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UnitVectorsTests.cpp
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1 // This file is part of the Acts project.
2 //
3 // Copyright (C) 2020 CERN for the benefit of the Acts project
4 //
5 // This Source Code Form is subject to the terms of the Mozilla Public
6 // License, v. 2.0. If a copy of the MPL was not distributed with this
7 // file, You can obtain one at http://mozilla.org/MPL/2.0/.
8 
9 #include <boost/test/unit_test.hpp>
10 
11 #include "Acts/Definitions/Algebra.hpp"
12 #include "Acts/Tests/CommonHelpers/FloatComparisons.hpp"
13 #include "Acts/Utilities/UnitVectors.hpp"
14 
15 #include <algorithm>
16 #include <cmath>
17 #include <limits>
18 
19 using Acts::Vector3;
20 
21 namespace {
22 constexpr auto eps = std::numeric_limits<double>::epsilon();
23 }
24 
25 BOOST_AUTO_TEST_SUITE(UnitVectors)
26 
27 BOOST_AUTO_TEST_CASE(DirectionPhiEta) {
28  using Acts::makeDirectionFromPhiEta;
29 
30  // along positive x
31  const auto xPos1 = makeDirectionFromPhiEta(0.0, 0.0);
32  CHECK_CLOSE_REL(xPos1.norm(), 1, eps);
33  CHECK_CLOSE_REL(xPos1.dot(Vector3(1, 0, 0)), 1, eps);
34  const auto xPos2 = makeDirectionFromPhiEta(2 * M_PI, 0.0);
35  CHECK_CLOSE_REL(xPos2.norm(), 1, eps);
36  CHECK_CLOSE_REL(xPos2.dot(Vector3(1, 0, 0)), 1, eps);
37  // along negative x
38  const auto xNeg1 = makeDirectionFromPhiEta(M_PI, 0.0);
39  CHECK_CLOSE_REL(xNeg1.norm(), 1, eps);
40  CHECK_CLOSE_REL(xNeg1.dot(Vector3(-1, 0, 0)), 1, eps);
41  const auto xNeg2 = makeDirectionFromPhiEta(-M_PI, 0.0);
42  CHECK_CLOSE_REL(xNeg2.norm(), 1, eps);
43  CHECK_CLOSE_REL(xNeg2.dot(Vector3(-1, 0, 0)), 1, eps);
44  // along positive y
45  const auto yPos1 = makeDirectionFromPhiEta(M_PI_2, 0.0);
46  CHECK_CLOSE_REL(yPos1.norm(), 1, eps);
47  CHECK_CLOSE_REL(yPos1.dot(Vector3(0, 1, 0)), 1, eps);
48  const auto yPos2 = makeDirectionFromPhiEta(-3 * M_PI_2, 0.0);
49  CHECK_CLOSE_REL(yPos2.norm(), 1, eps);
50  CHECK_CLOSE_REL(yPos2.dot(Vector3(0, 1, 0)), 1, eps);
51  // along negative y
52  const auto yNeg1 = makeDirectionFromPhiEta(-M_PI_2, 0.0);
53  CHECK_CLOSE_REL(yNeg1.norm(), 1, eps);
54  CHECK_CLOSE_REL(yNeg1.dot(Vector3(0, -1, 0)), 1, eps);
55  const auto yNeg2 = makeDirectionFromPhiEta(3 * M_PI_2, 0.0);
56  CHECK_CLOSE_REL(yNeg2.norm(), 1, eps);
57  CHECK_CLOSE_REL(yNeg2.dot(Vector3(0, -1, 0)), 1, eps);
58 
59  const auto inf = std::numeric_limits<double>::infinity();
60  // along positive z
61  const auto zPos1 = makeDirectionFromPhiEta(0.0, inf);
62  CHECK_CLOSE_REL(zPos1.norm(), 1, eps);
63  CHECK_CLOSE_REL(zPos1.dot(Vector3(0, 0, 1)), 1, eps);
64  const auto zPos2 = makeDirectionFromPhiEta(M_PI_2, inf);
65  CHECK_CLOSE_REL(zPos2.norm(), 1, eps);
66  CHECK_CLOSE_REL(zPos2.dot(Vector3(0, 0, 1)), 1, eps);
67  // along negative z
68  const auto zNeg1 = makeDirectionFromPhiEta(0.0, -inf);
69  CHECK_CLOSE_REL(zNeg1.norm(), 1, eps);
