/**
* \file geodesic.h
* \brief API for the geodesic routines in C
*
* This an implementation in C of the geodesic algorithms described in
* - C. F. F. Karney,
*
* Algorithms for geodesics,
* J. Geodesy 87, 43--55 (2013);
* DOI:
* 10.1007/s00190-012-0578-z;
* addenda:
* geod-addenda.html.
* .
* The principal advantages of these algorithms over previous ones (e.g.,
* Vincenty, 1975) are
* - accurate to round off for |f| < 1/50;
* - the solution of the inverse problem is always found;
* - differential and integral properties of geodesics are computed.
*
* The shortest path between two points on the ellipsoid at (\e lat1, \e
* lon1) and (\e lat2, \e lon2) is called the geodesic. Its length is
* \e s12 and the geodesic from point 1 to point 2 has forward azimuths
* \e azi1 and \e azi2 at the two end points.
*
* Traditionally two geodesic problems are considered:
* - the direct problem -- given \e lat1, \e lon1, \e s12, and \e azi1,
* determine \e lat2, \e lon2, and \e azi2. This is solved by the function
* geod_direct().
* - the inverse problem -- given \e lat1, \e lon1, and \e lat2, \e lon2,
* determine \e s12, \e azi1, and \e azi2. This is solved by the function
* geod_inverse().
*
* The ellipsoid is specified by its equatorial radius \e a (typically in
* meters) and flattening \e f. The routines are accurate to round off with
* double precision arithmetic provided that |f| < 1/50; for the
* WGS84 ellipsoid, the errors are less than 15 nanometers. (Reasonably
* accurate results are obtained for |f| < 1/5.) For a prolate
* ellipsoid, specify \e f < 0.
*
* The routines also calculate several other quantities of interest
* - \e S12 is the area between the geodesic from point 1 to point 2 and the
* equator; i.e., it is the area, measured counter-clockwise, of the
* quadrilateral with corners (\e lat1,\e lon1), (0,\e lon1), (0,\e lon2),
* and (\e lat2,\e lon2).
* - \e m12, the reduced length of the geodesic is defined such that if
* the initial azimuth is perturbed by \e dazi1 (radians) then the
* second point is displaced by \e m12 \e dazi1 in the direction
* perpendicular to the geodesic. On a curved surface the reduced
* length obeys a symmetry relation, \e m12 + \e m21 = 0. On a flat
* surface, we have \e m12 = \e s12.
* - \e M12 and \e M21 are geodesic scales. If two geodesics are
* parallel at point 1 and separated by a small distance \e dt, then
* they are separated by a distance \e M12 \e dt at point 2. \e M21
* is defined similarly (with the geodesics being parallel to one
* another at point 2). On a flat surface, we have \e M12 = \e M21
* = 1.
* - \e a12 is the arc length on the auxiliary sphere. This is a
* construct for converting the problem to one in spherical
* trigonometry. \e a12 is measured in degrees. The spherical arc
* length from one equator crossing to the next is always 180°.
*
* If points 1, 2, and 3 lie on a single geodesic, then the following
* addition rules hold:
* - \e s13 = \e s12 + \e s23
* - \e a13 = \e a12 + \e a23
* - \e S13 = \e S12 + \e S23
* - \e m13 = \e m12 \e M23 + \e m23 \e M21
* - \e M13 = \e M12 \e M23 − (1 − \e M12 \e M21) \e
* m23 / \e m12
* - \e M31 = \e M32 \e M21 − (1 − \e M23 \e M32) \e
* m12 / \e m23
*
* The shortest distance returned by the solution of the inverse problem is
* (obviously) uniquely defined. However, in a few special cases there are
* multiple azimuths which yield the same shortest distance. Here is a
* catalog of those cases:
* - \e lat1 = −\e lat2 (with neither point at a pole). If \e azi1 = \e
* azi2, the geodesic is unique. Otherwise there are two geodesics and the
* second one is obtained by setting [\e azi1, \e azi2] → [\e azi2, \e
* azi1], [\e M12, \e M21] → [\e M21, \e M12], \e S12 → −\e
* S12. (This occurs when the longitude difference is near ±180°
* for oblate ellipsoids.)
* - \e lon2 = \e lon1 ± 180° (with neither point at a pole). If \e
* azi1 = 0° or ±180°, the geodesic is unique. Otherwise
* there are two geodesics and the second one is obtained by setting [\e
* azi1, \e azi2] → [−\e azi1, −\e azi2], \e S12 →
* −\e S12. (This occurs when \e lat2 is near −\e lat1 for
* prolate ellipsoids.)
* - Points 1 and 2 at opposite poles. There are infinitely many geodesics
* which can be generated by setting [\e azi1, \e azi2] → [\e azi1, \e
* azi2] + [\e d, −\e d], for arbitrary \e d. (For spheres, this
* prescription applies when points 1 and 2 are antipodal.)
