15.5 Polygon Triangulation

• We consider simple polygons. That is, polygons that do not contain intersecting edges.

  

• An ear of a polygon is a triangle of the polygon made up of three consecutive nodes and enclosing no other nodes

  

• The two-ears theorem: Every polygon with more than three nodes has at least two non-overlapping ears

  Proof. By induction.

  • Assume this is not the case.

    

  • Find the enclosed node farthest from the base of the triangle made up of a node and its neighbors
  • Subdivided the polygon at the cord connecting the enclosed node and non-base node.

    

• Ear-cutting algorithm. Repeatedly find an ear and remove it from the search domain.
• Recursive algorithm.
  • Find the left- bottom-most node
  • If the node provides an, remove it from farther consideration

    

  • Otherwise, divide the polygon into two along the cord used in the proof.