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

Source
/*
 * Copyright 2016-2023, 2026 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 < 0.0) ? 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;
}

/**
 * Normalize an input longitude according to the specified normalization
 * @param  lng           Input longitude
 * @param  normalization Longitude normalization strategy
 * @return               Normalized longitude
 */
double normalizeLng(const double lng,
                    const LongitudeNormalization normalization) {
    switch (normalization) {
        case NORMALIZE_EAST:
            return lng < 0 ? lng + (double)M_2PI : lng;
        case NORMALIZE_WEST:
            return lng > 0 ? lng - (double)M_2PI : lng;
        default:
            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) * 0.5);
    double sinLng = sin((b->lng - a->lng) * 0.5);

    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.
 *
 * @param  a  the first lat/lng pair (in radians)
 * @param  b  the second lat/lng pair (in radians)
 *
 * @return    the great circle distance in kilometers between a and b
 */
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.
 *
 * @param  a  the first lat/lng pair (in radians)
 * @param  b  the second lat/lng pair (in radians)
 *
 * @return    the great circle distance in meters between a and b
 */
double H3_EXPORT(greatCircleDistanceM)(const LatLng *a, const LatLng *b) {
    return H3_EXPORT(greatCircleDistanceKm)(a, b) * 1000;
}

/*
 * 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;
}

/**
 * Length of a directed edge in radians.
 *
 * @param   edge  H3 directed edge
 * @param    length  length in radians
 * @return        E_SUCCESS on success, or an error code otherwise
 */
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.
 *
 * @param   edge  H3 directed edge
 * @param    length  length in kilometers
 * @return        E_SUCCESS on success, or an error code otherwise
 */
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.
 *
 * @param   edge  H3 directed edge
 * @param    length  length in meters
 * @return        E_SUCCESS on success, or an error code otherwise
 */
H3Error H3_EXPORT(edgeLengthM)(H3Index edge, double *length) {
    H3Error err = H3_EXPORT(edgeLengthKm)(edge, length);
    *length = *length * 1000;
    return err;
}