* - \e s12 = 0 (coincident points). There are infinitely many geodesics which
* can be generated by setting [\e azi1, \e azi2] → [\e azi1, \e azi2] +
* [\e d, \e d], for arbitrary \e d.
*
* These routines are a simple transcription of the corresponding C++ classes
* in GeographicLib. The
* "class data" is represented by the structs geod_geodesic, geod_geodesicline,
* geod_polygon and pointers to these objects are passed as initial arguments
* to the member functions. Most of the internal comments have been retained.
* However, in the process of transcription some documentation has been lost
* and the documentation for the C++ classes, GeographicLib::Geodesic,
* GeographicLib::GeodesicLine, and GeographicLib::PolygonAreaT, should be
* consulted. The C++ code remains the "reference implementation". Think
* twice about restructuring the internals of the C code since this may make
* porting fixes from the C++ code more difficult.
*
* Copyright (c) Charles Karney (2012-2021) and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
*
* This library was distributed with
* GeographicLib 1.52.
**********************************************************************/
#if !defined(GEODESIC_H)
#define GEODESIC_H 1
/**
* The major version of the geodesic library. (This tracks the version of
* GeographicLib.)
**********************************************************************/
#define GEODESIC_VERSION_MAJOR 1
/**
* The minor version of the geodesic library. (This tracks the version of
* GeographicLib.)
**********************************************************************/
#define GEODESIC_VERSION_MINOR 52
/**
* The patch level of the geodesic library. (This tracks the version of
* GeographicLib.)
**********************************************************************/
#define GEODESIC_VERSION_PATCH 0
/**
* Pack the version components into a single integer. Users should not rely on
* this particular packing of the components of the version number; see the
* documentation for GEODESIC_VERSION, below.
**********************************************************************/
#define GEODESIC_VERSION_NUM(a,b,c) ((((a) * 10000 + (b)) * 100) + (c))
/**
* The version of the geodesic library as a single integer, packed as MMmmmmpp
* where MM is the major version, mmmm is the minor version, and pp is the
* patch level. Users should not rely on this particular packing of the
* components of the version number. Instead they should use a test such as
* @code{.c}
#if GEODESIC_VERSION >= GEODESIC_VERSION_NUM(1,40,0)
...
#endif
* @endcode
**********************************************************************/
#define GEODESIC_VERSION \
GEODESIC_VERSION_NUM(GEODESIC_VERSION_MAJOR, \
GEODESIC_VERSION_MINOR, \
GEODESIC_VERSION_PATCH)
#if !defined(GEOD_DLL)
#if defined(_MSC_VER) && defined(PROJ_MSVC_DLL_EXPORT)
#define GEOD_DLL __declspec(dllexport)
#elif defined(__GNUC__)
#define GEOD_DLL __attribute__ ((visibility("default")))
#else
#define GEOD_DLL
#endif
#endif
#if defined(PROJ_RENAME_SYMBOLS)
#include "proj_symbol_rename.h"
#endif
#if defined(__cplusplus)
extern "C" {
#endif
/**
* The struct containing information about the ellipsoid. This must be
* initialized by geod_init() before use.
**********************************************************************/
struct geod_geodesic {
double a; /**< the equatorial radius */
double f; /**< the flattening */
/**< @cond SKIP */
double f1, e2, ep2, n, b, c2, etol2;
double A3x[6], C3x[15], C4x[21];
/**< @endcond */
};
/**
* The struct containing information about a single geodesic. This must be
* initialized by geod_lineinit(), geod_directline(), geod_gendirectline(),
* or geod_inverseline() before use.
**********************************************************************/
struct geod_geodesicline {
double lat1; /**< the starting latitude */
double lon1; /**< the starting longitude */
double azi1; /**< the starting azimuth */
double a; /**< the equatorial radius */
double f; /**< the flattening */
double salp1; /**< sine of \e azi1 */
double calp1; /**< cosine of \e azi1 */
double a13; /**< arc length to reference point */
double s13; /**< distance to reference point */
/**< @cond SKIP */
double b, c2, f1, salp0, calp0, k2,
ssig1, csig1, dn1, stau1, ctau1, somg1, comg1,
A1m1, A2m1, A3c, B11, B21, B31, A4, B41;
double C1a[6+1], C1pa[6+1], C2a[6+1], C3a[6], C4a[6];
/**< @endcond */
unsigned caps; /**< the capabilities */
};
/**
* The struct for accumulating information about a geodesic polygon. This is
* used for computing the perimeter and area of a polygon. This must be
* initialized by geod_polygon_init() before use.
**********************************************************************/
struct geod_polygon {
double lat; /**< the current latitude */
double lon; /**< the current longitude */
/**< @cond SKIP */
double lat0;
double lon0;
double A[2];
double P[2];
int polyline;
int crossings;
/**< @endcond */
unsigned num; /**< the number of points so far */
};
/**
* Initialize a geod_geodesic object.
