/* See LICENSE file for copyright and license details. */ #ifndef LIBTELLURIAN_H #define LIBTELLURIAN_H #if defined(__GNUC__) # define LIBTELLURIAN_CONST__ __attribute__((__const__, __warn_unused_result__)) # define LIBTELLURIAN_WUR__ __attribute__((__warn_unused_result__)) #else # define LIBTELLURIAN_CONST__ # define LIBTELLURIAN_WUR__ #endif /** * The Earth's equatorial radius, in meters */ #define LIBTELLURIAN_EQUATORIAL_RADIUS 6378137.0 /* a */ /** * The Earth's polar radius, in meters */ #define LIBTELLURIAN_POLAR_RADIUS 6356752.314245 /* b */ /** * The Earth's mean radius (arithmetic mean), in meters */ #define LIBTELLURIAN_MEAN_RADIUS 6371008.771415 /* (2a + b) / 3 */ /** * The Earth's volumetric radius (geometric mean), in meters */ #define LIBTELLURIAN_VOLUMETRIC_RADIUS 6371000.7900090935 /* ∛(a² * b) */ /** * The Earth's authalic radius (equal-area mean), in meters */ #define LIBTELLURIAN_AUTHALIC_RADIUS 6371007.180918414 /* √(a²/2 + (b² artanh e) / 2e) */ /** * The Earth's rectifying radius, in meters */ #define LIBTELLURIAN_RECTIFYING_RADIUS 6367449.14582 /* 2π⁻¹∫{0 → ½π} √(a² cos² φ + b² sin² φ) dφ ≅ ∛(½(√a³+√b³))² */ /** * The Earth's nominal equatorial radius, in meters */ #define LIBTELLURIAN_NOMINAL_EQUATORIAL_RADIUS 6378100. /** * The Earth's nominal polar radius, in meters */ #define LIBTELLURIAN_NOMINAL_POLAR_RADIUS 6356800. /** * The Earth's nominal radius, in meters */ #define LIBTELLURIAN_NOMINAL_RADIUS LIBTELLURIAN_NOMINAL_EQUATORIAL_RADIUS /** * The Earth's equatorial circumference, in meters */ #define LIBTELLURIAN_EQUATORIAL_CIRCUMFERENCE 40075016.68557849 /* 2bπ */ /** * The Earth's meridional circumference, in meters */ #define LIBTELLURIAN_MERIDIONAL_CIRCUMFERENCE 39940652.74224401 /* 2bπ */ /** * The Earth's mean circumference (arithmetic mean), in meters */ #define LIBTELLURIAN_MEAN_CIRCUMFERENCE 40030228.70446699 /* 2π(2a + b) / 3 */ /** * The Earth's volumetric circumference (geometric mean), in meters */ #define LIBTELLURIAN_VOLUMETRIC_CIRCUMFERENCE 40030178.555814676 /* 2π∛(a² * b) */ /** * The Earth's authalic circumference (equal-area mean), in meters */ #define LIBTELLURIAN_AUTHALIC_CIRCUMFERENCE 40030218.71108221 /* 2π√(a²/2 + (b² artanh e) / 2e) */ /** * The Earth's rectifying circumference, in meters */ #define LIBTELLURIAN_RECTIFYING_CIRCUMFERENCE 40007862.91722943 /* 4 ∫{0 → ½π} √(a² cos² φ + b² sin² φ) dφ */ /** * The Earth's gravity at the equator, in meters per square-second */ #define LIBTELLURIAN_EQUATORIAL_GRAVITY 9.7803253359 /** * The Earth's gravity at the poles, in meters per square-second */ #define LIBTELLURIAN_POLAR_GRAVITY 9.8321849378 /** * The Earth's normal gravity at the equator, in meters per square-second */ #define LIBTELLURIAN_NORMAL_EQUATORIAL_GRAVITY 9.7803267715 /** * The Earth's normal gravity at the poles, in meters per square-second */ #define LIBTELLURIAN_NORMAL_POLAR_GRAVITY 9.8321863685 /** * The Earth's mass, in kilograms */ #define LIBTELLURIAN_MASS_OF_EARTH 5.972168e24 /** * Calculate the distance of the nominal sea level (geocentric * radius), for some point on the Earth's surface, from the * centre of the Earth * * @param latitude GPS latitude coordinate, in degrees * @return The geocentric altitude of the sea level, in meters */ LIBTELLURIAN_CONST__ double libtellurian_sea_level(double latitude); /** * Calculate the distance of the nominal sea level (geocentric * radius), for some point on the Earth's surface, from the * centre of the Earth * * @param latitude GPS latitude coordinate, in radians * @return The geocentric altitude of the sea level, in meters */ LIBTELLURIAN_CONST__ double libtellurian_sea_level_radians(double latitude); /** * Calculate the distance between two points on the Earth's surface * * This function is gives an approximate value using * a sphere as a model for the Earth * * @param latitude1 GPS latitude coordinate for the first point, in degrees * @param longitude1 GPS longitude coordinate for the first point, in degrees * @param latitude2 GPS latitude coordinate for the second point, in degrees * @param longitude2 GPS longitude coordinate for the second point, in degrees * @return Approximate distance between the two points */ LIBTELLURIAN_CONST__ double libtellurian_coarse_distance(double latitude1, double longitude1, double latitude2, double longitude2); /** * Calculate the distance between two points on the Earth's surface * * This function is gives an approximate value using * a sphere as a model for the Earth * * @param latitude1 GPS latitude coordinate for the first point, in radians * @param longitude1 GPS longitude coordinate for the first point, in radians * @param latitude2 GPS latitude coordinate for the second point, in radians * @param longitude2 GPS longitude coordinate for the second point, in radians * @return Approximate distance between the two points */ LIBTELLURIAN_CONST__ double libtellurian_coarse_distance_radians(double latitude1, double longitude1, double latitude2, double longitude2); /** * Calculate the distance and azimuths between two points on the Earth's surface * * This function is gives good approximate values * using an oblate spheroid as a model for the Earth * * @param latitude1 GPS latitude coordinate for the first point, in degrees * @param longitude1 GPS longitude coordinate for the first point, in degrees * @param latitude2 GPS latitude coordinate for the second point, in degrees * @param longitude2 GPS longitude coordinate for the second point, in degrees * @param azimuth1_out Output parameter for the forward azimuth, in degrees, * at the first point; or `NULL` * @param azimuth2_out Output parameter for the forward azimuth, in degrees, * at the second point; or `NULL` * @return Approximate distance between the two points * * Calculating the the forward azimuths is not free, but it * is cheap to compute them (especially the first one) when * most of the computations for the distance have been * performed. If you have no need for an azimuth you can set * the corresponding output parameter to `NULL`, and the * function will not compute it. */ LIBTELLURIAN_WUR__ double libtellurian_distance(double latitude1, double longitude1, double latitude2, double longitude2, double *azimuth1_out, double *azimuth2_out); /** * Calculate the distance and azimuths between two points on the Earth's surface * * This function is gives good approximate values * using an oblate spheroid as a model for the Earth * * @param latitude1 GPS latitude coordinate for the first point, in radians * @param longitude1 GPS longitude coordinate for the first point, in radians * @param latitude2 GPS latitude coordinate for the second point, in radians * @param longitude2 GPS longitude coordinate for the second point, in radians * @param azimuth1_out Output parameter for the forward azimuth, in radians, * at the first point; or `NULL` * @param azimuth2_out Output parameter for the forward azimuth, in radians, * at the second point; or `NULL` * @return Approximate distance between the two points * * Calculating the the forward azimuths is not free, but it * is cheap to compute them (especially the first one) when * most of the computations for the distance have been * performed. If you have no need for an azimuth you can set * the corresponding output parameter to `NULL`, and the * function will not compute it. */ LIBTELLURIAN_WUR__ double libtellurian_distance_radians(double latitude1, double longitude1, double latitude2, double longitude2, double *azimuth1_out, double *azimuth2_out); /** * Calculate the azimuths between two points on the Earth's surface * * This function is gives good approximate values * using an oblate spheroid as a model for the Earth * * @param latitude1 GPS latitude coordinate for the first point, in degrees * @param longitude1 GPS longitude coordinate for the first point, in degrees * @param latitude2 GPS latitude coordinate for the second point, in degrees * @param longitude2 GPS longitude coordinate for the second point, in degrees * @param azimuth1_out Output parameter for the forward azimuth, in degrees, * at the first point; or `NULL` * @param azimuth2_out Output parameter for the forward azimuth, in degrees, * at the second point; or `NULL` * * This function is identical to libtellurian_distance` * except it does not compute the distance between the * points */ void libtellurian_azimuth(double latitude1, double longitude1, double latitude2, double longitude2, double *azimuth1_out, double *azimuth2_out); /** * Calculate the azimuths between two points on the Earth's surface * * This function is gives good approximate values * using an oblate spheroid as a model for the Earth * * @param latitude1 GPS latitude coordinate for the first point, in radians * @param longitude1 GPS longitude coordinate for the first point, in radians * @param latitude2 GPS latitude coordinate for the second point, in radians * @param longitude2 GPS longitude coordinate for the second point, in radians * @param azimuth1_out Output parameter for the forward azimuth, in radians, * at the first point; or `NULL` * @param azimuth2_out Output parameter for the forward azimuth, in radians, * at the second point; or `NULL` * * * This function is identical to libtellurian_distance_radians` * except it does not compute the distance between the points */ void libtellurian_azimuth_radians(double latitude1, double longitude1, double latitude2, double longitude2, double *azimuth1_out, double *azimuth2_out); /** * Calculate the location that is some distance away, * in some direction, from some point * * @param latitude1 GPS latitude coordinate for the starting point, in degrees * @param longitude1 GPS longitude coordinate for the starting point, in degrees * @param azimuth1 The direction to travel, in degrees * @param distance The distance to travel, in meters * @param latitude2_out Output parameter for the end point's GPS latitude * coordinate, in degrees; or `NULL` * @param longitude2_out Output parameter for the end point's GPS longitude * coordinate, in degrees; or `NULL` * @param azimuth2_out Output parameter for the direction from the end point * to the starting point, in degrees; or `NULL` */ void libtellurian_end_point(double latitude1, double longitude1, double azimuth1, double distance, double *latitude2_out, double *longitude2_out, double *azimuth2_out); /** * Calculate the location that is some distance away, * in some direction, from some point * * @param latitude1 GPS latitude coordinate for the starting point, in radians * @param longitude1 GPS longitude coordinate for the starting point, in radians * @param azimuth1 The direction to travel, in radians * @param distance The distance to travel, in meters * @param latitude2_out Output parameter for the end point's GPS latitude * coordinate, in radians; or `NULL` * @param longitude2_out Output parameter for the end point's GPS longitude * coordinate, in radians; or `NULL` * @param azimuth2_out Output parameter for the direction from the end point * to the starting point, in radians; or `NULL` */ void libtellurian_end_point_radians(double latitude1, double longitude1, double azimuth1, double distance, double *latitude2_out, double *longitude2_out, double *azimuth2_out); /** * Calculate the normal gravity for some point on * the Earth's surface, where the Earth's is model * as an oblate spheroid * * @param latitude GPS latitude coordinate, in degrees * @return The normal gravity, in meters per square-second */ LIBTELLURIAN_CONST__ double libtellurian_normal_gravity(double latitude); /** * Calculate the normal gravity for some point on * the Earth's surface, where the Earth's is model * as an oblate spheroid * * @param latitude GPS latitude coordinate, in radians * @return The normal gravity, in meters per square-second */ LIBTELLURIAN_CONST__ double libtellurian_normal_gravity_radians(double latitude); /** * Calculate the gravity adjusted for the elevation * above the altitude where the gravity is measure * * Altitudes above circa 100000 meters is out of range * for this function (that would be in outer space) * * @param gravity The gravity at sea level, in meters per square-second * @param latitude GPS latitude coordinate, in degrees * @param altitude Elevation above the gravity's measurement point, in meters * @return The height-adjusted gravity, in meters per square-second */ LIBTELLURIAN_CONST__ double libtellurian_elevated_gravity(double gravity, double latitude, double altitude); /** * Calculate the gravity adjusted for the elevation * above the altitude where the gravity is measure * * Altitudes above circa 100000 meters is out of range * for this function (that would be in outer space) * * @param gravity The gravity at sea level, in meters per square-second * @param latitude GPS latitude coordinate, in radians * @param altitude Elevation above the gravity's measurement point, in meters * @return The height-adjusted gravity, in meters per square-second */ LIBTELLURIAN_CONST__ double libtellurian_elevated_gravity_radians(double gravity, double latitude, double altitude); /** * Calculate the Earth's meridan radius of curvature at some latitude * * @param latitude GPS latitude coordinate, in degrees * @return The meridan radius of curvature, in meters */ LIBTELLURIAN_CONST__ double libtellurian_meridan_radius(double latitude); /** * Calculate the Earth's meridan radius of curvature at some latitude * * @param latitude GPS latitude coordinate, in radians * @return The meridan radius of curvature, in meters */ LIBTELLURIAN_CONST__ double libtellurian_meridan_radius_radians(double latitude); /** * Calculate the Earth's transverse radius of curvature at some latitude * * @param latitude GPS latitude coordinate, in degrees * @return The transverse radius of curvature, in meters */ LIBTELLURIAN_CONST__ double libtellurian_transverse_radius(double latitude); /** * Calculate the Earth's transverse radius of curvature at some latitude * * @param latitude GPS latitude coordinate, in radians * @return The transverse radius of curvature, in meters */ LIBTELLURIAN_CONST__ double libtellurian_transverse_radius_radians(double latitude); /** * Calculate the Earth's azimuthal radius of curvature * at some latitude for some azimuth * * @param latitude GPS latitude coordinate, in degrees * @param azimuth The azimuth, in degrees * @return The transverse radius of curvature, in meters */ LIBTELLURIAN_CONST__ double libtellurian_azimuthal_radius(double latitude, double azimuth); /** * Calculate the Earth's azimuthal radius of curvature * at some latitude for some azimuth * * @param latitude GPS latitude coordinate, in radians * @param azimuth The azimuth, in radians * @return The transverse radius of curvature, in meters */ LIBTELLURIAN_CONST__ double libtellurian_azimuthal_radius_radians(double latitude, double azimuth); /** * Calculate the Earth's Gaussian radius of curvature at some latitude * * @param latitude GPS latitude coordinate, in degrees * @return The Gaussian radius of curvature, in meters */ LIBTELLURIAN_CONST__ double libtellurian_gaussian_radius(double latitude); /** * Calculate the Earth's Gaussian radius of curvature at some latitude * * @param latitude GPS latitude coordinate, in radians * @return The Gaussian radius of curvature, in meters */ LIBTELLURIAN_CONST__ double libtellurian_gaussian_radius_radians(double latitude); #undef LIBTELLURIAN_CONST__ #undef LIBTELLURIAN_WUR__ #endif