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Given:

  • a quadrilateral mesh that forms the surface of a sphere
  • a linear projection from 3D to 2D (a 2x3 matrix)

The mesh is not convex in general, but it is regular enough that we know that the projected image of the mesh in the plane is a polygon without holes (the image is simply connected).

Is there a fast method for computing the area of this polygon ?

I can compute an approximate area by scan converting all the quadrilaterals, but maybe there is a clever algorithm that can give a more precise number. A method for computing this polygon explicitly would be OK.

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