*
* @param[out] g a pointer to the object to be initialized.
* @param[in] a the equatorial radius (meters).
* @param[in] f the flattening.
**********************************************************************/
void GEOD_DLL geod_init(struct geod_geodesic* g, double a, double f);
/**
* Solve the direct geodesic problem.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] azi1 azimuth at point 1 (degrees).
* @param[in] s12 distance from point 1 to point 2 (meters); it can be
* negative.
* @param[out] plat2 pointer to the latitude of point 2 (degrees).
* @param[out] plon2 pointer to the longitude of point 2 (degrees).
* @param[out] pazi2 pointer to the (forward) azimuth at point 2 (degrees).
*
* \e g must have been initialized with a call to geod_init(). \e lat1
* should be in the range [−90°, 90°]. The values of \e lon2
* and \e azi2 returned are in the range [−180°, 180°]. Any of
* the "return" arguments \e plat2, etc., may be replaced by 0, if you do not
* need some quantities computed.
*
* If either point is at a pole, the azimuth is defined by keeping the
* longitude fixed, writing \e lat = ±(90° − ε), and
* taking the limit ε → 0+. An arc length greater that 180°
* signifies a geodesic which is not a shortest path. (For a prolate
* ellipsoid, an additional condition is necessary for a shortest path: the
* longitudinal extent must not exceed of 180°.)
*
* Example, determine the point 10000 km NE of JFK:
@code{.c}
struct geod_geodesic g;
double lat, lon;
geod_init(&g, 6378137, 1/298.257223563);
geod_direct(&g, 40.64, -73.78, 45.0, 10e6, &lat, &lon, 0);
printf("%.5f %.5f\n", lat, lon);
@endcode
**********************************************************************/
void GEOD_DLL geod_direct(const struct geod_geodesic* g,
double lat1, double lon1, double azi1, double s12,
double* plat2, double* plon2, double* pazi2);
/**
* The general direct geodesic problem.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] azi1 azimuth at point 1 (degrees).
* @param[in] flags bitor'ed combination of geod_flags(); \e flags &
* GEOD_ARCMODE determines the meaning of \e s12_a12 and \e flags &
* GEOD_LONG_UNROLL "unrolls" \e lon2.
* @param[in] s12_a12 if \e flags & GEOD_ARCMODE is 0, this is the distance
* from point 1 to point 2 (meters); otherwise it is the arc length
* from point 1 to point 2 (degrees); it can be negative.
* @param[out] plat2 pointer to the latitude of point 2 (degrees).
* @param[out] plon2 pointer to the longitude of point 2 (degrees).
* @param[out] pazi2 pointer to the (forward) azimuth at point 2 (degrees).
* @param[out] ps12 pointer to the distance from point 1 to point 2
* (meters).
* @param[out] pm12 pointer to the reduced length of geodesic (meters).
* @param[out] pM12 pointer to the geodesic scale of point 2 relative to
* point 1 (dimensionless).
* @param[out] pM21 pointer to the geodesic scale of point 1 relative to
* point 2 (dimensionless).
* @param[out] pS12 pointer to the area under the geodesic
* (meters2).
* @return \e a12 arc length from point 1 to point 2 (degrees).
*
* \e g must have been initialized with a call to geod_init(). \e lat1
* should be in the range [−90°, 90°]. The function value \e
* a12 equals \e s12_a12 if \e flags & GEOD_ARCMODE. Any of the "return"
* arguments, \e plat2, etc., may be replaced by 0, if you do not need some
* quantities computed.
*
* With \e flags & GEOD_LONG_UNROLL bit set, the longitude is "unrolled" so
* that the quantity \e lon2 − \e lon1 indicates how many times and in
* what sense the geodesic encircles the ellipsoid.
**********************************************************************/
double GEOD_DLL geod_gendirect(const struct geod_geodesic* g,
double lat1, double lon1, double azi1,
unsigned flags, double s12_a12,
double* plat2, double* plon2, double* pazi2,
double* ps12, double* pm12,
double* pM12, double* pM21,
double* pS12);
/**
* Solve the inverse geodesic problem.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] lat2 latitude of point 2 (degrees).
* @param[in] lon2 longitude of point 2 (degrees).
* @param[out] ps12 pointer to the distance from point 1 to point 2
* (meters).
* @param[out] pazi1 pointer to the azimuth at point 1 (degrees).
* @param[out] pazi2 pointer to the (forward) azimuth at point 2 (degrees).
*
* \e g must have been initialized with a call to geod_init(). \e lat1 and
* \e lat2 should be in the range [−90°, 90°]. The values of
* \e azi1 and \e azi2 returned are in the range [−180°, 180°].
* Any of the "return" arguments, \e ps12, etc., may be replaced by 0, if you
* do not need some quantities computed.
*
* If either point is at a pole, the azimuth is defined by keeping the
* longitude fixed, writing \e lat = ±(90° − ε), and
* taking the limit ε → 0+.
