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+/*
+ * Copyright (c) 2013-2014, yinqiwen <yinqiwen@gmail.com>
+ * Copyright (c) 2014, Matt Stancliff <matt@genges.com>.
+ * Copyright (c) 2015-2016, Salvatore Sanfilippo <antirez@gmail.com>.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice,
+ * this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * * Neither the name of Redis nor the names of its contributors may be used
+ * to endorse or promote products derived from this software without
+ * specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
+ * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+ * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+ * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+ * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
+ * THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/* This is a C++ to C conversion from the ardb project.
+ * This file started out as:
+ * https://github.com/yinqiwen/ardb/blob/d42503/src/geo/geohash_helper.cpp
+ */
+
+#include "fmacros.h"
+#include "geohash_helper.h"
+#include "debugmacro.h"
+#include <math.h>
+
+#define D_R (M_PI / 180.0)
+#define R_MAJOR 6378137.0
+#define R_MINOR 6356752.3142
+#define RATIO (R_MINOR / R_MAJOR)
+#define ECCENT (sqrt(1.0 - (RATIO *RATIO)))
+#define COM (0.5 * ECCENT)
+
+/// @brief The usual PI/180 constant
+const double DEG_TO_RAD = 0.017453292519943295769236907684886;
+/// @brief Earth's quatratic mean radius for WGS-84
+const double EARTH_RADIUS_IN_METERS = 6372797.560856;
+
+const double MERCATOR_MAX = 20037726.37;
+const double MERCATOR_MIN = -20037726.37;
+
+static inline double deg_rad(double ang) { return ang * D_R; }
+static inline double rad_deg(double ang) { return ang / D_R; }
+
+/* This function is used in order to estimate the step (bits precision)
+ * of the 9 search area boxes during radius queries. */
+uint8_t geohashEstimateStepsByRadius(double range_meters, double lat) {
+ if (range_meters == 0) return 26;
+ int step = 1;
+ while (range_meters < MERCATOR_MAX) {
+ range_meters *= 2;
+ step++;
+ }
+ step -= 2; /* Make sure range is included in most of the base cases. */
+
+ /* Wider range towards the poles... Note: it is possible to do better
+ * than this approximation by computing the distance between meridians
+ * at this latitude, but this does the trick for now. */
+ if (lat > 66 || lat < -66) {
+ step--;
+ if (lat > 80 || lat < -80) step--;
+ }
+
+ /* Frame to valid range. */
+ if (step < 1) step = 1;
+ if (step > 26) step = 26;
+ return step;
+}
+
+/* Return the bounding box of the search area by shape (see geohash.h GeoShape)
+ * bounds[0] - bounds[2] is the minimum and maximum longitude
+ * while bounds[1] - bounds[3] is the minimum and maximum latitude.
+ * since the higher the latitude, the shorter the arc length, the box shape is as follows
+ * (left and right edges are actually bent), as shown in the following diagram:
+ *
+ * \-----------------/ -------- \-----------------/
+ * \ / / \ \ /
+ * \ (long,lat) / / (long,lat) \ \ (long,lat) /
+ * \ / / \ / \
+ * --------- /----------------\ /---------------\
+ * Northern Hemisphere Southern Hemisphere Around the equator
+ */
+int geohashBoundingBox(GeoShape *shape, double *bounds) {
+ if (!bounds) return 0;
+ double longitude = shape->xy[0];
+ double latitude = shape->xy[1];
+ double height = shape->conversion * (shape->type == CIRCULAR_TYPE ? shape->t.radius : shape->t.r.height/2);
+ double width = shape->conversion * (shape->type == CIRCULAR_TYPE ? shape->t.radius : shape->t.r.width/2);
+
+ const double lat_delta = rad_deg(height/EARTH_RADIUS_IN_METERS);
+ const double long_delta_top = rad_deg(width/EARTH_RADIUS_IN_METERS/cos(deg_rad(latitude+lat_delta)));
+ const double long_delta_bottom = rad_deg(width/EARTH_RADIUS_IN_METERS/cos(deg_rad(latitude-lat_delta)));
+ /* The directions of the northern and southern hemispheres
+ * are opposite, so we choice different points as min/max long/lat */
+ int southern_hemisphere = latitude < 0 ? 1 : 0;
+ bounds[0] = southern_hemisphere ? longitude-long_delta_bottom : longitude-long_delta_top;
+ bounds[2] = southern_hemisphere ? longitude+long_delta_bottom : longitude+long_delta_top;
+ bounds[1] = latitude - lat_delta;
+ bounds[3] = latitude + lat_delta;
+ return 1;
+}
+
+/* Calculate a set of areas (center + 8) that are able to cover a range query
+ * for the specified position and shape (see geohash.h GeoShape).