Coverage Report

Created: 2026-09-03 06:52

Line	Count	Source
1		/*
2		* Copyright 2016-2023, 2026 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	0	double _posAngleRads(double rads) {
37	0	double tmp = ((rads < 0.0) ? rads + M_2PI : rads);
38	0	if (rads >= M_2PI) tmp -= M_2PI;
39	0	return tmp;
40	0	}
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	0	double constrainLng(double lng) {
131	0	while (lng > M_PI) {
132	0	lng = lng - (2 * M_PI);
133	0	}
134	0	while (lng < -M_PI) {
135	0	lng = lng + (2 * M_PI);
136	0	}
137	0	return lng;
138	0	}
139
140		/**
141		* Normalize an input longitude according to the specified normalization
142		* @param lng Input longitude
143		* @param normalization Longitude normalization strategy
144		* @return Normalized longitude
145		*/
146		double normalizeLng(const double lng,
147	0	const LongitudeNormalization normalization) {
148	0	switch (normalization) {
149	0	case NORMALIZE_EAST:
150	0	return lng < 0 ? lng + (double)M_2PI : lng;
151	0	case NORMALIZE_WEST:
152	0	return lng > 0 ? lng - (double)M_2PI : lng;
153	0	default:
154	0	return lng;
155	0	}
156	0	}
157
158		/**
159		* The great circle distance in radians between two spherical coordinates.
160		*
161		* This function uses the Haversine formula.
162		* For math details, see:
163		* https://en.wikipedia.org/wiki/Haversine_formula
164		* https://www.movable-type.co.uk/scripts/latlong.html
165		*
166		* @param a the first lat/lng pair (in radians)
167		* @param b the second lat/lng pair (in radians)
168		*
169		* @return the great circle distance in radians between a and b
170		*/
171	0	double H3_EXPORT(greatCircleDistanceRads)(const LatLng a, const LatLng b) {
172	0	double sinLat = sin((b->lat - a->lat) * 0.5);
173	0	double sinLng = sin((b->lng - a->lng) * 0.5);
174
175	0	double A = sinLat * sinLat + cos(a->lat) * cos(b->lat) * sinLng * sinLng;
176
177	0	return 2 * atan2(sqrt(A), sqrt(1 - A));
178	0	}
179
180		/**
181		* The great circle distance in kilometers between two spherical coordinates.
182		*
183		* @param a the first lat/lng pair (in radians)
184		* @param b the second lat/lng pair (in radians)
185		*
186		* @return the great circle distance in kilometers between a and b
187		*/
188	0	double H3_EXPORT(greatCircleDistanceKm)(const LatLng a, const LatLng b) {
189	0	return H3_EXPORT(greatCircleDistanceRads)(a, b) * EARTH_RADIUS_KM;
190	0	}
191
192		/**
193		* The great circle distance in meters between two spherical coordinates.
194		*
195		* @param a the first lat/lng pair (in radians)
196		* @param b the second lat/lng pair (in radians)
197		*
198		* @return the great circle distance in meters between a and b
199		*/
200	0	double H3_EXPORT(greatCircleDistanceM)(const LatLng a, const LatLng b) {
201	0	return H3_EXPORT(greatCircleDistanceKm)(a, b) * 1000;
202	0	}
203
204		/*
205		* The following functions provide meta information about the H3 hexagons at
206		* each zoom level. Since there are only 16 total levels, these are current
207		* handled with hardwired static values, but it may be worthwhile to put these
208		* static values into another file that can be autogenerated by source code in
209		* the future.
210		*/
211
212	0	H3Error H3_EXPORT(getHexagonAreaAvgKm2)(int res, double *out) {
213	0	static const double areas[] = {
214	0	4.357449416078383e+06, 6.097884417941332e+05, 8.680178039899720e+04,
215	0	1.239343465508816e+04, 1.770347654491307e+03, 2.529038581819449e+02,
216	0	3.612906216441245e+01, 5.161293359717191e+00, 7.373275975944177e-01,
217	0	1.053325134272067e-01, 1.504750190766435e-02, 2.149643129451879e-03,
218	0	3.070918756316060e-04, 4.387026794728296e-05, 6.267181135324313e-06,
219	0	8.953115907605790e-07};
220	0	if (res < 0 \|\| res > MAX_H3_RES) {
221	0	return E_RES_DOMAIN;
222	0	}
223	0	*out = areas[res];
224	0	return E_SUCCESS;
225	0	}
226
227	0	H3Error H3_EXPORT(getHexagonAreaAvgM2)(int res, double *out) {
228	0	static const double areas[] = {
229	0	4.357449416078390e+12, 6.097884417941339e+11, 8.680178039899731e+10,
230	0	1.239343465508818e+10, 1.770347654491309e+09, 2.529038581819452e+08,
231	0	3.612906216441250e+07, 5.161293359717198e+06, 7.373275975944188e+05,
232	0	1.053325134272069e+05, 1.504750190766437e+04, 2.149643129451882e+03,
233	0	3.070918756316063e+02, 4.387026794728301e+01, 6.267181135324322e+00,
234	0	8.953115907605802e-01};
235	0	if (res < 0 \|\| res > MAX_H3_RES) {
236	0	return E_RES_DOMAIN;
237	0	}
238	0	*out = areas[res];
239	0	return E_SUCCESS;
240	0	}
241
242	0	H3Error H3_EXPORT(getHexagonEdgeLengthAvgKm)(int res, double *out) {
243	0	static const double lens[] = {
244	0	1281.256011, 483.0568391, 182.5129565, 68.97922179,
245	0	26.07175968, 9.854090990, 3.724532667, 1.406475763,
246	0	0.531414010, 0.200786148, 0.075863783, 0.028663897,
247	0	0.010830188, 0.004092010, 0.001546100, 0.000584169};
248	0	if (res < 0 \|\| res > MAX_H3_RES) {
249	0	return E_RES_DOMAIN;
250	0	}
251	0	*out = lens[res];
252	0	return E_SUCCESS;
253	0	}
254
255	0	H3Error H3_EXPORT(getHexagonEdgeLengthAvgM)(int res, double *out) {
256	0	static const double lens[] = {
257	0	1281256.011, 483056.8391, 182512.9565, 68979.22179,
258	0	26071.75968, 9854.090990, 3724.532667, 1406.475763,
259	0	531.4140101, 200.7861476, 75.86378287, 28.66389748,
260	0	10.83018784, 4.092010473, 1.546099657, 0.584168630};
261	0	if (res < 0 \|\| res > MAX_H3_RES) {
262	0	return E_RES_DOMAIN;
263	0	}
264	0	*out = lens[res];
265	0	return E_SUCCESS;
266	0	}
267
268	0	H3Error H3_EXPORT(getNumCells)(int res, int64_t *out) {
269	0	if (res < 0 \|\| res > MAX_H3_RES) {
270	0	return E_RES_DOMAIN;
271	0	}
272	0	out = 2 + 120 _ipow(7, res);
273	0	return E_SUCCESS;
274	0	}
275
276		/**
277		* Length of a directed edge in radians.
278		*
279		* @param edge H3 directed edge
280		* @param length length in radians
281		* @return E_SUCCESS on success, or an error code otherwise
282		*/
283	0	H3Error H3_EXPORT(edgeLengthRads)(H3Index edge, double *length) {
284	0	CellBoundary cb;
285
286	0	H3Error err = H3_EXPORT(directedEdgeToBoundary)(edge, &cb);
287	0	if (err) {
288	0	return err;
289	0	}
290
291	0	*length = 0.0;
292	0	for (int i = 0; i < cb.numVerts - 1; i++) {
293	0	*length +=
294	0	H3_EXPORT(greatCircleDistanceRads)(&cb.verts[i], &cb.verts[i + 1]);
295	0	}
296
297	0	return E_SUCCESS;
298	0	}
299
300		/**
301		* Length of a directed edge in kilometers.
302		*
303		* @param edge H3 directed edge
304		* @param length length in kilometers
305		* @return E_SUCCESS on success, or an error code otherwise
306		*/
307	0	H3Error H3_EXPORT(edgeLengthKm)(H3Index edge, double *length) {
308	0	H3Error err = H3_EXPORT(edgeLengthRads)(edge, length);
309	0	length = length * EARTH_RADIUS_KM;
310	0	return err;
311	0	}
312
313		/**
314		* Length of a directed edge in meters.
315		*
316		* @param edge H3 directed edge
317		* @param length length in meters
318		* @return E_SUCCESS on success, or an error code otherwise
319		*/
320	0	H3Error H3_EXPORT(edgeLengthM)(H3Index edge, double *length) {
321	0	H3Error err = H3_EXPORT(edgeLengthKm)(edge, length);
322	0	length = length * 1000;
323	0	return err;
324	0	}