*
* The solution to the inverse problem is found using Newton's method. If
* this fails to converge (this is very unlikely in geodetic applications
* but does occur for very eccentric ellipsoids), then the bisection method
* is used to refine the solution.
*
* Example, determine the distance between JFK and Singapore Changi Airport:
@code{.c}
struct geod_geodesic g;
double s12;
geod_init(&g, 6378137, 1/298.257223563);
geod_inverse(&g, 40.64, -73.78, 1.36, 103.99, &s12, 0, 0);
printf("%.3f\n", s12);
@endcode
**********************************************************************/
void GEOD_DLL geod_inverse(const struct geod_geodesic* g,
double lat1, double lon1,
double lat2, double lon2,
double* ps12, double* pazi1, double* pazi2);
/**
* The general inverse geodesic calculation.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] lat2 latitude of point 2 (degrees).
* @param[in] lon2 longitude of point 2 (degrees).
* @param[out] ps12 pointer to the distance from point 1 to point 2
* (meters).
* @param[out] pazi1 pointer to the azimuth at point 1 (degrees).
* @param[out] pazi2 pointer to the (forward) azimuth at point 2 (degrees).
* @param[out] pm12 pointer to the reduced length of geodesic (meters).
* @param[out] pM12 pointer to the geodesic scale of point 2 relative to
* point 1 (dimensionless).
* @param[out] pM21 pointer to the geodesic scale of point 1 relative to
* point 2 (dimensionless).
* @param[out] pS12 pointer to the area under the geodesic
* (meters2).
* @return \e a12 arc length from point 1 to point 2 (degrees).
*
* \e g must have been initialized with a call to geod_init(). \e lat1 and
* \e lat2 should be in the range [−90°, 90°]. Any of the
* "return" arguments \e ps12, etc., may be replaced by 0, if you do not need
* some quantities computed.
**********************************************************************/
double GEOD_DLL geod_geninverse(const struct geod_geodesic* g,
double lat1, double lon1,
double lat2, double lon2,
double* ps12, double* pazi1, double* pazi2,
double* pm12, double* pM12, double* pM21,
double* pS12);
/**
* Initialize a geod_geodesicline object.
*
* @param[out] l a pointer to the object to be initialized.
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] azi1 azimuth at point 1 (degrees).
* @param[in] caps bitor'ed combination of geod_mask() values specifying the
* capabilities the geod_geodesicline object should possess, i.e., which
* quantities can be returned in calls to geod_position() and
* geod_genposition().
*
* \e g must have been initialized with a call to geod_init(). \e lat1
* should be in the range [−90°, 90°].
*
* The geod_mask values are [see geod_mask()]:
* - \e caps |= GEOD_LATITUDE for the latitude \e lat2; this is
* added automatically,
* - \e caps |= GEOD_LONGITUDE for the latitude \e lon2,
* - \e caps |= GEOD_AZIMUTH for the latitude \e azi2; this is
* added automatically,
* - \e caps |= GEOD_DISTANCE for the distance \e s12,
* - \e caps |= GEOD_REDUCEDLENGTH for the reduced length \e m12,
* - \e caps |= GEOD_GEODESICSCALE for the geodesic scales \e M12
* and \e M21,
* - \e caps |= GEOD_AREA for the area \e S12,
* - \e caps |= GEOD_DISTANCE_IN permits the length of the
* geodesic to be given in terms of \e s12; without this capability the
* length can only be specified in terms of arc length.
* .
* A value of \e caps = 0 is treated as GEOD_LATITUDE | GEOD_LONGITUDE |
* GEOD_AZIMUTH | GEOD_DISTANCE_IN (to support the solution of the "standard"
* direct problem).
*
* When initialized by this function, point 3 is undefined (l->s13 = l->a13 =
* NaN).
**********************************************************************/
void GEOD_DLL geod_lineinit(struct geod_geodesicline* l,
const struct geod_geodesic* g,
double lat1, double lon1, double azi1,
unsigned caps);
/**
* Initialize a geod_geodesicline object in terms of the direct geodesic
* problem.
*
* @param[out] l a pointer to the object to be initialized.
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] azi1 azimuth at point 1 (degrees).
* @param[in] s12 distance from point 1 to point 2 (meters); it can be
* negative.
* @param[in] caps bitor'ed combination of geod_mask() values specifying the
* capabilities the geod_geodesicline object should possess, i.e., which
* quantities can be returned in calls to geod_position() and
* geod_genposition().
*
* This function sets point 3 of the geod_geodesicline to correspond to point
* 2 of the direct geodesic problem. See geod_lineinit() for more
* information.
**********************************************************************/
void GEOD_DLL geod_directline(struct geod_geodesicline* l,
const struct geod_geodesic* g,
double lat1, double lon1,
double azi1, double s12,
unsigned caps);
/**
* Initialize a geod_geodesicline object in terms of the direct geodesic
* problem specified in terms of either distance or arc length.