+ * the bounding box saved in shaple.bounds */
+GeoHashRadius geohashCalculateAreasByShapeWGS84(GeoShape *shape) {
+ GeoHashRange long_range, lat_range;
+ GeoHashRadius radius;
+ GeoHashBits hash;
+ GeoHashNeighbors neighbors;
+ GeoHashArea area;
+ double min_lon, max_lon, min_lat, max_lat;
+ int steps;
+
+ geohashBoundingBox(shape, shape->bounds);
+ min_lon = shape->bounds[0];
+ min_lat = shape->bounds[1];
+ max_lon = shape->bounds[2];
+ max_lat = shape->bounds[3];
+
+ double longitude = shape->xy[0];
+ double latitude = shape->xy[1];
+ /* radius_meters is calculated differently in different search types:
+ * 1) CIRCULAR_TYPE, just use radius.
+ * 2) RECTANGLE_TYPE, we use sqrt((width/2)^2 + (height/2)^2) to
+ * calculate the distance from the center point to the corner */
+ double radius_meters = shape->type == CIRCULAR_TYPE ? shape->t.radius :
+ sqrt((shape->t.r.width/2)*(shape->t.r.width/2) + (shape->t.r.height/2)*(shape->t.r.height/2));
+ radius_meters *= shape->conversion;
+
+ steps = geohashEstimateStepsByRadius(radius_meters,latitude);
+
+ geohashGetCoordRange(&long_range,&lat_range);
+ geohashEncode(&long_range,&lat_range,longitude,latitude,steps,&hash);
+ geohashNeighbors(&hash,&neighbors);
+ geohashDecode(long_range,lat_range,hash,&area);
+
+ /* Check if the step is enough at the limits of the covered area.
+ * Sometimes when the search area is near an edge of the
+ * area, the estimated step is not small enough, since one of the
+ * north / south / west / east square is too near to the search area
+ * to cover everything. */
+ int decrease_step = 0;
+ {
+ GeoHashArea north, south, east, west;
+
+ geohashDecode(long_range, lat_range, neighbors.north, &north);
+ geohashDecode(long_range, lat_range, neighbors.south, &south);
+ geohashDecode(long_range, lat_range, neighbors.east, &east);
+ geohashDecode(long_range, lat_range, neighbors.west, &west);
+
+ if (north.latitude.max < max_lat)
+ decrease_step = 1;
+ if (south.latitude.min > min_lat)
+ decrease_step = 1;
+ if (east.longitude.max < max_lon)
+ decrease_step = 1;
+ if (west.longitude.min > min_lon)
+ decrease_step = 1;
+ }
+
+ if (steps > 1 && decrease_step) {
+ steps--;
+ geohashEncode(&long_range,&lat_range,longitude,latitude,steps,&hash);
+ geohashNeighbors(&hash,&neighbors);
+ geohashDecode(long_range,lat_range,hash,&area);
+ }
+
+ /* Exclude the search areas that are useless. */
+ if (steps >= 2) {
+ if (area.latitude.min < min_lat) {
+ GZERO(neighbors.south);
+ GZERO(neighbors.south_west);
+ GZERO(neighbors.south_east);
+ }
+ if (area.latitude.max > max_lat) {
+ GZERO(neighbors.north);
+ GZERO(neighbors.north_east);
+ GZERO(neighbors.north_west);
+ }
+ if (area.longitude.min < min_lon) {
+ GZERO(neighbors.west);
+ GZERO(neighbors.south_west);
+ GZERO(neighbors.north_west);
+ }
+ if (area.longitude.max > max_lon) {
+ GZERO(neighbors.east);
+ GZERO(neighbors.south_east);
+ GZERO(neighbors.north_east);
+ }
+ }
+ radius.hash = hash;
+ radius.neighbors = neighbors;
+ radius.area = area;
+ return radius;
+}
+
+GeoHashFix52Bits geohashAlign52Bits(const GeoHashBits hash) {
+ uint64_t bits = hash.bits;
+ bits <<= (52 - hash.step * 2);
+ return bits;
+}
+
+/* Calculate distance using simplified haversine great circle distance formula.
