Envelope of a tile in Spherical Mercator

spherical-mercator.lisp

(defconstant EARTH_RADIUS 6378137.0)
(defconstant HALF_OF_EQUATOR (* PI EARTH_RADIUS))

(defun tile-size (zoom) (/ (* 2 HALF_OF_EQUATOR) (expt 2 zoom)))

(defun tile-envelope (x y z)
  (let ((size (tile-size z)))
    (list
        (+ (- HALF_OF_EQUATOR) (* x size))
        (- (+ HALF_OF_EQUATOR) (* (+ y 1) size))
        (+ (- HALF_OF_EQUATOR) (* (+ x 1) size))
        (- (+ HALF_OF_EQUATOR) (* y size)))))

(format t "~{~6$~^ ~}" (tile-envelope 112 672 11))