GeographicLib 2.5
DAuxLatitude.hpp
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1/**
2 * \file DAuxLatitude.hpp
3 * \brief Header for the GeographicLib::DAuxLatitude class
4 *
5 * Copyright (c) Charles Karney (2022-2023) <karney@alum.mit.edu> and licensed
6 * under the MIT/X11 License. For more information, see
7 * https://geographiclib.sourceforge.io/
8 **********************************************************************/
9
10#if !defined(GEOGRAPHICLIB_DAUXLATITUDE_HPP)
11#define GEOGRAPHICLIB_DAUXLATITUDE_HPP 1
12
13#include <GeographicLib/AuxLatitude.hpp>
14
15namespace GeographicLib {
16
17 /**
18 * \brief Divided differences of auxiliary latitudes.
19 *
20 * This class computed the divided differences of auxiliary latitudes and
21 * some other divided differences needed to support rhumb line calculations.
22 **********************************************************************/
23 class GEOGRAPHICLIB_EXPORT DAuxLatitude : public AuxLatitude {
24 private:
25 typedef Math::real real;
26 typedef AuxLatitude base;
27 public:
28 /**
29 * Constructor
30 *
31 * @param[in] a equatorial radius.
32 * @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
33 * Negative \e f gives a prolate ellipsoid.
34 * @exception GeographicErr if \e a or (1 &minus; \e f) \e a is not
35 * positive.
36 **********************************************************************/
37 DAuxLatitude(real a, real f) : AuxLatitude(a, f) {}
38 /**
39 * The divided difference of one auxiliary latitude with respect to
40 * another.
41 *
42 * @param[in] auxin an AuxLatitude::aux indicating the type of
43 * auxiliary latitude \e zeta.
44 * @param[in] auxout an AuxLatitude::aux indicating the type of
45 * auxiliary latitude \e eta.
46 * @param[in] zeta1 the first of the input auxiliary latitudeas.
47 * @param[in] zeta2 the second of the input auxiliary latitude.
48 * @return the divided difference (\e eta2 - \e eta1) / (\e zeta2 - \e
49 * zeta1).
50 *
51 * \note This routine uses the series method.
52 *
53 * In the expression for the divided difference above, the angle quantities
54 * should be understood as the conventional measure of angle (either in
55 * radians or in degrees).
56 *
57 * The Fourier coefficients for a specific \e auxin and \e auxout are
58 * computed and saved on the first call; the saved coefficients are used on
59 * subsequent calls. The series method is accurate for abs(\e f) &le;
60 * 1/150.
61 **********************************************************************/
62 Math::real DConvert(int auxin, int auxout,
63 const AuxAngle& zeta1, const AuxAngle& zeta2) const;
64 /**
65 * The divided difference of the parametric latitude with respect to the
66 * geographic latitude.
67 *
68 * @param[in] phi1 the first geographic latitude as an AuxAngle.
69 * @param[in] phi2 the second geographic latitude as an AuxAngle.
70 * @return the divided difference (\e beta2 - \e beta1) / (\e phi2 - \e
71 * phi1), where \e beta is the parametric latitude.
72 *
73 * \note This routine uses the exact formulas and is valid for arbitrary
74 * latitude.
75 **********************************************************************/
76 Math::real DParametric(const AuxAngle& phi1, const AuxAngle& phi2) const;
77 /**
78 * The divided difference of the rectifying latitude with respect to the
79 * geographic latitude.
80 *
81 * @param[in] phi1 the first geographic latitude as an AuxAngle.
82 * @param[in] phi2 the second geographic latitude as an AuxAngle.
83 * @return the divided difference (\e mu2 - \e mu1) / (\e phi2 - \e
84 * phi1), where \e mu is the rectifying latitude.
85 *
86 * \note This routine uses the exact formulas and is valid for arbitrary
87 * latitude.
88 **********************************************************************/
89 Math::real DRectifying(const AuxAngle& phi1, const AuxAngle& phi2) const;
90 /**
91 * The divided difference of the isometric latitude with respect to the
92 * geographic latitude.
93 *
94 * @param[in] phi1 the first geographic latitude as an AuxAngle.
95 * @param[in] phi2 the second geographic latitude as an AuxAngle.
96 * @return the divided difference (\e psi2 - \e psi1) / (\e phi2 - \e
97 * phi1), where \e psi = asinh( tan(\e chi) ) is the isometric latitude
98 * and \e chi is the conformal latitude.
99 *
100 * \note This routine uses the exact formulas and is valid for arbitrary
101 * latitude.
102 **********************************************************************/
103 Math::real DIsometric(const AuxAngle& phi1, const AuxAngle& phi2) const;
104 /**
105 * The divided difference of AuxLatitude::Clenshaw.
106 *
107 * @param[in] sinp if true sum the sine series, else sum the cosine series.
108 * @param[in] Delta either 1 \e or (zeta2 - zeta1) in radians.
109 * @param[in] szeta1 sin(\e zeta1).
