/src/h3/src/h3lib/lib/latLng.c

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/*
 * Copyright 2016-2021 Uber Technologies, Inc.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *         http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
/** @file latLng.c
 * @brief   Functions for working with lat/lng coordinates.
 */

#include "latLng.h"

#include <math.h>
#include <stdbool.h>

#include "constants.h"
#include "h3Assert.h"
#include "h3api.h"
#include "mathExtensions.h"

/**
 * Normalizes radians to a value between 0.0 and two PI.
 *
 * @param rads The input radians value.
 * @return The normalized radians value.
 */
double _posAngleRads(double rads) {
    double tmp = ((rads < 0.0L) ? rads + M_2PI : rads);
    if (rads >= M_2PI) tmp -= M_2PI;
    return tmp;
}

/**
 * Determines if the components of two spherical coordinates are within some
 * threshold distance of each other.
 *
 * @param p1 The first spherical coordinates.
 * @param p2 The second spherical coordinates.
 * @param threshold The threshold distance.
 * @return Whether or not the two coordinates are within the threshold distance
 *         of each other.
 */
bool geoAlmostEqualThreshold(const LatLng *p1, const LatLng *p2,
                             double threshold) {
    return fabs(p1->lat - p2->lat) < threshold &&
           fabs(p1->lng - p2->lng) < threshold;
}

/**
 * Determines if the components of two spherical coordinates are within our
 * standard epsilon distance of each other.
 *
 * @param p1 The first spherical coordinates.
 * @param p2 The second spherical coordinates.
 * @return Whether or not the two coordinates are within the epsilon distance
 *         of each other.
 */
bool geoAlmostEqual(const LatLng *p1, const LatLng *p2) {
    return geoAlmostEqualThreshold(p1, p2, EPSILON_RAD);
}

/**
 * Set the components of spherical coordinates in decimal degrees.
 *
 * @param p The spherical coordinates.
 * @param latDegs The desired latitude in decimal degrees.
 * @param lngDegs The desired longitude in decimal degrees.
 */
void setGeoDegs(LatLng *p, double latDegs, double lngDegs) {
    _setGeoRads(p, H3_EXPORT(degsToRads)(latDegs),
                H3_EXPORT(degsToRads)(lngDegs));
}

/**
 * Set the components of spherical coordinates in radians.
 *
 * @param p The spherical coordinates.
 * @param latRads The desired latitude in decimal radians.
 * @param lngRads The desired longitude in decimal radians.
 */
void _setGeoRads(LatLng *p, double latRads, double lngRads) {
    p->lat = latRads;
    p->lng = lngRads;
}

/**
 * Convert from decimal degrees to radians.
 *
 * @param degrees The decimal degrees.
 * @return The corresponding radians.
 */
double H3_EXPORT(degsToRads)(double degrees) { return degrees * M_PI_180; }

/**
 * Convert from radians to decimal degrees.
 *
 * @param radians The radians.
 * @return The corresponding decimal degrees.
 */
double H3_EXPORT(radsToDegs)(double radians) { return radians * M_180_PI; }

/**
 * constrainLat makes sure latitudes are in the proper bounds
 *
 * @param lat The original lat value
 * @return The corrected lat value
 */
double constrainLat(double lat) {
    while (lat > M_PI_2) {
        lat = lat - M_PI;
    }
    return lat;
}

/**
 * constrainLng makes sure longitudes are in the proper bounds
 *
 * @param lng The origin lng value
 * @return The corrected lng value
 */
double constrainLng(double lng) {
    while (lng > M_PI) {
        lng = lng - (2 * M_PI);
    }
    while (lng < -M_PI) {
        lng = lng + (2 * M_PI);
    }
    return lng;
}

/**
 * The great circle distance in radians between two spherical coordinates.
 *
 * This function uses the Haversine formula.
 * For math details, see:
 *     https://en.wikipedia.org/wiki/Haversine_formula
 *     https://www.movable-type.co.uk/scripts/latlong.html
 *
 * @param  a  the first lat/lng pair (in radians)
 * @param  b  the second lat/lng pair (in radians)
 *
 * @return    the great circle distance in radians between a and b
 */
double H3_EXPORT(greatCircleDistanceRads)(const LatLng *a, const LatLng *b) {
    double sinLat = sin((b->lat - a->lat) / 2.0);
    double sinLng = sin((b->lng - a->lng) / 2.0);

    double A = sinLat * sinLat + cos(a->lat) * cos(b->lat) * sinLng * sinLng;

    return 2 * atan2(sqrt(A), sqrt(1 - A));
}

/**
 * The great circle distance in kilometers between two spherical coordinates.
 */
double H3_EXPORT(greatCircleDistanceKm)(const LatLng *a, const LatLng *b) {
    return H3_EXPORT(greatCircleDistanceRads)(a, b) * EARTH_RADIUS_KM;
}