+ * Given longitude diff is 0 the asin(sqrt(a)) on the haversine is asin(sin(abs(u))).
+ * arcsin(sin(x)) equal to x when x ∈[−𝜋/2,𝜋/2]. Given latitude is between [−𝜋/2,𝜋/2]
+ * we can simplify arcsin(sin(x)) to x.
+ */
+double geohashGetLatDistance(double lat1d, double lat2d) {
+ return EARTH_RADIUS_IN_METERS * fabs(deg_rad(lat2d) - deg_rad(lat1d));
+}
+
+/* Calculate distance using haversine great circle distance formula. */
+double geohashGetDistance(double lon1d, double lat1d, double lon2d, double lat2d) {
+ double lat1r, lon1r, lat2r, lon2r, u, v, a;
+ lon1r = deg_rad(lon1d);
+ lon2r = deg_rad(lon2d);
+ v = sin((lon2r - lon1r) / 2);
+ /* if v == 0 we can avoid doing expensive math when lons are practically the same */
+ if (v == 0.0)
+ return geohashGetLatDistance(lat1d, lat2d);
+ lat1r = deg_rad(lat1d);
+ lat2r = deg_rad(lat2d);
+ u = sin((lat2r - lat1r) / 2);
+ a = u * u + cos(lat1r) * cos(lat2r) * v * v;
+ return 2.0 * EARTH_RADIUS_IN_METERS * asin(sqrt(a));
+}
+
+int geohashGetDistanceIfInRadius(double x1, double y1,
+ double x2, double y2, double radius,
+ double *distance) {
+ *distance = geohashGetDistance(x1, y1, x2, y2);
+ if (*distance > radius) return 0;
+ return 1;
+}
+
+int geohashGetDistanceIfInRadiusWGS84(double x1, double y1, double x2,
+ double y2, double radius,
+ double *distance) {
+ return geohashGetDistanceIfInRadius(x1, y1, x2, y2, radius, distance);
+}
+
+/* Judge whether a point is in the axis-aligned rectangle, when the distance
+ * between a searched point and the center point is less than or equal to
+ * height/2 or width/2 in height and width, the point is in the rectangle.
+ *
+ * width_m, height_m: the rectangle
+ * x1, y1 : the center of the box
+ * x2, y2 : the point to be searched
+ */
+int geohashGetDistanceIfInRectangle(double width_m, double height_m, double x1, double y1,
+ double x2, double y2, double *distance) {
+ /* latitude distance is less expensive to compute than longitude distance
+ * so we check first for the latitude condition */
+ double lat_distance = geohashGetLatDistance(y2, y1);
+ if (lat_distance > height_m/2) {
+ return 0;
+ }
+ double lon_distance = geohashGetDistance(x2, y2, x1, y2);
+ if (lon_distance > width_m/2) {
+ return 0;
+ }
+ *distance = geohashGetDistance(x1, y1, x2, y2);
+ return 1;
+}
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