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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/Tests/CommonHelpers/FloatComparisons.hpp"
12 #include "Acts/Utilities/UnitVectors.hpp"
13 
14 #include <limits>
15 
16 using Acts::Vector3D;
17 
18 namespace {
19 constexpr auto eps = std::numeric_limits<double>::epsilon();
20 }
21 
22 BOOST_AUTO_TEST_SUITE(UnitVectors)
23 
24 BOOST_AUTO_TEST_CASE(DirectionPhiEta) {
25  using Acts::makeDirectionUnitFromPhiEta;
26 
27  // along positive x
28  const auto xPos1 = makeDirectionUnitFromPhiEta(0.0, 0.0);
29  CHECK_CLOSE_REL(xPos1.norm(), 1, eps);
30  CHECK_CLOSE_REL(xPos1.dot(Vector3D(1, 0, 0)), 1, eps);
31  const auto xPos2 = makeDirectionUnitFromPhiEta(2 * M_PI, 0.0);
32  CHECK_CLOSE_REL(xPos2.norm(), 1, eps);
33  CHECK_CLOSE_REL(xPos2.dot(Vector3D(1, 0, 0)), 1, eps);
34  // along negative x
35  const auto xNeg1 = makeDirectionUnitFromPhiEta(M_PI, 0.0);
36  CHECK_CLOSE_REL(xNeg1.norm(), 1, eps);
37  CHECK_CLOSE_REL(xNeg1.dot(Vector3D(-1, 0, 0)), 1, eps);
38  const auto xNeg2 = makeDirectionUnitFromPhiEta(-M_PI, 0.0);
39  CHECK_CLOSE_REL(xNeg2.norm(), 1, eps);
40  CHECK_CLOSE_REL(xNeg2.dot(Vector3D(-1, 0, 0)), 1, eps);
41  // along positive y
42  const auto yPos1 = makeDirectionUnitFromPhiEta(M_PI_2, 0.0);
43  CHECK_CLOSE_REL(yPos1.norm(), 1, eps);
44  CHECK_CLOSE_REL(yPos1.dot(Vector3D(0, 1, 0)), 1, eps);
45  const auto yPos2 = makeDirectionUnitFromPhiEta(-3 * M_PI_2, 0.0);
46  CHECK_CLOSE_REL(yPos2.norm(), 1, eps);
47  CHECK_CLOSE_REL(yPos2.dot(Vector3D(0, 1, 0)), 1, eps);
48  // along negative y
49  const auto yNeg1 = makeDirectionUnitFromPhiEta(-M_PI_2, 0.0);
50  CHECK_CLOSE_REL(yNeg1.norm(), 1, eps);
51  CHECK_CLOSE_REL(yNeg1.dot(Vector3D(0, -1, 0)), 1, eps);
52  const auto yNeg2 = makeDirectionUnitFromPhiEta(3 * M_PI_2, 0.0);
53  CHECK_CLOSE_REL(yNeg2.norm(), 1, eps);
54  CHECK_CLOSE_REL(yNeg2.dot(Vector3D(0, -1, 0)), 1, eps);
55 
56  const auto inf = std::numeric_limits<double>::infinity();
57  // along positive z
58  const auto zPos1 = makeDirectionUnitFromPhiEta(0.0, inf);
59  CHECK_CLOSE_REL(zPos1.norm(), 1, eps);
60  CHECK_CLOSE_REL(zPos1.dot(Vector3D(0, 0, 1)), 1, eps);
61  const auto zPos2 = makeDirectionUnitFromPhiEta(M_PI_2, inf);
62  CHECK_CLOSE_REL(zPos2.norm(), 1, eps);
63  CHECK_CLOSE_REL(zPos2.dot(Vector3D(0, 0, 1)), 1, eps);
64  // along negative z
65  const auto zNeg1 = makeDirectionUnitFromPhiEta(0.0, -inf);
66  CHECK_CLOSE_REL(zNeg1.norm(), 1, eps);
67  CHECK_CLOSE_REL(zNeg1.dot(Vector3D(0, 0, -1)), 1, eps);
68  const auto zNeg2 = makeDirectionUnitFromPhiEta(M_PI_2, -inf);
69  CHECK_CLOSE_REL(zNeg2.norm(), 1, eps);
70  CHECK_CLOSE_REL(zNeg2.dot(Vector3D(0, 0, -1)), 1, eps);
71 
72  // mixed direction
73  const auto mixed1 = makeDirectionUnitFromPhiEta(M_PI_4, 1.0);