/**
 * The great circle distance in meters between two spherical coordinates.
 */
double H3_EXPORT(greatCircleDistanceM)(const LatLng *a, const LatLng *b) {
    return H3_EXPORT(greatCircleDistanceKm)(a, b) * 1000;
}

/**
 * Determines the azimuth to p2 from p1 in radians.
 *
 * @param p1 The first spherical coordinates.
 * @param p2 The second spherical coordinates.
 * @return The azimuth in radians from p1 to p2.
 */
double _geoAzimuthRads(const LatLng *p1, const LatLng *p2) {
    return atan2(cos(p2->lat) * sin(p2->lng - p1->lng),
                 cos(p1->lat) * sin(p2->lat) -
                     sin(p1->lat) * cos(p2->lat) * cos(p2->lng - p1->lng));
}

/**
 * Computes the point on the sphere a specified azimuth and distance from
 * another point.
 *
 * @param p1 The first spherical coordinates.
 * @param az The desired azimuth from p1.
 * @param distance The desired distance from p1, must be non-negative.
 * @param p2 The spherical coordinates at the desired azimuth and distance from
 * p1.
 */
void _geoAzDistanceRads(const LatLng *p1, double az, double distance,
                        LatLng *p2) {
    if (distance < EPSILON) {
        *p2 = *p1;
        return;
    }

    double sinlat, sinlng, coslng;

    az = _posAngleRads(az);

    // check for due north/south azimuth
    if (az < EPSILON || fabs(az - M_PI) < EPSILON) {
        if (az < EPSILON)  // due north
            p2->lat = p1->lat + distance;
        else  // due south
            p2->lat = p1->lat - distance;

        if (fabs(p2->lat - M_PI_2) < EPSILON)  // north pole
        {
            p2->lat = M_PI_2;
            p2->lng = 0.0;
        } else if (fabs(p2->lat + M_PI_2) < EPSILON)  // south pole
        {
            p2->lat = -M_PI_2;
            p2->lng = 0.0;
        } else
            p2->lng = constrainLng(p1->lng);
    } else  // not due north or south
    {
        sinlat = sin(p1->lat) * cos(distance) +
                 cos(p1->lat) * sin(distance) * cos(az);
        if (sinlat > 1.0) sinlat = 1.0;
        if (sinlat < -1.0) sinlat = -1.0;
        p2->lat = asin(sinlat);
        if (fabs(p2->lat - M_PI_2) < EPSILON)  // north pole
        {
            p2->lat = M_PI_2;
            p2->lng = 0.0;
        } else if (fabs(p2->lat + M_PI_2) < EPSILON)  // south pole
        {
            p2->lat = -M_PI_2;
            p2->lng = 0.0;
        } else {
            sinlng = sin(az) * sin(distance) / cos(p2->lat);
            coslng = (cos(distance) - sin(p1->lat) * sin(p2->lat)) /
                     cos(p1->lat) / cos(p2->lat);
            if (sinlng > 1.0) sinlng = 1.0;
            if (sinlng < -1.0) sinlng = -1.0;
            if (coslng > 1.0) coslng = 1.0;
            if (coslng < -1.0) coslng = -1.0;
            p2->lng = constrainLng(p1->lng + atan2(sinlng, coslng));
        }
    }
}

/*
 * The following functions provide meta information about the H3 hexagons at
 * each zoom level. Since there are only 16 total levels, these are current
 * handled with hardwired static values, but it may be worthwhile to put these
 * static values into another file that can be autogenerated by source code in
 * the future.
 */

H3Error H3_EXPORT(getHexagonAreaAvgKm2)(int res, double *out) {
    static const double areas[] = {
        4.357449416078383e+06, 6.097884417941332e+05, 8.680178039899720e+04,
        1.239343465508816e+04, 1.770347654491307e+03, 2.529038581819449e+02,
        3.612906216441245e+01, 5.161293359717191e+00, 7.373275975944177e-01,
        1.053325134272067e-01, 1.504750190766435e-02, 2.149643129451879e-03,
        3.070918756316060e-04, 4.387026794728296e-05, 6.267181135324313e-06,
        8.953115907605790e-07};
    if (res < 0 || res > MAX_H3_RES) {
        return E_RES_DOMAIN;
    }
    *out = areas[res];
    return E_SUCCESS;
}

