Kstars

greatcircle.cpp
1 /*
2  SPDX-FileCopyrightText: 2021 Hy Murveit <[email protected]>
3 
4  SPDX-License-Identifier: GPL-2.0-or-later
5 */
6 
7 #include "greatcircle.h"
8 
9 #include "kstars_debug.h"
10 #include "Options.h"
11 #include "skymap.h"
12 #include "skyqpainter.h"
13 #include "projections/projector.h"
14 #include "skypoint.h"
15 #include "kstars.h"
16 
17 #include <QStatusBar>
18 
19 namespace
20 {
21 
22 double d2r(double degrees)
23 {
24  return degrees * 2.0 * M_PI / 360.0;
25 }
26 
27 double r2d(double radians)
28 {
29  return (radians * 360.0 / (2 * M_PI));
30 }
31 
32 } // namespace
33 
34 // This implements the equations in:
35 // https://en.wikipedia.org/wiki/Great-circle_navigation
36 
37 GreatCircle::GreatCircle(double az1, double alt1, double az2, double alt2) {
38  // convert inputs to radians.
39  az1 = d2r(az1);
40  az2 = d2r(az2);
41  alt1 = d2r(alt1);
42  alt2 = d2r(alt2);
43 
44  const double daz = az2 - az1;
45  const double alpha1 = atan2(
46  (cos(alt2) * sin(daz)),
47  (cos(alt1) * sin(alt2) - (sin(alt1) * cos(alt2) * cos(daz))));
48 
49  const double term1 = cos(alt1) * sin(alt2) - (sin(alt1) * cos(alt2) * cos(daz));
50  const double term2 = cos(alt2) * sin(daz);
51  const double sigma12 = atan2(
52  sqrt( term1 * term1 + term2 * term2),
53  (sin(alt1) * sin(alt2) + (cos(alt1) * cos(alt2) * cos(daz))));
54 
55  const double term3 = cos(alpha1);
56  const double term4 = sin(alpha1);
57  const double term5 = sin(alt1);
58  const double alpha0 = atan2(
59  (sin(alpha1) * cos(alt1)),
60  sqrt(term3 * term3 + term4 * term4 * term5 * term5));
61 
62  if ((alt1 == 0) && (alpha1 == 0.5 * M_PI))
63  sigma01 = 0;
64  else
65  sigma01 = atan2(tan(alt1), cos(alpha1));
66 
67  sigma02 = sigma01 + sigma12;
68 
69  const double lambda01 = atan2(sin(alpha0) * sin(sigma01), cos(sigma01));
70 
71  lambda0 = az1 - lambda01;
72 
73  cosAlpha0 = cos(alpha0);
74  sinAlpha0 = sin(alpha0);
75 }
76 
77 void GreatCircle::waypoint(double fraction, double *az, double *alt)
78 {
79  double sigma = (1-fraction) * sigma01 + fraction * sigma02;
80  double cosSigma = cos(sigma);
81  double sinSigma = sin(sigma);
82 
83  *alt = r2d(atan2(
84  (cosAlpha0 * sinSigma),
85  (sqrt(cosSigma * cosSigma + sinAlpha0 * sinAlpha0 * sinSigma * sinSigma))));
86 
87  double LL0 = atan2((sinAlpha0 * sinSigma), cosSigma);
88 
89  *az = r2d(LL0 + lambda0);
90 }
void waypoint(double fraction, double *az, double *alt)
Return the azimuth and altitude for a waypoint.
Definition: greatcircle.cpp:77
GreatCircle(double az1, double alt1, double az2, double alt2)
Construct a GreatCircle object for a path between az1,alt1 to az2,alt2.
Definition: greatcircle.cpp:37
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