Why Positive Area Imply a Positive Interior



  1. The area of each sub-triangle gives the edge equation's sign at the origin
  2. Assume a positive area
    thus, the sum of the sub-triangles areas are positive
  3. Each point within the triangle falls within exactly one subtriangle
    thus, subtriangles with negative areas will lie outside of the triangle
  4. Since the negative-subtriangle areas are outside of the triangle
    the edge equations are positive inside
Lecture 7 Slide 19a 6.837 Fall '98