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
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
|
// Copyright 2008, Google Inc. All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// 1. Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// 2. Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// 3. Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR IMPLIED
// WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
// EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
// OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
// WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
// OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
// ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
// This file contains the unit tests for the mathematical functions.
#include "kml/base/math_util.h"
#include "boost/scoped_ptr.hpp"
#include "gtest/gtest.h"
namespace kmlbase {
TEST(BaseMathTest, TestAzimuthBetweenPoints) {
// Sanity checks.
ASSERT_DOUBLE_EQ(0.0, AzimuthBetweenPoints(0,0,1,0));
ASSERT_DOUBLE_EQ(90.0, AzimuthBetweenPoints(0,0,0,1));
ASSERT_DOUBLE_EQ(180.0, AzimuthBetweenPoints(0,0,-1,0));
ASSERT_DOUBLE_EQ(-90.0, AzimuthBetweenPoints(0,0,0,-1));
ASSERT_NEAR(-180.0, AzimuthBetweenPoints(0,0,-1,-0.0000001), 0.0001);
// The example from the Aviation Formulary.
const double kLAX_lat = 33.944066;
const double kLAX_lng = -118.408294;
const double kJFK_lat = 40.642480;
const double kJFK_lng = -73.788071;
// The known azimuth from LAX to JFK.
const double kAzimuth = 65.8687;
double az1 = AzimuthBetweenPoints(kLAX_lat, kLAX_lng, kJFK_lat, kJFK_lng);
ASSERT_NEAR(kAzimuth, az1, 0.0001);
// The return flight.
const double kAzimuthReturn = -86.1617;
double az2 = AzimuthBetweenPoints(kJFK_lat, kJFK_lng, kLAX_lat, kLAX_lng);
ASSERT_NEAR(kAzimuthReturn, az2, 0.0001);
}
TEST(BaseMathTest, TestDistanceBetweenPoints) {
const double kLAX_lat = 33.944066;
const double kLAX_lng = -118.408294;
const double kJFK_lat = 40.642480;
const double kJFK_lng = -73.788071;
// The known great circle distance in meters between LAX and JFK.
const double kDistance = 3970683.0;
double d = DistanceBetweenPoints(kLAX_lat, kLAX_lng, kJFK_lat, kJFK_lng);
ASSERT_NEAR(kDistance, d, 0.1);
}
TEST(BaseMathTest, TestDistanceBetweenPoints3d) {
ASSERT_DOUBLE_EQ(0.0, DistanceBetweenPoints3d(0,0,0,0,0,0));
ASSERT_DOUBLE_EQ(1.0, DistanceBetweenPoints3d(0,0,0,0,0,1));
ASSERT_DOUBLE_EQ(1000.0, DistanceBetweenPoints3d(0,0,0,0,0,1000));
// Assert the 2d example works here.
double expected = 3970683.0;
ASSERT_NEAR(expected,
DistanceBetweenPoints3d(33.944066, -118.408294, 0,
40.642480, -73.788071, 0), 0.1);
// Put JFK 10,000 km in the sky:
expected = 4094670.171;
ASSERT_NEAR(expected,
DistanceBetweenPoints3d(33.944066, -118.408294, 0,
40.642480, -73.788071, 1000000.0), 0.1);
}
TEST(BaseMathTest, TestElevationBetweenPoints) {
double lat_from = 0;
double lng_from = 0;
double alt_from = 0;
double lat_to = 0.0000000000001;
double lng_to = 0.0000000000001;
// This is basically a flat line.
double alt_to = 0.0;
ASSERT_NEAR(
0.0, ElevationBetweenPoints(lat_from, lng_from, alt_from,
lat_to, lng_to, alt_to),
0.001);
// Near-vertical.
