73*bf2c3715SXin Li pl2 = pl1;
74*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry)
75*bf2c3715SXin Li .absDistance((rot*translation) * p1), Scalar(1) );
76*bf2c3715SXin Li VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
77*bf2c3715SXin Li }
78*bf2c3715SXin Li
79*bf2c3715SXin Li // casting
80*bf2c3715SXin Li const int Dim = HyperplaneType::AmbientDimAtCompileTime;
81*bf2c3715SXin Li typedef typename GetDifferentType<Scalar>::type OtherScalar;
82*bf2c3715SXin Li Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>();
83*bf2c3715SXin Li VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);
84*bf2c3715SXin Li Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>();
85*bf2c3715SXin Li VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);
86*bf2c3715SXin Li }
87*bf2c3715SXin Li
lines()88*bf2c3715SXin Li template<typename Scalar> void lines()
89*bf2c3715SXin Li {
90*bf2c3715SXin Li using std::abs;
91*bf2c3715SXin Li typedef Hyperplane<Scalar, 2> HLine;
92*bf2c3715SXin Li typedef ParametrizedLine<Scalar, 2> PLine;
93*bf2c3715SXin Li typedef Matrix<Scalar,2,1> Vector;
94*bf2c3715SXin Li typedef Matrix<Scalar,3,1> CoeffsType;
95*bf2c3715SXin Li
96*bf2c3715SXin Li for(int i = 0; i < 10; i++)
97*bf2c3715SXin Li {
98*bf2c3715SXin Li Vector center = Vector::Random();
99*bf2c3715SXin Li Vector u = Vector::Random();
100*bf2c3715SXin Li Vector v = Vector::Random();
101*bf2c3715SXin Li Scalar a = internal::random<Scalar>();
102*bf2c3715SXin Li while (abs(a-1) < Scalar(1e-4)) a = internal::random<Scalar>();
103*bf2c3715SXin Li while (u.norm() < Scalar(1e-4)) u = Vector::Random();
104*bf2c3715SXin Li while (v.norm() < Scalar(1e-4)) v = Vector::Random();
105*bf2c3715SXin Li
106*bf2c3715SXin Li HLine line_u = HLine::Through(center + u, center + a*u);
107*bf2c3715SXin Li HLine line_v = HLine::Through(center + v, center + a*v);
108*bf2c3715SXin Li
109*bf2c3715SXin Li // the line equations should be normalized so that a^2+b^2=1
110*bf2c3715SXin Li VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
111*bf2c3715SXin Li VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
112*bf2c3715SXin Li
113*bf2c3715SXin Li Vector result = line_u.intersection(line_v);
114*bf2c3715SXin Li
115*bf2c3715SXin Li // the lines should intersect at the point we called "center"
116*bf2c3715SXin Li if(abs(a-1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized()))<Scalar(0.9))
117*bf2c3715SXin Li VERIFY_IS_APPROX(result, center);
118*bf2c3715SXin Li
119*bf2c3715SXin Li // check conversions between two types of lines
120*bf2c3715SXin Li PLine pl(line_u); // gcc 3.3 will crash if we don't name this variable.
121*bf2c3715SXin Li HLine line_u2(pl);
122*bf2c3715SXin Li CoeffsType converted_coeffs = line_u2.coeffs();
123*bf2c3715SXin Li if(line_u2.normal().dot(line_u.normal())<Scalar(0))
124*bf2c3715SXin Li converted_coeffs = -line_u2.coeffs();
125*bf2c3715SXin Li VERIFY(line_u.coeffs().isApprox(converted_coeffs));
126*bf2c3715SXin Li }
127*bf2c3715SXin Li }
128*bf2c3715SXin Li
planes()129*bf2c3715SXin Li template<typename Scalar> void planes()
130*bf2c3715SXin Li {
131*bf2c3715SXin Li using std::abs;
132*bf2c3715SXin Li typedef Hyperplane<Scalar, 3> Plane;
133*bf2c3715SXin Li typedef Matrix<Scalar,3,1> Vector;
134*bf2c3715SXin Li
135*bf2c3715SXin Li for(int i = 0; i < 10; i++)
136*bf2c3715SXin Li {
137*bf2c3715SXin Li Vector v0 = Vector::Random();
138*bf2c3715SXin Li Vector v1(v0), v2(v0);
139*bf2c3715SXin Li if(internal::random<double>(0,1)>0.25)
140*bf2c3715SXin Li v1 += Vector::Random();
141*bf2c3715SXin Li if(internal::random<double>(0,1)>0.25)
142*bf2c3715SXin Li v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
143*bf2c3715SXin Li if(internal::random<double>(0,1)>0.25)
144*bf2c3715SXin Li v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
145*bf2c3715SXin Li
146*bf2c3715SXin Li Plane p0 = Plane::Through(v0, v1, v2);
147*bf2c3715SXin Li
148*bf2c3715SXin Li VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1));
149*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1));
150*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1));
151*bf2c3715SXin Li VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1));
152*bf2c3715SXin Li }
153*bf2c3715SXin Li }
154*bf2c3715SXin Li
hyperplane_alignment()155*bf2c3715SXin Li template<typename Scalar> void hyperplane_alignment()
156*bf2c3715SXin Li {
157*bf2c3715SXin Li typedef Hyperplane<Scalar,3,AutoAlign> Plane3a;
158*bf2c3715SXin Li typedef Hyperplane<Scalar,3,DontAlign> Plane3u;
159*bf2c3715SXin Li
160*bf2c3715SXin Li EIGEN_ALIGN_MAX Scalar array1[4];
161*bf2c3715SXin Li EIGEN_ALIGN_MAX Scalar array2[4];
162*bf2c3715SXin Li EIGEN_ALIGN_MAX Scalar array3[4+1];
163*bf2c3715SXin Li Scalar* array3u = array3+1;
164*bf2c3715SXin Li
165*bf2c3715SXin Li Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a;
166*bf2c3715SXin Li Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u;
167*bf2c3715SXin Li Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u;
168*bf2c3715SXin Li
169*bf2c3715SXin Li p1->coeffs().setRandom();
170*bf2c3715SXin Li *p2 = *p1;
171*bf2c3715SXin Li *p3 = *p1;
172*bf2c3715SXin Li
173*bf2c3715SXin Li VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs());
174*bf2c3715SXin Li VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs());
175*bf2c3715SXin Li }
176*bf2c3715SXin Li
177*bf2c3715SXin Li
EIGEN_DECLARE_TEST(geo_hyperplane)178*bf2c3715SXin Li EIGEN_DECLARE_TEST(geo_hyperplane)
179*bf2c3715SXin Li {
180*bf2c3715SXin Li for(int i = 0; i < g_repeat; i++) {
181*bf2c3715SXin Li CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) );
182*bf2c3715SXin Li CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) );
183*bf2c3715SXin Li CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) );
184*bf2c3715SXin Li CALL_SUBTEST_2( hyperplane_alignment<float>() );
185*bf2c3715SXin Li CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) );
186*bf2c3715SXin Li CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) );
187*bf2c3715SXin Li CALL_SUBTEST_1( lines<float>() );
188*bf2c3715SXin Li CALL_SUBTEST_3( lines<double>() );
189*bf2c3715SXin Li CALL_SUBTEST_2( planes<float>() );
190*bf2c3715SXin Li CALL_SUBTEST_5( planes<double>() );
191*bf2c3715SXin Li }
192*bf2c3715SXin Li }
193