H3Error H3_EXPORT(getHexagonAreaAvgM2)(int res, double *out) {
    static const double areas[] = {
        4.357449416078390e+12, 6.097884417941339e+11, 8.680178039899731e+10,
        1.239343465508818e+10, 1.770347654491309e+09, 2.529038581819452e+08,
        3.612906216441250e+07, 5.161293359717198e+06, 7.373275975944188e+05,
        1.053325134272069e+05, 1.504750190766437e+04, 2.149643129451882e+03,
        3.070918756316063e+02, 4.387026794728301e+01, 6.267181135324322e+00,
        8.953115907605802e-01};
    if (res < 0 || res > MAX_H3_RES) {
        return E_RES_DOMAIN;
    }
    *out = areas[res];
    return E_SUCCESS;
}

H3Error H3_EXPORT(getHexagonEdgeLengthAvgKm)(int res, double *out) {
    static const double lens[] = {
        1281.256011, 483.0568391, 182.5129565, 68.97922179,
        26.07175968, 9.854090990, 3.724532667, 1.406475763,
        0.531414010, 0.200786148, 0.075863783, 0.028663897,
        0.010830188, 0.004092010, 0.001546100, 0.000584169};
    if (res < 0 || res > MAX_H3_RES) {
        return E_RES_DOMAIN;
    }
    *out = lens[res];
    return E_SUCCESS;
}

H3Error H3_EXPORT(getHexagonEdgeLengthAvgM)(int res, double *out) {
    static const double lens[] = {
        1281256.011, 483056.8391, 182512.9565, 68979.22179,
        26071.75968, 9854.090990, 3724.532667, 1406.475763,
        531.4140101, 200.7861476, 75.86378287, 28.66389748,
        10.83018784, 4.092010473, 1.546099657, 0.584168630};
    if (res < 0 || res > MAX_H3_RES) {
        return E_RES_DOMAIN;
    }
    *out = lens[res];
    return E_SUCCESS;
}

H3Error H3_EXPORT(getNumCells)(int res, int64_t *out) {
    if (res < 0 || res > MAX_H3_RES) {
        return E_RES_DOMAIN;
    }
    *out = 2 + 120 * _ipow(7, res);
    return E_SUCCESS;
}

/**
 * Surface area in radians^2 of spherical triangle on unit sphere.
 *
 * For the math, see:
 * https://en.wikipedia.org/wiki/Spherical_trigonometry#Area_and_spherical_excess
 *
 * @param   a  length of triangle side A in radians
 * @param   b  length of triangle side B in radians
 * @param   c  length of triangle side C in radians
 *
 * @return     area in radians^2 of triangle on unit sphere
 */
double triangleEdgeLengthsToArea(double a, double b, double c) {
    double s = (a + b + c) / 2;

    a = (s - a) / 2;
    b = (s - b) / 2;
    c = (s - c) / 2;
    s = s / 2;

    return 4 * atan(sqrt(tan(s) * tan(a) * tan(b) * tan(c)));
}

/**
 * Compute area in radians^2 of a spherical triangle, given its vertices.
 *
 * @param   a  vertex lat/lng in radians
 * @param   b  vertex lat/lng in radians
 * @param   c  vertex lat/lng in radians
 *
 * @return     area of triangle on unit sphere, in radians^2
 */
double triangleArea(const LatLng *a, const LatLng *b, const LatLng *c) {
    return triangleEdgeLengthsToArea(H3_EXPORT(greatCircleDistanceRads)(a, b),
                                     H3_EXPORT(greatCircleDistanceRads)(b, c),
                                     H3_EXPORT(greatCircleDistanceRads)(c, a));
}

