One usually computes the midpoint along the great circle
then compares the distance it is from the straight line
between the endpoints and recursively does this for the
resulting segments until the error term is 'good enough.
The algorithm goes something like
DrawGreatCircle(error,pt1,pt2,style):
proj_pt1 = WorldToDevice(ProjFwd(pt1))
proj_pt2 = WorldToDevice(ProjFwd(pt2))
mid_pt = MidPointGreatCircle(pt1,pt2)
proj_mid = WorldToDevice(ProjFwd(mid_pt))
if distPointLine2D (proj_mid, Line2D(proj_pt1,proj_pt2)) < error:
DrawLine(proj_pt1,proj_pt2,style)
else:
DrawGreatCircle(error,pt1,mid_pt)
DrawGreatCircle(error,mid_pt,pt2)
http://williams.best.vwh.net/avform.htm#Intermediate
HTH
Norman
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