*
* @param[out] l a pointer to the object to be initialized.
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] azi1 azimuth at point 1 (degrees).
* @param[in] flags either GEOD_NOFLAGS or GEOD_ARCMODE to determining the
* meaning of the \e s12_a12.
* @param[in] s12_a12 if \e flags = GEOD_NOFLAGS, this is the distance
* from point 1 to point 2 (meters); if \e flags = GEOD_ARCMODE, it is
* the arc length from point 1 to point 2 (degrees); it can be
* negative.
* @param[in] caps bitor'ed combination of geod_mask() values specifying the
* capabilities the geod_geodesicline object should possess, i.e., which
* quantities can be returned in calls to geod_position() and
* geod_genposition().
*
* This function sets point 3 of the geod_geodesicline to correspond to point
* 2 of the direct geodesic problem. See geod_lineinit() for more
* information.
**********************************************************************/
void GEOD_DLL geod_gendirectline(struct geod_geodesicline* l,
const struct geod_geodesic* g,
double lat1, double lon1, double azi1,
unsigned flags, double s12_a12,
unsigned caps);
/**
* Initialize a geod_geodesicline object in terms of the inverse geodesic
* problem.
*
* @param[out] l a pointer to the object to be initialized.
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] lat2 latitude of point 2 (degrees).
* @param[in] lon2 longitude of point 2 (degrees).
* @param[in] caps bitor'ed combination of geod_mask() values specifying the
* capabilities the geod_geodesicline object should possess, i.e., which
* quantities can be returned in calls to geod_position() and
* geod_genposition().
*
* This function sets point 3 of the geod_geodesicline to correspond to point
* 2 of the inverse geodesic problem. See geod_lineinit() for more
* information.
**********************************************************************/
void GEOD_DLL geod_inverseline(struct geod_geodesicline* l,
const struct geod_geodesic* g,
double lat1, double lon1,
double lat2, double lon2,
unsigned caps);
/**
* Compute the position along a geod_geodesicline.
*
* @param[in] l a pointer to the geod_geodesicline object specifying the
* geodesic line.
* @param[in] s12 distance from point 1 to point 2 (meters); it can be
* negative.
* @param[out] plat2 pointer to the latitude of point 2 (degrees).
* @param[out] plon2 pointer to the longitude of point 2 (degrees); requires
* that \e l was initialized with \e caps |= GEOD_LONGITUDE.
* @param[out] pazi2 pointer to the (forward) azimuth at point 2 (degrees).
*
* \e l must have been initialized with a call, e.g., to geod_lineinit(),
* with \e caps |= GEOD_DISTANCE_IN (or \e caps = 0). The values of \e lon2
* and \e azi2 returned are in the range [−180°, 180°]. Any of
* the "return" arguments \e plat2, etc., may be replaced by 0, if you do not
* need some quantities computed.
*
* Example, compute way points between JFK and Singapore Changi Airport
* the "obvious" way using geod_direct():
@code{.c}
struct geod_geodesic g;
double s12, azi1, lat[101],lon[101];
int i;
geod_init(&g, 6378137, 1/298.257223563);
geod_inverse(&g, 40.64, -73.78, 1.36, 103.99, &s12, &azi1, 0);
for (i = 0; i < 101; ++i) {
geod_direct(&g, 40.64, -73.78, azi1, i * s12 * 0.01, lat + i, lon + i, 0);
printf("%.5f %.5f\n", lat[i], lon[i]);
}
@endcode
* A faster way using geod_position():
@code{.c}
struct geod_geodesic g;
struct geod_geodesicline l;
double lat[101],lon[101];
int i;
geod_init(&g, 6378137, 1/298.257223563);
geod_inverseline(&l, &g, 40.64, -73.78, 1.36, 103.99, 0);
for (i = 0; i <= 100; ++i) {
geod_position(&l, i * l.s13 * 0.01, lat + i, lon + i, 0);
printf("%.5f %.5f\n", lat[i], lon[i]);
}
@endcode
**********************************************************************/
void GEOD_DLL geod_position(const struct geod_geodesicline* l, double s12,
double* plat2, double* plon2, double* pazi2);
/**
* The general position function.
*
* @param[in] l a pointer to the geod_geodesicline object specifying the
* geodesic line.
* @param[in] flags bitor'ed combination of geod_flags(); \e flags &
* GEOD_ARCMODE determines the meaning of \e s12_a12 and \e flags &
* GEOD_LONG_UNROLL "unrolls" \e lon2; if \e flags & GEOD_ARCMODE is 0,
* then \e l must have been initialized with \e caps |= GEOD_DISTANCE_IN.
* @param[in] s12_a12 if \e flags & GEOD_ARCMODE is 0, this is the
* distance from point 1 to point 2 (meters); otherwise it is the
* arc length from point 1 to point 2 (degrees); it can be
* negative.
* @param[out] plat2 pointer to the latitude of point 2 (degrees).
