NETGeographicLib  1.50.1
Gnomonic.h
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1 #pragma once
2 /**
3  * \file NETGeographicLib/Gnomonic.h
4  * \brief Header for NETGeographicLib::Gnomonic class
5  *
6  * NETGeographicLib is copyright (c) Scott Heiman (2013)
7  * GeographicLib is Copyright (c) Charles Karney (2010-2012)
8  * <charles@karney.com> and licensed under the MIT/X11 License.
9  * For more information, see
10  * https://geographiclib.sourceforge.io/
11  **********************************************************************/
12 
13 namespace NETGeographicLib
14 {
15  ref class Geodesic;
16  /**
17  * \brief .NET wrapper for GeographicLib::Gnomonic.
18  *
19  * This class allows .NET applications to access GeographicLib::Gnomonic.
20  *
21  * %Gnomonic projection centered at an arbitrary position \e C on the
22  * ellipsoid. This projection is derived in Section 8 of
23  * - C. F. F. Karney,
24  * <a href="https://doi.org/10.1007/s00190-012-0578-z">
25  * Algorithms for geodesics</a>,
26  * J. Geodesy <b>87</b>, 43--55 (2013);
27  * DOI: <a href="https://doi.org/10.1007/s00190-012-0578-z">
28  * 10.1007/s00190-012-0578-z</a>;
29  * addenda: <a href="https://geographiclib.sourceforge.io/geod-addenda.html">
30  * geod-addenda.html</a>.
31  * .
32  * The projection of \e P is defined as follows: compute the geodesic line
33  * from \e C to \e P; compute the reduced length \e m12, geodesic scale \e
34  * M12, and &rho; = <i>m12</i>/\e M12; finally \e x = &rho; sin \e azi1; \e
35  * y = &rho; cos \e azi1, where \e azi1 is the azimuth of the geodesic at \e
36  * C. The Gnomonic::Forward and Gnomonic::Reverse methods also return the
37  * azimuth \e azi of the geodesic at \e P and reciprocal scale \e rk in the
38  * azimuthal direction. The scale in the radial direction if
39  * 1/<i>rk</i><sup>2</sup>.
40  *
41  * For a sphere, &rho; is reduces to \e a tan(<i>s12</i>/<i>a</i>), where \e
42  * s12 is the length of the geodesic from \e C to \e P, and the gnomonic
43  * projection has the property that all geodesics appear as straight lines.
44  * For an ellipsoid, this property holds only for geodesics interesting the
45  * centers. However geodesic segments close to the center are approximately
46  * straight.
47  *
48  * Consider a geodesic segment of length \e l. Let \e T be the point on the
49  * geodesic (extended if necessary) closest to \e C the center of the
50  * projection and \e t be the distance \e CT. To lowest order, the maximum
51  * deviation (as a true distance) of the corresponding gnomonic line segment
52  * (i.e., with the same end points) from the geodesic is<br>
53  * <br>
54  * (<i>K</i>(<i>T</i>) - <i>K</i>(<i>C</i>))
55  * <i>l</i><sup>2</sup> \e t / 32.<br>
56  * <br>
57  * where \e K is the Gaussian curvature.
58  *
59  * This result applies for any surface. For an ellipsoid of revolution,
60  * consider all geodesics whose end points are within a distance \e r of \e
61  * C. For a given \e r, the deviation is maximum when the latitude of \e C
62  * is 45&deg;, when endpoints are a distance \e r away, and when their
63  * azimuths from the center are &plusmn; 45&deg; or &plusmn; 135&deg;.
64  * To lowest order in \e r and the flattening \e f, the deviation is \e f
65  * (<i>r</i>/2<i>a</i>)<sup>3</sup> \e r.
66  *
67  * The conversions all take place using a Geodesic object (by default
68  * Geodesic::WGS84). For more information on geodesics see \ref geodesic.
69  *
70  * <b>CAUTION:</b> The definition of this projection for a sphere is
71  * standard. However, there is no standard for how it should be extended to
72  * an ellipsoid. The choices are:
73  * - Declare that the projection is undefined for an ellipsoid.
74  * - Project to a tangent plane from the center of the ellipsoid. This
75  * causes great ellipses to appear as straight lines in the projection;
76  * i.e., it generalizes the spherical great circle to a great ellipse.