70  CHECK_CLOSE_REL(zNeg1.dot(Vector3(0, 0, -1)), 1, eps);
71  const auto zNeg2 = makeDirectionFromPhiEta(M_PI_2, -inf);
72  CHECK_CLOSE_REL(zNeg2.norm(), 1, eps);
73  CHECK_CLOSE_REL(zNeg2.dot(Vector3(0, 0, -1)), 1, eps);
74 
75  // mixed direction
76  const auto mixed1 = makeDirectionFromPhiEta(M_PI_4, 1.0);
77  CHECK_CLOSE_REL(mixed1.norm(), 1, eps);
78  CHECK_CLOSE_REL(
79  mixed1.dot(Vector3(1, 1, M_SQRT2 * std::sinh(1.0)).normalized()), 1, eps);
80  const auto mixed2 = makeDirectionFromPhiEta(M_PI_4, -1.0);
81  CHECK_CLOSE_REL(mixed2.norm(), 1, eps);
82  CHECK_CLOSE_REL(
83  mixed2.dot(Vector3(1, 1, M_SQRT2 * std::sinh(-1.0)).normalized()), 1,
84  eps);
85  const auto mixed3 = makeDirectionFromPhiEta(-M_PI_4, -1.0);
86  CHECK_CLOSE_REL(mixed3.norm(), 1, eps);
87  CHECK_CLOSE_REL(
88  mixed3.dot(Vector3(1, -1, M_SQRT2 * std::sinh(-1.0)).normalized()), 1,
89  eps);
90 }
91 
92 BOOST_AUTO_TEST_CASE(DirectionPhiTheta) {
93  using Acts::makeDirectionFromPhiTheta;
94 
95  // along positive x
96  const auto xPos1 = makeDirectionFromPhiTheta(0.0, M_PI_2);
97  CHECK_CLOSE_REL(xPos1.norm(), 1, eps);
98  CHECK_CLOSE_REL(xPos1.dot(Vector3(1, 0, 0)), 1, eps);
99  const auto xPos2 = makeDirectionFromPhiTheta(2 * M_PI, M_PI_2);
100  CHECK_CLOSE_REL(xPos2.norm(), 1, eps);
101  CHECK_CLOSE_REL(xPos2.dot(Vector3(1, 0, 0)), 1, eps);
102  // along negative x
103  const auto xNeg1 = makeDirectionFromPhiTheta(M_PI, M_PI_2);
104  CHECK_CLOSE_REL(xNeg1.norm(), 1, eps);
105  CHECK_CLOSE_REL(xNeg1.dot(Vector3(-1, 0, 0)), 1, eps);
106  const auto xNeg2 = makeDirectionFromPhiTheta(-M_PI, M_PI_2);
107  CHECK_CLOSE_REL(xNeg2.norm(), 1, eps);
108  CHECK_CLOSE_REL(xNeg2.dot(Vector3(-1, 0, 0)), 1, eps);
109  // along positive y
110  const auto yPos1 = makeDirectionFromPhiTheta(M_PI_2, M_PI_2);
111  CHECK_CLOSE_REL(yPos1.norm(), 1, eps);
112  CHECK_CLOSE_REL(yPos1.dot(Vector3(0, 1, 0)), 1, eps);
113  const auto yPos2 = makeDirectionFromPhiTheta(-3 * M_PI_2, M_PI_2);
114  CHECK_CLOSE_REL(yPos2.norm(), 1, eps);
115  CHECK_CLOSE_REL(yPos2.dot(Vector3(0, 1, 0)), 1, eps);
116  // along negative y
117  const auto yNeg1 = makeDirectionFromPhiTheta(-M_PI_2, M_PI_2);
118  CHECK_CLOSE_REL(yNeg1.norm(), 1, eps);
119  CHECK_CLOSE_REL(yNeg1.dot(Vector3(0, -1, 0)), 1, eps);
120  const auto yNeg2 = makeDirectionFromPhiTheta(3 * M_PI_2, M_PI_2);
121  CHECK_CLOSE_REL(yNeg2.norm(), 1, eps);
122  CHECK_CLOSE_REL(yNeg2.dot(Vector3(0, -1, 0)), 1, eps);
123 
124  // along positive z
125  const auto zPos1 = makeDirectionFromPhiTheta(0.0, 0.0);
126  CHECK_CLOSE_REL(zPos1.norm(), 1, eps);
127  CHECK_CLOSE_REL(zPos1.dot(Vector3(0, 0, 1)), 1, eps);
128  const auto zPos2 = makeDirectionFromPhiTheta(M_PI_2, 0.0);
129  CHECK_CLOSE_REL(zPos2.norm(), 1, eps);
130  CHECK_CLOSE_REL(zPos2.dot(Vector3(0, 0, 1)), 1, eps);
131  // along negative z
132  const auto zNeg1 = makeDirectionFromPhiTheta(0.0, M_PI);
