Why Positive Area Imply a Positive Interior
- The area of each sub-triangle gives the edge equation's sign at the origin
- Assume a positive area
thus, the sum of the sub-triangles areas are positive
- Each point within the triangle falls within exactly one subtriangle
thus, subtriangles with negative areas will lie outside of the triangle
- Since the negative-subtriangle areas are outside of the triangle
the edge equations are positive inside
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