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redis/src/geohash_helper.c

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/*
* Copyright (c) 2013-2014, yinqiwen <yinqiwen@gmail.com>
* Copyright (c) 2014, Matt Stancliff <matt@genges.com>.
* Copyright (c) 2015-current, Redis Ltd.
* 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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