alt_to = 10000;
ASSERT_NEAR(
90.0, ElevationBetweenPoints(lat_from, lng_from, alt_from,
lat_to, lng_to, alt_to),
0.001);
lat_to = 0.145;
alt_to = 609.6;
ASSERT_NEAR(
2.1667, ElevationBetweenPoints(lat_from, lng_from, alt_from,
lat_to, lng_to, alt_to),
0.001);
lat_from = 37.0;
lng_from = -121.98;
alt_from = 600;
lat_to = 37.0;
lng_to = -122.0;
alt_to = 200;
ASSERT_NEAR(
-12.7004, ElevationBetweenPoints(lat_from, lng_from, alt_from,
lat_to, lng_to, alt_to),
0.001);
}
TEST(BaseMathTest, TestLatLngOnRadialFromPoint) {
// See http://williams.best.vwh.net/avform.htm#Example
// Coordinates of LAX.
const double kLAX_lat = 33.944066;
const double kLAX_lng = -118.408294;
// A distance and radial.
const double kDistance = 185200.0;
const double kRadial = 66.0;
// The known-accurate coordinates of the point along that radial from LAX.
const double kRadial_lat = 34.608154;
const double kRadial_lng = -116.558327;
Vec3 v = LatLngOnRadialFromPoint(kLAX_lat, kLAX_lng, kDistance, kRadial);
ASSERT_NEAR(kRadial_lat, v.get_latitude(), 0.000001);
ASSERT_NEAR(kRadial_lng, v.get_longitude(), 0.000001);
}
// Tests the GroundDistanceFromRangeAndElevation() function.
TEST(BaseMathTest, TestGroundDistanceFromRangeAndElevation) {
ASSERT_NEAR(100.0, GroundDistanceFromRangeAndElevation(100.0, 0.0),
0.000001);
ASSERT_NEAR(99.939083, GroundDistanceFromRangeAndElevation(100.0, 2.0),
0.000001);
ASSERT_NEAR(17.364818, GroundDistanceFromRangeAndElevation(100.0, 80.0),
0.000001);
ASSERT_NEAR(0.0, GroundDistanceFromRangeAndElevation(100.0, 90.0),
0.000001);
ASSERT_NEAR(17.364818, GroundDistanceFromRangeAndElevation(100.0, 100.0),
0.000001);
}
// Tests the HeightFromRangeAndElevation() function.
TEST(BaseMathTest, TestHeightFromRangeAndElevation) {
ASSERT_NEAR(0.0, HeightFromRangeAndElevation(100.0, 0.0),
0.000001);
ASSERT_NEAR(3.489950, HeightFromRangeAndElevation(100.0, 2.0),
0.000001);
ASSERT_NEAR(98.480775, HeightFromRangeAndElevation(100.0, 80.0),
0.000001);
ASSERT_NEAR(100.0, HeightFromRangeAndElevation(100.0, 90.0),
0.000001);
ASSERT_NEAR(98.480775, HeightFromRangeAndElevation(100.0, 100.0),
0.000001);
}
// Tese test the conversion functions.
TEST(BaseMathTest, TestDegToRad) {
ASSERT_DOUBLE_EQ(0.0, DegToRad(0.0));
ASSERT_DOUBLE_EQ(M_PI, DegToRad(180.0));
ASSERT_DOUBLE_EQ(M_PI / 2, DegToRad(90.0));
ASSERT_DOUBLE_EQ(M_PI / -2, DegToRad(-90.0));
}
TEST(BaseMathTest, TestRadToDeg) {
ASSERT_DOUBLE_EQ(0.0, RadToDeg(0));
ASSERT_DOUBLE_EQ(360.0, RadToDeg(2 * M_PI));
ASSERT_DOUBLE_EQ(90.0, RadToDeg(M_PI / 2));
ASSERT_DOUBLE_EQ(-90.0, RadToDeg(M_PI / -2));
}
TEST(BaseMathTest, TestMetersToRadians) {
ASSERT_DOUBLE_EQ(0, MetersToRadians(0));
ASSERT_DOUBLE_EQ(1, MetersToRadians(6366710));
}
TEST(BaseMathTest, TestRadiansToMeters) {
ASSERT_DOUBLE_EQ(0, RadiansToMeters(0));
ASSERT_DOUBLE_EQ(6366710, RadiansToMeters(1));
}
} // end namespace kmlbase
|