/**
 * Area of H3 cell in radians^2.
 *
 * The area is calculated by breaking the cell into spherical triangles and
 * summing up their areas. Note that some H3 cells (hexagons and pentagons)
 * are irregular, and have more than 6 or 5 sides.
 *
 * todo: optimize the computation by re-using the edges shared between triangles
 *
 * @param   cell  H3 cell
 * @param    out  cell area in radians^2
 * @return        E_SUCCESS on success, or an error code otherwise
 */
H3Error H3_EXPORT(cellAreaRads2)(H3Index cell, double *out) {
    LatLng c;
    CellBoundary cb;
    H3Error err = H3_EXPORT(cellToLatLng)(cell, &c);
    if (err) {
        return err;
    }
    err = H3_EXPORT(cellToBoundary)(cell, &cb);
    if (NEVER(err)) {
        // Uncoverable because cellToLatLng will have returned an error already
        return err;
    }

    double area = 0.0;
    for (int i = 0; i < cb.numVerts; i++) {
        int j = (i + 1) % cb.numVerts;
        area += triangleArea(&cb.verts[i], &cb.verts[j], &c);
    }

    *out = area;
    return E_SUCCESS;
}

/**
 * Area of H3 cell in kilometers^2.
 */
H3Error H3_EXPORT(cellAreaKm2)(H3Index cell, double *out) {
    H3Error err = H3_EXPORT(cellAreaRads2)(cell, out);
    if (!err) {
        *out = *out * EARTH_RADIUS_KM * EARTH_RADIUS_KM;
    }
    return err;
}

/**
 * Area of H3 cell in meters^2.
 */
H3Error H3_EXPORT(cellAreaM2)(H3Index cell, double *out) {
    H3Error err = H3_EXPORT(cellAreaKm2)(cell, out);
    if (!err) {
        *out = *out * 1000 * 1000;
    }
    return err;
}

/**
 * Length of a directed edge in radians.
 *
 * @param   edge  H3 directed edge
 *
 * @return        length in radians
 */
H3Error H3_EXPORT(edgeLengthRads)(H3Index edge, double *length) {
    CellBoundary cb;

    H3Error err = H3_EXPORT(directedEdgeToBoundary)(edge, &cb);
    if (err) {
        return err;
    }

    *length = 0.0;
    for (int i = 0; i < cb.numVerts - 1; i++) {
        *length +=
            H3_EXPORT(greatCircleDistanceRads)(&cb.verts[i], &cb.verts[i + 1]);
    }

    return E_SUCCESS;
}

/**
 * Length of a directed edge in kilometers.
 */
H3Error H3_EXPORT(edgeLengthKm)(H3Index edge, double *length) {
    H3Error err = H3_EXPORT(edgeLengthRads)(edge, length);
    *length = *length * EARTH_RADIUS_KM;
    return err;
}

/**
 * Length of a directed edge in meters.
 */
H3Error H3_EXPORT(edgeLengthM)(H3Index edge, double *length) {
    H3Error err = H3_EXPORT(edgeLengthKm)(edge, length);
    *length = *length * 1000;
    return err;
}