74  CHECK_CLOSE_REL(mixed1.norm(), 1, eps);
75  CHECK_CLOSE_REL(
76  mixed1.dot(Vector3D(1, 1, M_SQRT2 * std::sinh(1.0)).normalized()), 1,
77  eps);
78  const auto mixed2 = makeDirectionUnitFromPhiEta(M_PI_4, -1.0);
79  CHECK_CLOSE_REL(mixed2.norm(), 1, eps);
80  CHECK_CLOSE_REL(
81  mixed2.dot(Vector3D(1, 1, M_SQRT2 * std::sinh(-1.0)).normalized()), 1,
82  eps);
83  const auto mixed3 = makeDirectionUnitFromPhiEta(-M_PI_4, -1.0);
84  CHECK_CLOSE_REL(mixed3.norm(), 1, eps);
85  CHECK_CLOSE_REL(
86  mixed3.dot(Vector3D(1, -1, M_SQRT2 * std::sinh(-1.0)).normalized()), 1,
87  eps);
88 }
89 
90 BOOST_AUTO_TEST_CASE(DirectionPhiTheta) {
91  using Acts::makeDirectionUnitFromPhiTheta;
92 
93  // along positive x
94  const auto xPos1 = makeDirectionUnitFromPhiTheta(0.0, M_PI_2);
95  CHECK_CLOSE_REL(xPos1.norm(), 1, eps);
96  CHECK_CLOSE_REL(xPos1.dot(Vector3D(1, 0, 0)), 1, eps);
97  const auto xPos2 = makeDirectionUnitFromPhiTheta(2 * M_PI, M_PI_2);
98  CHECK_CLOSE_REL(xPos2.norm(), 1, eps);
99  CHECK_CLOSE_REL(xPos2.dot(Vector3D(1, 0, 0)), 1, eps);
100  // along negative x
101  const auto xNeg1 = makeDirectionUnitFromPhiTheta(M_PI, M_PI_2);
102  CHECK_CLOSE_REL(xNeg1.norm(), 1, eps);
103  CHECK_CLOSE_REL(xNeg1.dot(Vector3D(-1, 0, 0)), 1, eps);
104  const auto xNeg2 = makeDirectionUnitFromPhiTheta(-M_PI, M_PI_2);
105  CHECK_CLOSE_REL(xNeg2.norm(), 1, eps);
106  CHECK_CLOSE_REL(xNeg2.dot(Vector3D(-1, 0, 0)), 1, eps);
107  // along positive y
108  const auto yPos1 = makeDirectionUnitFromPhiTheta(M_PI_2, M_PI_2);
109  CHECK_CLOSE_REL(yPos1.norm(), 1, eps);
110  CHECK_CLOSE_REL(yPos1.dot(Vector3D(0, 1, 0)), 1, eps);
111  const auto yPos2 = makeDirectionUnitFromPhiTheta(-3 * M_PI_2, M_PI_2);
112  CHECK_CLOSE_REL(yPos2.norm(), 1, eps);
113  CHECK_CLOSE_REL(yPos2.dot(Vector3D(0, 1, 0)), 1, eps);
114  // along negative y
115  const auto yNeg1 = makeDirectionUnitFromPhiTheta(-M_PI_2, M_PI_2);
116  CHECK_CLOSE_REL(yNeg1.norm(), 1, eps);
117  CHECK_CLOSE_REL(yNeg1.dot(Vector3D(0, -1, 0)), 1, eps);
118  const auto yNeg2 = makeDirectionUnitFromPhiTheta(3 * M_PI_2, M_PI_2);
119  CHECK_CLOSE_REL(yNeg2.norm(), 1, eps);
120  CHECK_CLOSE_REL(yNeg2.dot(Vector3D(0, -1, 0)), 1, eps);
121 
122  // along positive z
123  const auto zPos1 = makeDirectionUnitFromPhiTheta(0.0, 0.0);
124  CHECK_CLOSE_REL(zPos1.norm(), 1, eps);
125  CHECK_CLOSE_REL(zPos1.dot(Vector3D(0, 0, 1)), 1, eps);
126  const auto zPos2 = makeDirectionUnitFromPhiTheta(M_PI_2, 0.0);
127  CHECK_CLOSE_REL(zPos2.norm(), 1, eps);
128  CHECK_CLOSE_REL(zPos2.dot(Vector3D(0, 0, 1)), 1, eps);
129  // along negative z
130  const auto zNeg1 = makeDirectionUnitFromPhiTheta(0.0, M_PI);
131  CHECK_CLOSE_REL(zNeg1.norm(), 1, eps);
132  CHECK_CLOSE_REL(zNeg1.dot(Vector3D(0, 0, -1)), 1, eps);
133  const auto zNeg2 = makeDirectionUnitFromPhiTheta(M_PI_2, M_PI);
