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Added clarifications

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Alexey Milovidov 2019-12-09 20:25:16 +03:00
parent 2db25df706
commit 1e3b9af66f
1 changed files with 24 additions and 2 deletions
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26
dbms/src/Functions/greatCircleDistance.cpp
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@ -42,8 +42,30 @@ constexpr size_t COS_LUT_SIZE = 1024; // maxerr 0.00063%
constexpr size_t ASIN_SQRT_LUT_SIZE = 512;
constexpr size_t METRIC_LUT_SIZE = 1024;
/// Earth mean diameter in meters, https://en.wikipedia.org/wiki/Earth
constexpr float EARTH_DIAMETER = 2 * 6371000;
/** We use "WGS-84 ellipsoidal quadratic mean radius of Earth" as the approximation to calculate distances on sphere.
* The motivation for it is explained here: https://math.wikia.org/wiki/Ellipsoidal_quadratic_mean_radius
*
* Brief explanation:
* - the radius of sphere is choosen to minimize the difference between distance on that sphere and distance on WGS-84 ellipsoid between two points,
* averaged uniformly (?) by all angles (?) between points.
* This sounds not clear enough for me: what set we are averaging and by what measure?
*
* The value should be calculated this way:
* WITH 6378137.0 AS a, 6356752.314245 AS b SELECT sqrt(3 * a * a + b * b) / 2
*
* But for unknown reason, slightly different value is used.
* This constant may be changed in future with a note about backward incompatible change in the changelog.
*
* See also:
* https://github.com/Project-OSRM/osrm-backend/blob/bb1f4a025a3cefd3598a38b9d3e55485d1080ec5/third_party/libosmium/include/osmium/geom/haversine.hpp#L58-L59
* https://github.com/Project-OSRM/osrm-backend/issues/5051
* https://github.com/mapbox/turf-swift/issues/26
* https://github.com/Project-OSRM/osrm-backend/pull/5041
* https://en.wikipedia.org/wiki/Talk:Great-circle_distance/Archive_1
*/
constexpr float EARTH_RADIUS = 6372797.560856;
constexpr float EARTH_DIAMETER = 2 * EARTH_RADIUS;
float cos_lut[COS_LUT_SIZE + 1]; /// cos(x) table
float asin_sqrt_lut[ASIN_SQRT_LUT_SIZE + 1]; /// asin(sqrt(x)) * earth_diameter table