* @param[out] plon2 pointer to the longitude of point 2 (degrees); requires
* that \e l was initialized with \e caps |= GEOD_LONGITUDE.
* @param[out] pazi2 pointer to the (forward) azimuth at point 2 (degrees).
* @param[out] ps12 pointer to the distance from point 1 to point 2
* (meters); requires that \e l was initialized with \e caps |=
* GEOD_DISTANCE.
* @param[out] pm12 pointer to the reduced length of geodesic (meters);
* requires that \e l was initialized with \e caps |= GEOD_REDUCEDLENGTH.
* @param[out] pM12 pointer to the geodesic scale of point 2 relative to
* point 1 (dimensionless); requires that \e l was initialized with \e caps
* |= GEOD_GEODESICSCALE.
* @param[out] pM21 pointer to the geodesic scale of point 1 relative to
* point 2 (dimensionless); requires that \e l was initialized with \e caps
* |= GEOD_GEODESICSCALE.
* @param[out] pS12 pointer to the area under the geodesic
* (meters2); requires that \e l was initialized with \e caps |=
* GEOD_AREA.
* @return \e a12 arc length from point 1 to point 2 (degrees).
*
* \e l must have been initialized with a call to geod_lineinit() with \e
* caps |= GEOD_DISTANCE_IN. The value \e azi2 returned is in the range
* [−180°, 180°]. Any of the "return" arguments \e plat2,
* etc., may be replaced by 0, if you do not need some quantities
* computed. Requesting a value which \e l is not capable of computing
* is not an error; the corresponding argument will not be altered.
*
* With \e flags & GEOD_LONG_UNROLL bit set, the longitude is "unrolled" so
* that the quantity \e lon2 − \e lon1 indicates how many times and in
* what sense the geodesic encircles the ellipsoid.
*
* Example, compute way points between JFK and Singapore Changi Airport using
* geod_genposition(). In this example, the points are evenly space in arc
* length (and so only approximately equally spaced in distance). This is
* faster than using geod_position() and would be appropriate if drawing the
* path on a map.
@code{.c}
struct geod_geodesic g;
struct geod_geodesicline l;
double lat[101], lon[101];
int i;
geod_init(&g, 6378137, 1/298.257223563);
geod_inverseline(&l, &g, 40.64, -73.78, 1.36, 103.99,
GEOD_LATITUDE | GEOD_LONGITUDE);
for (i = 0; i <= 100; ++i) {
geod_genposition(&l, GEOD_ARCMODE, i * l.a13 * 0.01,
lat + i, lon + i, 0, 0, 0, 0, 0, 0);
printf("%.5f %.5f\n", lat[i], lon[i]);
}
@endcode
**********************************************************************/
double GEOD_DLL geod_genposition(const struct geod_geodesicline* l,
unsigned flags, double s12_a12,
double* plat2, double* plon2, double* pazi2,
double* ps12, double* pm12,
double* pM12, double* pM21,
double* pS12);
/**
* Specify position of point 3 in terms of distance.
*
* @param[in,out] l a pointer to the geod_geodesicline object.
* @param[in] s13 the distance from point 1 to point 3 (meters); it
* can be negative.
*
* This is only useful if the geod_geodesicline object has been constructed
* with \e caps |= GEOD_DISTANCE_IN.
**********************************************************************/
void GEOD_DLL geod_setdistance(struct geod_geodesicline* l, double s13);
/**
* Specify position of point 3 in terms of either distance or arc length.
*
* @param[in,out] l a pointer to the geod_geodesicline object.
* @param[in] flags either GEOD_NOFLAGS or GEOD_ARCMODE to determining the
* meaning of the \e s13_a13.
* @param[in] s13_a13 if \e flags = GEOD_NOFLAGS, this is the distance
* from point 1 to point 3 (meters); if \e flags = GEOD_ARCMODE, it is
* the arc length from point 1 to point 3 (degrees); it can be
* negative.
*
* If flags = GEOD_NOFLAGS, this calls geod_setdistance(). If flags =
* GEOD_ARCMODE, the \e s13 is only set if the geod_geodesicline object has
* been constructed with \e caps |= GEOD_DISTANCE.
**********************************************************************/
void GEOD_DLL geod_gensetdistance(struct geod_geodesicline* l,
unsigned flags, double s13_a13);
/**
* Initialize a geod_polygon object.
*
* @param[out] p a pointer to the object to be initialized.
* @param[in] polylinep non-zero if a polyline instead of a polygon.
*
* If \e polylinep is zero, then the sequence of vertices and edges added by
* geod_polygon_addpoint() and geod_polygon_addedge() define a polygon and
* the perimeter and area are returned by geod_polygon_compute(). If \e
* polylinep is non-zero, then the vertices and edges define a polyline and
* only the perimeter is returned by geod_polygon_compute().