77  * This was proposed by independently by Bowring and Williams in 1997.
78  * - Project to the conformal sphere with the constant of integration chosen
79  * so that the values of the latitude match for the center point and
80  * perform a central projection onto the plane tangent to the conformal
81  * sphere at the center point. This causes normal sections through the
82  * center point to appear as straight lines in the projection; i.e., it
83  * generalizes the spherical great circle to a normal section. This was
84  * proposed by I. G. Letoval'tsev, Generalization of the %Gnomonic
85  * Projection for a Spheroid and the Principal Geodetic Problems Involved
86  * in the Alignment of Surface Routes, Geodesy and Aerophotography (5),
87  * 271--274 (1963).
88  * - The projection given here. This causes geodesics close to the center
89  * point to appear as straight lines in the projection; i.e., it
90  * generalizes the spherical great circle to a geodesic.
91  *
92  * C# Example:
93  * \include example-Gnomonic.cs
94  * Managed C++ Example:
95  * \include example-Gnomonic.cpp
96  * Visual Basic Example:
97  * \include example-Gnomonic.vb
98  *
99  * <B>INTERFACE DIFFERENCES:</B><BR>
100  * A default constructor has been provided that assumes WGS84 parameters.
101  *
102  * The EquatorialRadius and Flattening functions are implemented as properties.
103  **********************************************************************/
104  public ref class Gnomonic
105  {
106  private:
107  // the pointer to the unmanaged GeographicLib::Gnomonic.
108  const GeographicLib::Gnomonic* m_pGnomonic;
109 
110  // The finalizer frees the unmanaged memory when the object is destroyed.
111  !Gnomonic(void);
112  public:
113  /**
114  * Constructor for Gnomonic.
115  *
116  * @param[in] earth the Geodesic object to use for geodesic calculations.
117  **********************************************************************/
118  Gnomonic( Geodesic^ earth );
119 
120  /**
121  * The default constructor assumes a WGS84 ellipsoid..
122  **********************************************************************/
124 
125  /**
126  * The destructor calls the finalizer
127  **********************************************************************/
129  { this->!Gnomonic(); }
130 
131  /**
132  * Forward projection, from geographic to gnomonic.
133  *
134  * @param[in] lat0 latitude of center point of projection (degrees).
135  * @param[in] lon0 longitude of center point of projection (degrees).
136  * @param[in] lat latitude of point (degrees).
137  * @param[in] lon longitude of point (degrees).
138  * @param[out] x easting of point (meters).
139  * @param[out] y northing of point (meters).
140  * @param[out] azi azimuth of geodesic at point (degrees).
141  * @param[out] rk reciprocal of azimuthal scale at point.
142  *
143  * \e lat0 and \e lat should be in the range [&minus;90&deg;, 90&deg;].
144  * The scale of the projection is 1/<i>rk</i><sup>2</sup> in the
145  * "radial" direction, \e azi clockwise from true north, and is 1/\e rk
146  * in the direction perpendicular to this. If the point lies "over the
147  * horizon", i.e., if \e rk &le; 0, then NaNs are returned for \e x and
148  * \e y (the correct values are returned for \e azi and \e rk). A call
149  * to Forward followed by a call to Reverse will return the original
150  * (\e lat, \e lon) (to within roundoff) provided the point in not over
151  * the horizon.
152  **********************************************************************/
153  void Forward(double lat0, double lon0, double lat, double lon,
154  [System::Runtime::InteropServices::Out] double% x,
155  [System::Runtime::InteropServices::Out] double% y,
156  [System::Runtime::InteropServices::Out] double% azi,
157  [System::Runtime::InteropServices::Out] double% rk);
158 
159  /**
160  * Reverse projection, from gnomonic to geographic.
161  *
162  * @param[in] lat0 latitude of center point of projection (degrees).
163  * @param[in] lon0 longitude of center point of projection (degrees).
164  * @param[in] x easting of point (meters).
165  * @param[in] y northing of point (meters).
166  * @param[out] lat latitude of point (degrees).
167  * @param[out] lon longitude of point (degrees).
168  * @param[out] azi azimuth of geodesic at point (degrees).
169  * @param[out] rk reciprocal of azimuthal scale at point.
