🚀 go-pugleaf

In article <1992Aug25.195204.28914@eng.ufl.edu> Ed Deeters:
> Hi, does anyone know a fast way to determine if a point(x,y) is inside
> or outside of a polygon when the polygon is defined by n points(x,y)
> given in a clockwise manner?

If the polygon is convex, or if you are trying to check if the given
point is inside the convex hull of the given points then you can use
linear programming to do so.
Assume that the coordinates of point i are given by the vector x(i)
then the formulation would be:
x = c(i) * x(i)
sum_i c(i) = 1
c(i) >= 0

x is the coordinate vector of the point you are trying to see whether
it is inside or outside the polygon. c(i) is the unknown. Use linear
programming to see if the problem has a feasible solution or not.
-Samer