mapping - Geometry of a radial coordinate to Cartesian with bounding points -


i need find 4 points in latitude/longitude format surrounding given center point , resulting algorithm (if possible).

known information: equal distances each "bin" center of point (radar) outward. example = .54 nautical miles.

1 degree beam width. center point of "bin"

this image in polar coordinates (i think similar radial coordinates???):

enter image description here

i need convert polar/radial cartesian , should able formula.

x = r × cos( θ ) y = r × sin( θ )

so need find "bin" outline coordinates (4 corners) can draw polygon in cartesian coordinate space.

i'm using delphi/pascal coding, might able convert other languages if have sample algorithm.

thanks suggestions or sample algorithms. regards, bryan

you need convert same coordinate system , impose distance criteria follows:

  1. convert center point geographic coordinates polar coordinates yield (rc, θc)
  2. convert center point polar cartesian coordinates using equations yielding (xc, yc)

  3. the corner points on right side of center points (xr, yr) satisfy equation

    (xr - xc)2 + (yr - yc)2 = d2

    [rrcos(θc+0.5o) - xc]2 + [rrsin(θc+0.5o) - yc]2 = d2

where d=distance between center point , corner points

everything known in above equation except rr. should yield quadratic equation 2 solutions can solve. 2 corner points on right side.

  1. repeat step 3 angle θc-0.5o corner points on left side.

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