170  *
171  * \e lat0 should be in the range [&minus;90&deg;, 90&deg;]. \e lat
172  * will be in the range [&minus;90&deg;, 90&deg;] and \e lon will be in
173  * the range [&minus;180&deg;, 180&deg;). The scale of the projection
174  * is 1/\e rk<sup>2</sup> in the "radial" direction, \e azi clockwise
175  * from true north, and is 1/\e rk in the direction perpendicular to
176  * this. Even though all inputs should return a valid \e lat and \e
177  * lon, it's possible that the procedure fails to converge for very
178  * large \e x or \e y; in this case NaNs are returned for all the
179  * output arguments. A call to Reverse followed by a call to Forward
180  * will return the original (\e x, \e y) (to roundoff).
181  **********************************************************************/
182  void Reverse(double lat0, double lon0, double x, double y,
183  [System::Runtime::InteropServices::Out] double% lat,
184  [System::Runtime::InteropServices::Out] double% lon,
185  [System::Runtime::InteropServices::Out] double% azi,
186  [System::Runtime::InteropServices::Out] double% rk);
187 
188  /**
189  * Gnomonic::Forward without returning the azimuth and scale.
190  **********************************************************************/
191  void Forward(double lat0, double lon0, double lat, double lon,
192  [System::Runtime::InteropServices::Out] double% x,
193  [System::Runtime::InteropServices::Out] double% y);
194 
195  /**
196  * Gnomonic::Reverse without returning the azimuth and scale.
197  **********************************************************************/
198  void Reverse(double lat0, double lon0, double x, double y,
199  [System::Runtime::InteropServices::Out] double% lat,
200  [System::Runtime::InteropServices::Out] double% lon);
201 
202  /** \name Inspector functions
203  **********************************************************************/
204  ///@{
205  /**
206  * @return \e a the equatorial radius of the ellipsoid (meters). This is
207  * the value inherited from the Geodesic object used in the constructor.
208  **********************************************************************/
209  property double EquatorialRadius { double get(); }
210 
211  /**
212  * @return \e f the flattening of the ellipsoid. This is the value
213  * inherited from the Geodesic object used in the constructor.
214  **********************************************************************/
215  property double Flattening { double get(); }
216  ///@}
217  };
218 } // namespace NETGeographicLib
NETGeographicLib::Gnomonic
.NET wrapper for GeographicLib::Gnomonic.
Definition: Gnomonic.h:105
NETGeographicLib::Gnomonic::EquatorialRadius
double EquatorialRadius
Definition: Gnomonic.h:209
NETGeographicLib::Gnomonic::~Gnomonic
~Gnomonic()
Definition: Gnomonic.h:128
NETGeographicLib::Gnomonic::Forward
void Forward(double lat0, double lon0, double lat, double lon, [System::Runtime::InteropServices::Out] double% x, [System::Runtime::InteropServices::Out] double% y)
GeographicLib::Gnomonic
NETGeographicLib::Gnomonic::Reverse
void Reverse(double lat0, double lon0, double x, double y, [System::Runtime::InteropServices::Out] double% lat, [System::Runtime::InteropServices::Out] double% lon)
NETGeographicLib::Gnomonic::Forward
void Forward(double lat0, double lon0, double lat, double lon, [System::Runtime::InteropServices::Out] double% x, [System::Runtime::InteropServices::Out] double% y, [System::Runtime::InteropServices::Out] double% azi, [System::Runtime::InteropServices::Out] double% rk)
NETGeographicLib::Gnomonic::Gnomonic
Gnomonic(Geodesic^ earth)
NETGeographicLib::Geodesic
.NET wrapper for GeographicLib::Geodesic.
Definition: Geodesic.h:171
NETGeographicLib::Gnomonic::Flattening
double Flattening
Definition: Gnomonic.h:215
NETGeographicLib::Gnomonic::Gnomonic
Gnomonic()
NETGeographicLib
Definition: Accumulator.h:14
NETGeographicLib::Gnomonic::Reverse
void Reverse(double lat0, double lon0, double x, double y, [System::Runtime::InteropServices::Out] double% lat, [System::Runtime::InteropServices::Out] double% lon, [System::Runtime::InteropServices::Out] double% azi, [System::Runtime::InteropServices::Out] double% rk)