110 * @param[in] czeta1 cos(\e zeta1).
111 * @param[in] szeta2 sin(\e zeta2).
112 * @param[in] czeta2 cos(\e zeta2).
113 * @param[in] c the array of coefficients.
114 * @param[in] K the number of coefficients.
115 * @return the divided difference.
116 *
117 * The result is
118 * <pre>
119 * ( AuxLatitude::Clenshaw(sinp, szeta2, czeta2, c, K) -
120 * AuxLatitude::Clenshaw(sinp, szeta1, czeta1, c, K) ) / Delta
121 * </pre>
122 *
123 * \warning \e Delta **must** be either 1 or (\e zeta2 - \e zeta1);
124 * other values will return nonsense.
125 **********************************************************************/
126 static Math::real DClenshaw(bool sinp, real Delta,
127 real szeta1, real czeta1,
128 real szeta2, real czeta2,
129 const real c[], int K);
130 /**
131 * The divided difference of the isometric latitude with respect to the
132 * conformal latitude.
133 *
134 * @param[in] x tan(\e chi1).
135 * @param[in] y tan(\e chi2).
136 * @return the divided difference (\e psi2 - \e psi1) / (\e chi2 - \e
137 * chi1), where \e psi = asinh( tan(\e chi) ).
138 *
139 * \note This parameters for this routine are the \e tangents of conformal
140 * latitude.
141 *
142 * This routine computes Dasinh(x, y) / Datan(x, y).
143 **********************************************************************/
144 static Math::real Dlam(real x, real y) {
145 using std::isnan; using std::isinf;
146 return x == y ? base::sc(x) :
147 (isnan(x) || isnan(y) ? std::numeric_limits<real>::quiet_NaN() :
148 (isinf(x) || isinf(y) ? std::numeric_limits<real>::infinity() :
149 Dasinh(x, y) / Datan(x, y)));
150 }
151 // Dp0Dpsi in terms of chi
152 /**
153 * The divided difference of the spherical rhumb area term with respect to
154 * the isometric latitude.
155 *
156 * @param[in] x tan(\e chi1).
157 * @param[in] y tan(\e chi2).
158 * @return the divided difference (p0(\e chi2) - p0(\e chi1)) / (\e psi2 -
159 * \e psi1), where p0(\e chi) = log( sec(\e chi) ) and \e psi = asinh(
160 * tan(\e chi) ).
161 *
162 * \note This parameters for this routine are the \e tangents of conformal
163 * latitude.
164 **********************************************************************/
165 static Math::real Dp0Dpsi(real x, real y) {
166 using std::isnan; using std::isinf; using std::copysign;
167 return x == y ? base::sn(x) :
168 (isnan(x + y) ? x + y : // N.B. nan for inf-inf
169 (isinf(x) ? copysign(real(1), x) :
170 (isinf(y) ? copysign(real(1), y) :
171 Dasinh(h(x), h(y)) * Dh(x, y) / Dasinh(x, y))));
172 }
173 protected: // so TestAux can access these functions
174 /// \cond SKIP
175 // (sn(y) - sn(x)) / (y - x)
176 static real Dsn(real x, real y);
177 static real Datan(real x, real y);
178 static real Dasinh(real x, real y);
179 // h(tan(x)) = tan(x) * sin(x) / 2
180 static real h(real x) { return x * base::sn(x) / 2; }
181 static real Dh(real x, real y);
182 real Datanhee(real tphi1, real tphi2) const;
183 /// \endcond
184 private:
185 static real Dsin(real x, real y) {
186 using std::sin; using std::cos;
187 real d = (x - y) / 2;
188 return cos((x + y) / 2) * (d != 0 ? sin(d) / d : 1);
189 }
190 // (E(x) - E(y)) / (x - y)
191 real DE(const AuxAngle& X, const AuxAngle& Y) const;
192 };
193
194} // namespace GeographicLib
195
196#endif // GEOGRAPHICLIB_DAUXLATITUDE_HPP
AuxLatitude.hpp
Header for the GeographicLib::AuxLatitude class.
GEOGRAPHICLIB_EXPORT
#define GEOGRAPHICLIB_EXPORT
Definition Constants.hpp:67
real
GeographicLib::Math::real real
Definition GeodSolve.cpp:28
GeographicLib::AuxAngle
An accurate representation of angles.
Definition AuxAngle.hpp:47
GeographicLib::AuxLatitude
Conversions between auxiliary latitudes.
Definition AuxLatitude.hpp:75
GeographicLib::DAuxLatitude
Divided differences of auxiliary latitudes.
Definition DAuxLatitude.hpp:23
GeographicLib::DAuxLatitude::Dlam
static Math::real Dlam(real x, real y)
Definition DAuxLatitude.hpp:144
GeographicLib::DAuxLatitude::Dp0Dpsi
static Math::real Dp0Dpsi(real x, real y)
Definition DAuxLatitude.hpp:165
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12