Minimum degree triangulation for rectangular domains

This paper describes an optimal triangulation algorithm for rectangles. We derive lower bounds on the maximum degree of triangulation, and show that our triangulation algorithm matches the lower bounds. Several important observations are also made, including a zig-zag condition that can verify whether a triangulation can minimizes the maximum degree to 4 or not. In addition, this paper identifies the necessary and sufficient condition that there exists a maximum degree 4 triangulation for convex polygons, and gives a linear time checking algorithm.