Coverage Report

Created: 2023-09-25 06:55

Line	Count	Source (jump to first uncovered line)
1		/*
2		* Copyright 2016-2021 Uber Technologies, Inc.
3		*
4		* Licensed under the Apache License, Version 2.0 (the "License");
5		* you may not use this file except in compliance with the License.
6		* You may obtain a copy of the License at
7		*
8		* http://www.apache.org/licenses/LICENSE-2.0
9		*
10		* Unless required by applicable law or agreed to in writing, software
11		* distributed under the License is distributed on an "AS IS" BASIS,
12		* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13		* See the License for the specific language governing permissions and
14		* limitations under the License.
15		*/
16		/** @file latLng.c
17		* @brief Functions for working with lat/lng coordinates.
18		*/
19
20		#include "latLng.h"
21
22		#include <math.h>
23		#include <stdbool.h>
24
25		#include "constants.h"
26		#include "h3Assert.h"
27		#include "h3api.h"
28		#include "mathExtensions.h"
29
30		/**
31		* Normalizes radians to a value between 0.0 and two PI.
32		*
33		* @param rads The input radians value.
34		* @return The normalized radians value.
35		*/
36	138M	double _posAngleRads(double rads) {
37	138M	double tmp = ((rads < 0.0L) ? rads + M_2PI : rads);
38	138M	if (rads >= M_2PI) tmp -= M_2PI;
39	138M	return tmp;
40	138M	}
41
42		/**
43		* Determines if the components of two spherical coordinates are within some
44		* threshold distance of each other.
45		*
46		* @param p1 The first spherical coordinates.
47		* @param p2 The second spherical coordinates.
48		* @param threshold The threshold distance.
49		* @return Whether or not the two coordinates are within the threshold distance
50		* of each other.
51		*/
52		bool geoAlmostEqualThreshold(const LatLng p1, const LatLng p2,
53	0	double threshold) {
54	0	return fabs(p1->lat - p2->lat) < threshold &&
55	0	fabs(p1->lng - p2->lng) < threshold;
56	0	}
57
58		/**
59		* Determines if the components of two spherical coordinates are within our
60		* standard epsilon distance of each other.
61		*
62		* @param p1 The first spherical coordinates.
63		* @param p2 The second spherical coordinates.
64		* @return Whether or not the two coordinates are within the epsilon distance
65		* of each other.
66		*/
67	0	bool geoAlmostEqual(const LatLng p1, const LatLng p2) {
68	0	return geoAlmostEqualThreshold(p1, p2, EPSILON_RAD);
69	0	}
70
71		/**
72		* Set the components of spherical coordinates in decimal degrees.
73		*
74		* @param p The spherical coordinates.
75		* @param latDegs The desired latitude in decimal degrees.
76		* @param lngDegs The desired longitude in decimal degrees.
77		*/
78	0	void setGeoDegs(LatLng *p, double latDegs, double lngDegs) {
79	0	_setGeoRads(p, H3_EXPORT(degsToRads)(latDegs),
80	0	H3_EXPORT(degsToRads)(lngDegs));
81	0	}
82
83		/**
84		* Set the components of spherical coordinates in radians.
85		*
86		* @param p The spherical coordinates.
87		* @param latRads The desired latitude in decimal radians.
88		* @param lngRads The desired longitude in decimal radians.
89		*/
90	0	void _setGeoRads(LatLng *p, double latRads, double lngRads) {
91	0	p->lat = latRads;
92	0	p->lng = lngRads;
93	0	}
94
95		/**
96		* Convert from decimal degrees to radians.
97		*
98		* @param degrees The decimal degrees.
99		* @return The corresponding radians.
100		*/
101	0	double H3_EXPORT(degsToRads)(double degrees) { return degrees * M_PI_180; }
102
103		/**
104		* Convert from radians to decimal degrees.
105		*
106		* @param radians The radians.
107		* @return The corresponding decimal degrees.
108		*/
109	0	double H3_EXPORT(radsToDegs)(double radians) { return radians * M_180_PI; }
110
111		/**
112		* constrainLat makes sure latitudes are in the proper bounds
113		*
114		* @param lat The original lat value