134  CHECK_CLOSE_REL(zNeg2.norm(), 1, eps);
135  CHECK_CLOSE_REL(zNeg2.dot(Vector3D(0, 0, -1)), 1, eps);
136 
137  // mixed direction
138  const auto mixed1 = makeDirectionUnitFromPhiTheta(M_PI_4, M_PI_4);
139  CHECK_CLOSE_REL(mixed1.norm(), 1, eps);
140  CHECK_CLOSE_REL(mixed1.dot(Vector3D(1, 1, M_SQRT2).normalized()), 1, eps);
141  const auto mixed2 = makeDirectionUnitFromPhiTheta(M_PI_4, 3 * M_PI_4);
142  CHECK_CLOSE_REL(mixed2.norm(), 1, eps);
143  CHECK_CLOSE_REL(mixed2.dot(Vector3D(1, 1, -M_SQRT2).normalized()), 1, eps);
144  const auto mixed3 = makeDirectionUnitFromPhiTheta(-M_PI_4, 3 * M_PI_4);
145  CHECK_CLOSE_REL(mixed3.norm(), 1, eps);
146  CHECK_CLOSE_REL(mixed3.dot(Vector3D(1, -1, -M_SQRT2).normalized()), 1, eps);
147 }
148 
149 namespace {
150 template <typename Direction, typename RefUnitU, typename RefUnitV>
151 void testCurvilinear(const Eigen::MatrixBase<Direction>& direction,
152  const Eigen::MatrixBase<RefUnitU>& refU,
153  const Eigen::MatrixBase<RefUnitV>& refV) {
154  const auto u = Acts::makeCurvilinearUnitU(direction);
155  const auto uv = Acts::makeCurvilinearUnitVectors(direction);
156  // verify normalization
157  CHECK_CLOSE_ABS(u.norm(), 1, eps);
158  CHECK_CLOSE_ABS(uv.first.norm(), 1, eps);
159  CHECK_CLOSE_ABS(uv.second.norm(), 1, eps);
160  // verify orthonormality
161  CHECK_SMALL(u.dot(direction), eps);
162  CHECK_SMALL(uv.first.dot(direction), eps);
163  CHECK_SMALL(uv.second.dot(direction), eps);
164  CHECK_SMALL(uv.first.dot(uv.second), eps);
165  // verify u is in the x-y plane
166  CHECK_SMALL(u[2], eps);
167  CHECK_SMALL(uv.first[2], eps);
168  // verify references. do not use element-wise comparison to avoid issues with
169  // small, epsilon-like differences.
170  CHECK_CLOSE_ABS(u.dot(refU), 1, eps);
171  CHECK_CLOSE_ABS(uv.first.dot(refU), 1, eps);
172  CHECK_CLOSE_ABS(uv.second.dot(refV), 1, eps);
173 }
174 } // namespace
175 
176 BOOST_AUTO_TEST_CASE(CurvilinearTransverse) {
177  // curvilinear system w/ direction in the transverse plane
178  testCurvilinear(Vector3D(1, 1, 0), Vector3D(-1, 1, 0).normalized(),
179  Vector3D(0, 0, 1).normalized());
180 }
181 
182 BOOST_AUTO_TEST_CASE(CurvilinearPositiveZ) {
183  // curvilinear system w/ direction along z
184  testCurvilinear(Vector3D(0, 0, 1), Vector3D(1, 0, 0), Vector3D(0, 1, 0));
185 }
186 
187 BOOST_AUTO_TEST_CASE(CurvilinearNegativeZ) {
188  // curvilinear system w/ direction along z
189  testCurvilinear(Vector3D(0, 0, -1), Vector3D(1, 0, 0), Vector3D(0, -1, 0));
190 }
191 
192 BOOST_AUTO_TEST_CASE(CurvilinearCloseToZ) {
193  // curvilinear system w/ direction close to z
194  testCurvilinear(Vector3D(0, 32 * eps, 1 - 32 * eps), Vector3D(-1, 0, 0),
195  Vector3D(0, -1, 32 * eps));
196 }
197 
198 BOOST_AUTO_TEST_SUITE_END()