*
* The area and perimeter are accumulated at two times the standard floating
* point precision to guard against the loss of accuracy with many-sided
* polygons. At any point you can ask for the perimeter and area so far.
*
* An example of the use of this function is given in the documentation for
* geod_polygon_compute().
**********************************************************************/
void GEOD_DLL geod_polygon_init(struct geod_polygon* p, int polylinep);
/**
* Clear the polygon, allowing a new polygon to be started.
*
* @param[in,out] p a pointer to the object to be cleared.
**********************************************************************/
void GEOD_DLL geod_polygon_clear(struct geod_polygon* p);
/**
* Add a point to the polygon or polyline.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in,out] p a pointer to the geod_polygon object specifying the
* polygon.
* @param[in] lat the latitude of the point (degrees).
* @param[in] lon the longitude of the point (degrees).
*
* \e g and \e p must have been initialized with calls to geod_init() and
* geod_polygon_init(), respectively. The same \e g must be used for all the
* points and edges in a polygon. \e lat should be in the range
* [−90°, 90°].
*
* An example of the use of this function is given in the documentation for
* geod_polygon_compute().
**********************************************************************/
void GEOD_DLL geod_polygon_addpoint(const struct geod_geodesic* g,
struct geod_polygon* p,
double lat, double lon);
/**
* Add an edge to the polygon or polyline.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in,out] p a pointer to the geod_polygon object specifying the
* polygon.
* @param[in] azi azimuth at current point (degrees).
* @param[in] s distance from current point to next point (meters).
*
* \e g and \e p must have been initialized with calls to geod_init() and
* geod_polygon_init(), respectively. The same \e g must be used for all the
* points and edges in a polygon. This does nothing if no points have been
* added yet. The \e lat and \e lon fields of \e p give the location of the
* new vertex.
**********************************************************************/
void GEOD_DLL geod_polygon_addedge(const struct geod_geodesic* g,
struct geod_polygon* p,
double azi, double s);
/**
* Return the results for a polygon.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] p a pointer to the geod_polygon object specifying the polygon.
* @param[in] reverse if non-zero then clockwise (instead of
* counter-clockwise) traversal counts as a positive area.
* @param[in] sign if non-zero then return a signed result for the area if
* the polygon is traversed in the "wrong" direction instead of returning
* the area for the rest of the earth.
* @param[out] pA pointer to the area of the polygon (meters2);
* only set if \e polyline is non-zero in the call to geod_polygon_init().
* @param[out] pP pointer to the perimeter of the polygon or length of the
* polyline (meters).
* @return the number of points.
*
* The area and perimeter are accumulated at two times the standard floating
* point precision to guard against the loss of accuracy with many-sided
* polygons. Arbitrarily complex polygons are allowed. In the case of
* self-intersecting polygons the area is accumulated "algebraically", e.g.,
* the areas of the 2 loops in a figure-8 polygon will partially cancel.
* There's no need to "close" the polygon by repeating the first vertex. Set
* \e pA or \e pP to zero, if you do not want the corresponding quantity
* returned.
*
* More points can be added to the polygon after this call.
*
* Example, compute the perimeter and area of the geodesic triangle with
* vertices (0°N,0°E), (0°N,90°E), (90°N,0°E).
@code{.c}
double A, P;
int n;
struct geod_geodesic g;
struct geod_polygon p;
geod_init(&g, 6378137, 1/298.257223563);
geod_polygon_init(&p, 0);
geod_polygon_addpoint(&g, &p, 0, 0);
geod_polygon_addpoint(&g, &p, 0, 90);
geod_polygon_addpoint(&g, &p, 90, 0);
n = geod_polygon_compute(&g, &p, 0, 1, &A, &P);
printf("%d %.8f %.3f\n", n, P, A);
@endcode
**********************************************************************/
unsigned GEOD_DLL geod_polygon_compute(const struct geod_geodesic* g,
const struct geod_polygon* p,
int reverse, int sign,
double* pA, double* pP);
/**
* Return the results assuming a tentative final test point is added;
* however, the data for the test point is not saved. This lets you report a
* running result for the perimeter and area as the user moves the mouse
* cursor. Ordinary floating point arithmetic is used to accumulate the data
* for the test point; thus the area and perimeter returned are less accurate
* than if geod_polygon_addpoint() and geod_polygon_compute() are used.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] p a pointer to the geod_polygon object specifying the polygon.
* @param[in] lat the latitude of the test point (degrees).
* @param[in] lon the longitude of the test point (degrees).
* @param[in] reverse if non-zero then clockwise (instead of
* counter-clockwise) traversal counts as a positive area.
* @param[in] sign if non-zero then return a signed result for the area if
* the polygon is traversed in the "wrong" direction instead of returning
* the area for the rest of the earth.
* @param[out] pA pointer to the area of the polygon (meters2);
* only set if \e polyline is non-zero in the call to geod_polygon_init().
* @param[out] pP pointer to the perimeter of the polygon or length of the
* polyline (meters).