115		* @return The corrected lat value
116		*/
117	0	double constrainLat(double lat) {
118	0	while (lat > M_PI_2) {
119	0	lat = lat - M_PI;
120	0	}
121	0	return lat;
122	0	}
123
124		/**
125		* constrainLng makes sure longitudes are in the proper bounds
126		*
127		* @param lng The origin lng value
128		* @return The corrected lng value
129		*/
130	39.6M	double constrainLng(double lng) {
131	40.9M	while (lng > M_PI) {
132	1.37M	lng = lng - (2 * M_PI);
133	1.37M	}
134	40.0M	while (lng < -M_PI) {
135	438k	lng = lng + (2 * M_PI);
136	438k	}
137	39.6M	return lng;
138	39.6M	}
139
140		/**
141		* The great circle distance in radians between two spherical coordinates.
142		*
143		* This function uses the Haversine formula.
144		* For math details, see:
145		* https://en.wikipedia.org/wiki/Haversine_formula
146		* https://www.movable-type.co.uk/scripts/latlong.html
147		*
148		* @param a the first lat/lng pair (in radians)
149		* @param b the second lat/lng pair (in radians)
150		*
151		* @return the great circle distance in radians between a and b
152		*/
153	1.18M	double H3_EXPORT(greatCircleDistanceRads)(const LatLng a, const LatLng b) {
154	1.18M	double sinLat = sin((b->lat - a->lat) / 2.0);
155	1.18M	double sinLng = sin((b->lng - a->lng) / 2.0);
156
157	1.18M	double A = sinLat * sinLat + cos(a->lat) * cos(b->lat) * sinLng * sinLng;
158
159	1.18M	return 2 * atan2(sqrt(A), sqrt(1 - A));
160	1.18M	}
161
162		/**
163		* The great circle distance in kilometers between two spherical coordinates.
164		*/
165	1.18M	double H3_EXPORT(greatCircleDistanceKm)(const LatLng a, const LatLng b) {
166	1.18M	return H3_EXPORT(greatCircleDistanceRads)(a, b) * EARTH_RADIUS_KM;
167	1.18M	}
168
169		/**
170		* The great circle distance in meters between two spherical coordinates.
171		*/
172	0	double H3_EXPORT(greatCircleDistanceM)(const LatLng a, const LatLng b) {
173	0	return H3_EXPORT(greatCircleDistanceKm)(a, b) * 1000;
174	0	}
175
176		/**
177		* Determines the azimuth to p2 from p1 in radians.
178		*
179		* @param p1 The first spherical coordinates.
180		* @param p2 The second spherical coordinates.
181		* @return The azimuth in radians from p1 to p2.
182		*/
183	10.1M	double _geoAzimuthRads(const LatLng p1, const LatLng p2) {
184	10.1M	return atan2(cos(p2->lat) * sin(p2->lng - p1->lng),
185	10.1M	cos(p1->lat) * sin(p2->lat) -
186	10.1M	sin(p1->lat) * cos(p2->lat) * cos(p2->lng - p1->lng));
187	10.1M	}
188
189		/**
190		* Computes the point on the sphere a specified azimuth and distance from
191		* another point.
192		*
193		* @param p1 The first spherical coordinates.
194		* @param az The desired azimuth from p1.
195		* @param distance The desired distance from p1, must be non-negative.
196		* @param p2 The spherical coordinates at the desired azimuth and distance from
197		* p1.
198		*/
199		void _geoAzDistanceRads(const LatLng *p1, double az, double distance,
200	39.6M	LatLng *p2) {
201	39.6M	if (distance < EPSILON) {
202	0	p2 = p1;
203	0	return;
204	0	}
205
206	39.6M	double sinlat, sinlng, coslng;
207
208	39.6M	az = _posAngleRads(az);
209
210		// check for due north/south azimuth
211	39.6M	if (az < EPSILON \|\| fabs(az - M_PI) < EPSILON) {
212	0	if (az < EPSILON) // due north
213	0	p2->lat = p1->lat + distance;
214	0	else // due south
215	0	p2->lat = p1->lat - distance;
216
217	0	if (fabs(p2->lat - M_PI_2) < EPSILON) // north pole
218	0	{
219	0	p2->lat = M_PI_2;
220	0	p2->lng = 0.0;
221	0	} else if (fabs(p2->lat + M_PI_2) < EPSILON) // south pole
222	0	{
223	0	p2->lat = -M_PI_2;
224	0	p2->lng = 0.0;
225	0	} else
226	0	p2->lng = constrainLng(p1->lng);
227	0	} else // not due north or south
228	39.6M	{
229	39.6M	sinlat = sin(p1->lat) * cos(distance) +
230	39.6M	cos(p1->lat) * sin(distance) * cos(az);
231	39.6M	if (sinlat > 1.0) sinlat = 1.0;
232	39.6M	if (sinlat < -1.0) sinlat = -1.0;