133  CHECK_CLOSE_REL(zNeg1.norm(), 1, eps);
134  CHECK_CLOSE_REL(zNeg1.dot(Vector3(0, 0, -1)), 1, eps);
135  const auto zNeg2 = makeDirectionFromPhiTheta(M_PI_2, M_PI);
136  CHECK_CLOSE_REL(zNeg2.norm(), 1, eps);
137  CHECK_CLOSE_REL(zNeg2.dot(Vector3(0, 0, -1)), 1, eps);
138 
139  // mixed direction
140  const auto mixed1 = makeDirectionFromPhiTheta(M_PI_4, M_PI_4);
141  CHECK_CLOSE_REL(mixed1.norm(), 1, eps);
142  CHECK_CLOSE_REL(mixed1.dot(Vector3(1, 1, M_SQRT2).normalized()), 1, eps);
143  const auto mixed2 = makeDirectionFromPhiTheta(M_PI_4, 3 * M_PI_4);
144  CHECK_CLOSE_REL(mixed2.norm(), 1, eps);
145  CHECK_CLOSE_REL(mixed2.dot(Vector3(1, 1, -M_SQRT2).normalized()), 1, eps);
146  const auto mixed3 = makeDirectionFromPhiTheta(-M_PI_4, 3 * M_PI_4);
147  CHECK_CLOSE_REL(mixed3.norm(), 1, eps);
148  CHECK_CLOSE_REL(mixed3.dot(Vector3(1, -1, -M_SQRT2).normalized()), 1, eps);
149 }
150 
151 namespace {
152 template <typename Direction, typename RefUnitU, typename RefUnitV>
153 void testCurvilinear(const Eigen::MatrixBase<Direction>& direction,
154  const Eigen::MatrixBase<RefUnitU>& refU,
155  const Eigen::MatrixBase<RefUnitV>& refV) {
156  const auto u = Acts::makeCurvilinearUnitU(direction);
157  const auto uv = Acts::makeCurvilinearUnitVectors(direction);
158  // verify normalization
159  CHECK_CLOSE_ABS(u.norm(), 1, eps);
160  CHECK_CLOSE_ABS(uv.first.norm(), 1, eps);
161  CHECK_CLOSE_ABS(uv.second.norm(), 1, eps);
162  // verify orthonormality
163  CHECK_SMALL(u.dot(direction), eps);
164  CHECK_SMALL(uv.first.dot(direction), eps);
165  CHECK_SMALL(uv.second.dot(direction), eps);
166  CHECK_SMALL(uv.first.dot(uv.second), eps);
167  // verify u is in the x-y plane
168  CHECK_SMALL(u[2], eps);
169  CHECK_SMALL(uv.first[2], eps);
170  // verify references. do not use element-wise comparison to avoid issues with
171  // small, epsilon-like differences.
172  CHECK_CLOSE_ABS(u.dot(refU), 1, eps);
173  CHECK_CLOSE_ABS(uv.first.dot(refU), 1, eps);
174  CHECK_CLOSE_ABS(uv.second.dot(refV), 1, eps);
175 }
176 } // namespace
177 
178 BOOST_AUTO_TEST_CASE(CurvilinearTransverse) {
179  // curvilinear system w/ direction in the transverse plane
180  testCurvilinear(Vector3(1, 1, 0), Vector3(-1, 1, 0).normalized(),
181  Vector3(0, 0, 1).normalized());
182 }
183 
184 BOOST_AUTO_TEST_CASE(CurvilinearPositiveZ) {
185  // curvilinear system w/ direction along z
186  testCurvilinear(Vector3(0, 0, 1), Vector3(1, 0, 0), Vector3(0, 1, 0));
187 }
188 
189 BOOST_AUTO_TEST_CASE(CurvilinearNegativeZ) {
190  // curvilinear system w/ direction along z
191  testCurvilinear(Vector3(0, 0, -1), Vector3(1, 0, 0), Vector3(0, -1, 0));
192 }
193 
194 BOOST_AUTO_TEST_CASE(CurvilinearCloseToZ) {
195  // curvilinear system w/ direction close to z
196  testCurvilinear(Vector3(0, 32 * eps, 1 - 32 * eps), Vector3(-1, 0, 0),
197  Vector3(0, -1, 32 * eps));
198 }
199 
200 BOOST_AUTO_TEST_SUITE_END()