LSST Applications  21.0.0-172-gfb10e10a+18fedfabac,22.0.0+297cba6710,22.0.0+80564b0ff1,22.0.0+8d77f4f51a,22.0.0+a28f4c53b1,22.0.0+dcf3732eb2,22.0.1-1-g7d6de66+2a20fdde0d,22.0.1-1-g8e32f31+297cba6710,22.0.1-1-geca5380+7fa3b7d9b6,22.0.1-12-g44dc1dc+2a20fdde0d,22.0.1-15-g6a90155+515f58c32b,22.0.1-16-g9282f48+790f5f2caa,22.0.1-2-g92698f7+dcf3732eb2,22.0.1-2-ga9b0f51+7fa3b7d9b6,22.0.1-2-gd1925c9+bf4f0e694f,22.0.1-24-g1ad7a390+a9625a72a8,22.0.1-25-g5bf6245+3ad8ecd50b,22.0.1-25-gb120d7b+8b5510f75f,22.0.1-27-g97737f7+2a20fdde0d,22.0.1-32-gf62ce7b1+aa4237961e,22.0.1-4-g0b3f228+2a20fdde0d,22.0.1-4-g243d05b+871c1b8305,22.0.1-4-g3a563be+32dcf1063f,22.0.1-4-g44f2e3d+9e4ab0f4fa,22.0.1-42-gca6935d93+ba5e5ca3eb,22.0.1-5-g15c806e+85460ae5f3,22.0.1-5-g58711c4+611d128589,22.0.1-5-g75bb458+99c117b92f,22.0.1-6-g1c63a23+7fa3b7d9b6,22.0.1-6-g50866e6+84ff5a128b,22.0.1-6-g8d3140d+720564cf76,22.0.1-6-gd805d02+cc5644f571,22.0.1-8-ge5750ce+85460ae5f3,master-g6e05de7fdc+babf819c66,master-g99da0e417a+8d77f4f51a,w.2021.48
LSST Data Management Base Package
NormalizedAngle.cc
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1 /*
2  * LSST Data Management System
3  * Copyright 2014-2015 AURA/LSST.
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5  * This product includes software developed by the
6  * LSST Project (http://www.lsst.org/).
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22 
25 
27 
28 #include "lsst/sphgeom/LonLat.h"
29 #include "lsst/sphgeom/Vector3d.h"
30 
31 
32 namespace lsst {
33 namespace sphgeom {
34 
36  NormalizedAngle const & b)
37 {
39  double a1 = std::fabs(a.asRadians() - b.asRadians());
40  double a2 = 2.0 * PI - a1;
41  x._a = Angle(std::min(a1, a2));
42  return x;
43 }
44 
46  NormalizedAngle const & b)
47 {
49  double c = 0.5 * (a.asRadians() + b.asRadians());
50  if (a <= b) {
51  x._a = Angle(c);
52  } else {
53  // The result is (a + b + 2π) / 2, normalized to [0, 2π)
54  x._a = Angle((c < PI) ? (c + PI) : (c - PI));
55  }
56  return x;
57 }
58 
60  double x = sin((p1.getLon() - p2.getLon()) * 0.5);
61  x *= x;
62  double y = sin((p1.getLat() - p2.getLat()) * 0.5);
63  y *= y;
64  double z = cos((p1.getLat() + p2.getLat()) * 0.5);
65  z *= z;
66  // Compute the square of the sine of half of the desired angle. This is
67  // easily shown to be be one fourth of the squared Euclidian distance
68  // (chord length) between p1 and p2.
69  double sha2 = (x * (z - y) + y);
70  // Avoid domain errors in asin and sqrt due to rounding errors.
71  if (sha2 < 0.0) {
72  _a = Angle(0.0);
73  } else if (sha2 >= 1.0) {
74  _a = Angle(PI);
75  } else {
76  _a = Angle(2.0 * std::asin(std::sqrt(sha2)));
77  }
78 }
79 
81  double s = v1.cross(v2).getNorm();
82  double c = v1.dot(v2);
83  if (s == 0.0 && c == 0.0) {
84  // Avoid the atan2(±0, -0) = ±PI special case.
85  _a = Angle(0.0);
86  } else {
87  _a = Angle(std::atan2(s, c));
88  }
89 }
90 
91 }} // namespace lsst::sphgeom
double x
This file contains a class representing spherical coordinates.
double z
Definition: Match.cc:44
This file declares a class for representing normalized angles.
int y
Definition: SpanSet.cc:48
table::Key< int > b
table::Key< int > a
This file declares a class for representing vectors in ℝ³.
T asin(T... args)
T atan2(T... args)
LonLat represents a spherical coordinate (longitude/latitude angle) pair.
Definition: LonLat.h:48
Angle getLat() const
Definition: LonLat.h:90
NormalizedAngle getLon() const
Definition: LonLat.h:88
NormalizedAngle is an angle that lies in the range [0, 2π), with one exception - a NormalizedAngle ca...
NormalizedAngle()=default
This constructor creates a NormalizedAngle with a value of zero.
static NormalizedAngle between(NormalizedAngle const &a, NormalizedAngle const &b)
For two angles a and b, between(a, b) returns the smaller of a.getAngleTo(b) and b....
static NormalizedAngle center(NormalizedAngle const &a, NormalizedAngle const &b)
For two normalized angles a and b, center(a, b) returns the angle m such that a.getAngleTo(m) is equa...
Vector3d is a vector in ℝ³ with components stored in double precision.
Definition: Vector3d.h:44
double dot(Vector3d const &v) const
dot returns the inner product of this vector and v.
Definition: Vector3d.h:73
double getNorm() const
getNorm returns the L2 norm of this vector.
Definition: Vector3d.h:81
Vector3d cross(Vector3d const &v) const
cross returns the cross product of this vector and v.
Definition: Vector3d.h:101
T fabs(T... args)
T min(T... args)
lsst::geom::Angle Angle
Definition: misc.h:33
double sin(Angle const &a)
Definition: Angle.h:102
double cos(Angle const &a)
Definition: Angle.h:103
constexpr double PI
Definition: constants.h:36
A base class for image defects.
T sqrt(T... args)