233	39.6M	p2->lat = asin(sinlat);
234	39.6M	if (fabs(p2->lat - M_PI_2) < EPSILON) // north pole
235	0	{
236	0	p2->lat = M_PI_2;
237	0	p2->lng = 0.0;
238	39.6M	} else if (fabs(p2->lat + M_PI_2) < EPSILON) // south pole
239	0	{
240	0	p2->lat = -M_PI_2;
241	0	p2->lng = 0.0;
242	39.6M	} else {
243	39.6M	sinlng = sin(az) * sin(distance) / cos(p2->lat);
244	39.6M	coslng = (cos(distance) - sin(p1->lat) * sin(p2->lat)) /
245	39.6M	cos(p1->lat) / cos(p2->lat);
246	39.6M	if (sinlng > 1.0) sinlng = 1.0;
247	39.6M	if (sinlng < -1.0) sinlng = -1.0;
248	39.6M	if (coslng > 1.0) coslng = 1.0;
249	39.6M	if (coslng < -1.0) coslng = -1.0;
250	39.6M	p2->lng = constrainLng(p1->lng + atan2(sinlng, coslng));
251	39.6M	}
252	39.6M	}
253	39.6M	}
254
255		/*
256		* The following functions provide meta information about the H3 hexagons at
257		* each zoom level. Since there are only 16 total levels, these are current
258		* handled with hardwired static values, but it may be worthwhile to put these
259		* static values into another file that can be autogenerated by source code in
260		* the future.
261		*/
262
263	0	H3Error H3_EXPORT(getHexagonAreaAvgKm2)(int res, double *out) {
264	0	static const double areas[] = {
265	0	4.357449416078383e+06, 6.097884417941332e+05, 8.680178039899720e+04,
266	0	1.239343465508816e+04, 1.770347654491307e+03, 2.529038581819449e+02,
267	0	3.612906216441245e+01, 5.161293359717191e+00, 7.373275975944177e-01,
268	0	1.053325134272067e-01, 1.504750190766435e-02, 2.149643129451879e-03,
269	0	3.070918756316060e-04, 4.387026794728296e-05, 6.267181135324313e-06,
270	0	8.953115907605790e-07};
271	0	if (res < 0 \|\| res > MAX_H3_RES) {
272	0	return E_RES_DOMAIN;
273	0	}
274	0	*out = areas[res];
275	0	return E_SUCCESS;
276	0	}
277
278	0	H3Error H3_EXPORT(getHexagonAreaAvgM2)(int res, double *out) {
279	0	static const double areas[] = {
280	0	4.357449416078390e+12, 6.097884417941339e+11, 8.680178039899731e+10,
281	0	1.239343465508818e+10, 1.770347654491309e+09, 2.529038581819452e+08,
282	0	3.612906216441250e+07, 5.161293359717198e+06, 7.373275975944188e+05,
283	0	1.053325134272069e+05, 1.504750190766437e+04, 2.149643129451882e+03,
284	0	3.070918756316063e+02, 4.387026794728301e+01, 6.267181135324322e+00,
285	0	8.953115907605802e-01};
286	0	if (res < 0 \|\| res > MAX_H3_RES) {
287	0	return E_RES_DOMAIN;
288	0	}
289	0	*out = areas[res];
290	0	return E_SUCCESS;
291	0	}
292
293	0	H3Error H3_EXPORT(getHexagonEdgeLengthAvgKm)(int res, double *out) {
294	0	static const double lens[] = {
295	0	1281.256011, 483.0568391, 182.5129565, 68.97922179,
296	0	26.07175968, 9.854090990, 3.724532667, 1.406475763,
297	0	0.531414010, 0.200786148, 0.075863783, 0.028663897,
298	0	0.010830188, 0.004092010, 0.001546100, 0.000584169};
299	0	if (res < 0 \|\| res > MAX_H3_RES) {
300	0	return E_RES_DOMAIN;
301	0	}
302	0	*out = lens[res];
303	0	return E_SUCCESS;
304	0	}
305
306	0	H3Error H3_EXPORT(getHexagonEdgeLengthAvgM)(int res, double *out) {
307	0	static const double lens[] = {
308	0	1281256.011, 483056.8391, 182512.9565, 68979.22179,
309	0	26071.75968, 9854.090990, 3724.532667, 1406.475763,
310	0	531.4140101, 200.7861476, 75.86378287, 28.66389748,
311	0	10.83018784, 4.092010473, 1.546099657, 0.584168630};
312	0	if (res < 0 \|\| res > MAX_H3_RES) {
313	0	return E_RES_DOMAIN;
314	0	}
315	0	*out = lens[res];
316	0	return E_SUCCESS;
317	0	}
318
319	0	H3Error H3_EXPORT(getNumCells)(int res, int64_t *out) {
320	0	if (res < 0 \|\| res > MAX_H3_RES) {
321	0	return E_RES_DOMAIN;
322	0	}
323	0	out = 2 + 120 _ipow(7, res);
324	0	return E_SUCCESS;
325	0	}
326
327		/**
328		* Surface area in radians^2 of spherical triangle on unit sphere.
329		*
330		* For the math, see:
331		* https://en.wikipedia.org/wiki/Spherical_trigonometry#Area_and_spherical_excess
332		*
