Translation matrix in spherical coordinates system

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I'm using WorldWind software to draw segments (polyline) on the globe to materialize an aircraft flightplan. Each point in a flightplan is named waypoint. Waypoints are expressed in geographical coordinates with a latitude a longitude (no altitude yet). I whish to draw an area 4000 meter width around the flightplan, name of this distance is d.

In Euclidian system it's trivial to compute the factor {dx,dy} of a translation matrix:

  • alpha = atan2( ye-ys, xe-xs )
  • dx = d * cos( alpha )
  • dy = d * sin( alpha )

But I don't known how to compute {lat,lon} as {y,x} with spherical coordinates system.