* @return the number of points.
*
* \e lat should be in the range [−90°, 90°].
**********************************************************************/
unsigned GEOD_DLL geod_polygon_testpoint(const struct geod_geodesic* g,
const struct geod_polygon* p,
double lat, double lon,
int reverse, int sign,
double* pA, double* pP);
/**
* Return the results assuming a tentative final test point is added via an
* azimuth and distance; however, the data for the test point is not saved.
* This lets you report a running result for the perimeter and area as the
* user moves the mouse cursor. Ordinary floating point arithmetic is used
* to accumulate the data for the test point; thus the area and perimeter
* returned are less accurate than if geod_polygon_addedge() and
* geod_polygon_compute() are used.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] p a pointer to the geod_polygon object specifying the polygon.
* @param[in] azi azimuth at current point (degrees).
* @param[in] s distance from current point to final test point (meters).
* @param[in] reverse if non-zero then clockwise (instead of
* counter-clockwise) traversal counts as a positive area.
* @param[in] sign if non-zero then return a signed result for the area if
* the polygon is traversed in the "wrong" direction instead of returning
* the area for the rest of the earth.
* @param[out] pA pointer to the area of the polygon (meters2);
* only set if \e polyline is non-zero in the call to geod_polygon_init().
* @param[out] pP pointer to the perimeter of the polygon or length of the
* polyline (meters).
* @return the number of points.
**********************************************************************/
unsigned GEOD_DLL geod_polygon_testedge(const struct geod_geodesic* g,
const struct geod_polygon* p,
double azi, double s,
int reverse, int sign,
double* pA, double* pP);
/**
* A simple interface for computing the area of a geodesic polygon.
*
* @param[in] g a pointer to the geod_geodesic object specifying the
* ellipsoid.
* @param[in] lats an array of latitudes of the polygon vertices (degrees).
* @param[in] lons an array of longitudes of the polygon vertices (degrees).
* @param[in] n the number of vertices.
* @param[out] pA pointer to the area of the polygon (meters2).
* @param[out] pP pointer to the perimeter of the polygon (meters).
*
* \e lats should be in the range [−90°, 90°].
*
* Arbitrarily complex polygons are allowed. In the case self-intersecting
* of polygons the area is accumulated "algebraically", e.g., the areas of
* the 2 loops in a figure-8 polygon will partially cancel. There's no need
* to "close" the polygon by repeating the first vertex. The area returned
* is signed with counter-clockwise traversal being treated as positive.
*
* Example, compute the area of Antarctica:
@code{.c}
double
lats[] = {-72.9, -71.9, -74.9, -74.3, -77.5, -77.4, -71.7, -65.9, -65.7,
-66.6, -66.9, -69.8, -70.0, -71.0, -77.3, -77.9, -74.7},
lons[] = {-74, -102, -102, -131, -163, 163, 172, 140, 113,
88, 59, 25, -4, -14, -33, -46, -61};
struct geod_geodesic g;
double A, P;
geod_init(&g, 6378137, 1/298.257223563);
geod_polygonarea(&g, lats, lons, (sizeof lats) / (sizeof lats[0]), &A, &P);
printf("%.0f %.2f\n", A, P);
@endcode
**********************************************************************/
void GEOD_DLL geod_polygonarea(const struct geod_geodesic* g,
double lats[], double lons[], int n,
double* pA, double* pP);
/**
* mask values for the \e caps argument to geod_lineinit().
**********************************************************************/
enum geod_mask {
GEOD_NONE = 0U, /**< Calculate nothing */
GEOD_LATITUDE = 1U<<7 | 0U, /**< Calculate latitude */
GEOD_LONGITUDE = 1U<<8 | 1U<<3, /**< Calculate longitude */
GEOD_AZIMUTH = 1U<<9 | 0U, /**< Calculate azimuth */
GEOD_DISTANCE = 1U<<10 | 1U<<0, /**< Calculate distance */
GEOD_DISTANCE_IN = 1U<<11 | 1U<<0 | 1U<<1,/**< Allow distance as input */
GEOD_REDUCEDLENGTH= 1U<<12 | 1U<<0 | 1U<<2,/**< Calculate reduced length */
GEOD_GEODESICSCALE= 1U<<13 | 1U<<0 | 1U<<2,/**< Calculate geodesic scale */
GEOD_AREA = 1U<<14 | 1U<<4, /**< Calculate reduced length */
GEOD_ALL = 0x7F80U| 0x1FU /**< Calculate everything */
};
/**
* flag values for the \e flags argument to geod_gendirect() and
* geod_genposition()
**********************************************************************/
enum geod_flags {
GEOD_NOFLAGS = 0U, /**< No flags */
GEOD_ARCMODE = 1U<<0, /**< Position given in terms of arc distance */
GEOD_LONG_UNROLL = 1U<<15 /**< Unroll the longitude */
};
#if defined(__cplusplus)
}
#endif
#endif