ST_DWithin function implementation for MySQL 8.0

ST_Epgs3857_DWithin.sql

-- Made by Jairo Tylera
-- (github.com/Tylerian)
-- (c) 2019 - present
-- Released under MIT X11 License

CREATE
  DEFINER=`root`@`localhost`
FUNCTION
  `ST_Epgs3857_DWithin`(p1 POINT, p2 POINT, distance_mts FLOAT)
RETURNS
  tinyint(4)
DETERMINISTIC
BEGIN
  DECLARE bounds POLYGON;
  SET bounds = ST_Epgs3857_Expand(p2, distance_mts);
  RETURN ST_Contains(bounds, p1);
END

ST_Epgs3857_Expand.sql

-- Made by Jairo Tylera
-- (github.com/Tylerian)
-- (c) 2019 - present
-- Released under MIT X11 License

CREATE
  DEFINER=`root`@`localhost`
FUNCTION
  `ST_Epgs3857_Expand`(point POINT, radius INTEGER)
RETURNS
  polygon
DETERMINISTIC
BEGIN
  DECLARE hypo DOUBLE;
  DECLARE midx DOUBLE;
  DECLARE midy DOUBLE;
  DECLARE poly VARCHAR(256);
  DECLARE xmax DOUBLE;
  DECLARE xmin DOUBLE;
  DECLARE ymax DOUBLE;
  DECLARE ymin DOUBLE;

  SET midx = ST_X(point);
  SET midy = ST_Y(point);
  SET hypo = SQRT(POW(radius / COS(midy * PI() / 180), 2) * 2);

  SET xmin = ROUND(midx - hypo, 2);
  SET xmax = ROUND(midx + hypo, 2);
  SET ymin = ROUND(midy - hypo, 2);
  SET ymax = ROUND(midy + hypo, 2);

  SET poly = CONCAT('POLYGON((',
               xmin, ' ', ymin, ',',
               xmin, ' ', ymax, ',',
               xmax, ' ', ymax, ',',
               xmax, ' ', ymin, ',',
               xmin, ' ', ymin, '))');

  RETURN ST_PolyFromText(poly, 3857);
END

ST_Epgs3857_To_Epgs4326.sql

-- Made by Jairo Tylera
-- (github.com/Tylerian)
-- (c) 2019 - present
-- Released under MIT X11 License

CREATE
  DEFINER=`root`@`localhost`
FUNCTION
  `ST_Epgs3857_To_Epgs4326`(point POINT)
RETURNS
  point
DETERMINISTIC
BEGIN
  DECLARE lat DOUBLE;
  DECLARE lon DOUBLE;
  DECLARE shift DOUBLE;
  DECLARE x DOUBLE;
  DECLARE y DOUBLE;
	
  SET x = ST_X(point);
  SET y = ST_Y(point);
  SET shift = 20037508.342789244;
	
  SET lon = (x / shift) * 180.0;
  SET lat = (y / shift) * 180.0;
	
  SET lat = 180.0 / PI() * (2.0 * ATAN(EXP(lat * PI() / 180.0)) - PI() / 2.0);
	
  RETURN ST_PointFromText(CONCAT('POINT(', ROUND(lat, 5), ' ', ROUND(lon, 5), ')'), 4326);
END

ST_Epgs4326_To_Epgs3857.sql

-- Made by Jairo Tylera
-- (github.com/Tylerian)
-- (c) 2019 - present
-- Released under MIT X11 License

CREATE
  DEFINER=`root`@`localhost`
FUNCTION
  `ST_Epgs4326_To_Epgs3857`(point POINT)
RETURNS
  point
DETERMINISTIC
BEGIN
  DECLARE lat DOUBLE;
  DECLARE lon DOUBLE;
  DECLARE shift DOUBLE;
  DECLARE x DOUBLE;
  DECLARE y DOUBLE;
	
  SET lat = ST_Latitude(point);
  SET lon = ST_Longitude(point);
  SET shift = 20037508.342789244;
	
  SET x = lon * shift / 180.0;
  SET y = LOG(TAN((90.0 + lat) * PI() / 360.0)) / (PI() / 180.0);
  
  SET y = y * shift / 180.0;
	
  RETURN ST_PointFromText(CONCAT('POINT(', ROUND(x, 2), ' ', ROUND(y, 2), ')'), 3857);
END

this checks if is within bounding rectangle, and not within distance, which is circular