333		* @param a length of triangle side A in radians
334		* @param b length of triangle side B in radians
335		* @param c length of triangle side C in radians
336		*
337		* @return area in radians^2 of triangle on unit sphere
338		*/
339	0	double triangleEdgeLengthsToArea(double a, double b, double c) {
340	0	double s = (a + b + c) / 2;
341
342	0	a = (s - a) / 2;
343	0	b = (s - b) / 2;
344	0	c = (s - c) / 2;
345	0	s = s / 2;
346
347	0	return 4 * atan(sqrt(tan(s) * tan(a) * tan(b) * tan(c)));
348	0	}
349
350		/**
351		* Compute area in radians^2 of a spherical triangle, given its vertices.
352		*
353		* @param a vertex lat/lng in radians
354		* @param b vertex lat/lng in radians
355		* @param c vertex lat/lng in radians
356		*
357		* @return area of triangle on unit sphere, in radians^2
358		*/
359	0	double triangleArea(const LatLng a, const LatLng b, const LatLng *c) {
360	0	return triangleEdgeLengthsToArea(H3_EXPORT(greatCircleDistanceRads)(a, b),
361	0	H3_EXPORT(greatCircleDistanceRads)(b, c),
362	0	H3_EXPORT(greatCircleDistanceRads)(c, a));
363	0	}
364
365		/**
366		* Area of H3 cell in radians^2.
367		*
368		* The area is calculated by breaking the cell into spherical triangles and
369		* summing up their areas. Note that some H3 cells (hexagons and pentagons)
370		* are irregular, and have more than 6 or 5 sides.
371		*
372		* todo: optimize the computation by re-using the edges shared between triangles
373		*
374		* @param cell H3 cell
375		* @param out cell area in radians^2
376		* @return E_SUCCESS on success, or an error code otherwise
377		*/
378	0	H3Error H3_EXPORT(cellAreaRads2)(H3Index cell, double *out) {
379	0	LatLng c;
380	0	CellBoundary cb;
381	0	H3Error err = H3_EXPORT(cellToLatLng)(cell, &c);
382	0	if (err) {
383	0	return err;
384	0	}
385	0	err = H3_EXPORT(cellToBoundary)(cell, &cb);
386	0	if (NEVER(err)) {
387		// Uncoverable because cellToLatLng will have returned an error already
388	0	return err;
389	0	}
390
391	0	double area = 0.0;
392	0	for (int i = 0; i < cb.numVerts; i++) {
393	0	int j = (i + 1) % cb.numVerts;
394	0	area += triangleArea(&cb.verts[i], &cb.verts[j], &c);
395	0	}
396
397	0	*out = area;
398	0	return E_SUCCESS;
399	0	}
400
401		/**
402		* Area of H3 cell in kilometers^2.
403		*/
404	0	H3Error H3_EXPORT(cellAreaKm2)(H3Index cell, double *out) {
405	0	H3Error err = H3_EXPORT(cellAreaRads2)(cell, out);
406	0	if (!err) {
407	0	out = out * EARTH_RADIUS_KM * EARTH_RADIUS_KM;
408	0	}
409	0	return err;
410	0	}
411
412		/**
413		* Area of H3 cell in meters^2.
414		*/
415	0	H3Error H3_EXPORT(cellAreaM2)(H3Index cell, double *out) {
416	0	H3Error err = H3_EXPORT(cellAreaKm2)(cell, out);
417	0	if (!err) {
418	0	out = out * 1000 * 1000;
419	0	}
420	0	return err;
421	0	}
422
423		/**
424		* Length of a directed edge in radians.
425		*
426		* @param edge H3 directed edge
427		*
428		* @return length in radians
429		*/
430	0	H3Error H3_EXPORT(edgeLengthRads)(H3Index edge, double *length) {
431	0	CellBoundary cb;
432
433	0	H3Error err = H3_EXPORT(directedEdgeToBoundary)(edge, &cb);
434	0	if (err) {
435	0	return err;
436	0	}
437
438	0	*length = 0.0;
439	0	for (int i = 0; i < cb.numVerts - 1; i++) {
440	0	*length +=
441	0	H3_EXPORT(greatCircleDistanceRads)(&cb.verts[i], &cb.verts[i + 1]);
442	0	}
443
444	0	return E_SUCCESS;
445	0	}
446
447		/**
448		* Length of a directed edge in kilometers.
449		*/
450	0	H3Error H3_EXPORT(edgeLengthKm)(H3Index edge, double *length) {
451	0	H3Error err = H3_EXPORT(edgeLengthRads)(edge, length);
452	0	length = length * EARTH_RADIUS_KM;
453	0	return err;
454	0	}
455
456		/**
457		* Length of a directed edge in meters.
458		*/
459	0	H3Error H3_EXPORT(edgeLengthM)(H3Index edge, double *length) {
460	0	H3Error err = H3_EXPORT(edgeLengthKm)(edge, length);
461	0	length = length * 1000;
462	0	return err;
463	0	}