Minimum weight triangulation (MWT) is a polygon triangulation scheme that minimizes total edge length. It has been shown that the MWT is the best triangulation for 3D area interpolations, where inappropriate triangulations could lead to poor results, as is shown below:

bad triangulation

good triangulation

There is a dynamic programming algorithm that solves MWT for simple polygons (not only convex ones) with O(n^3) time and O(n^2) space complexity, as is described here. Following is my implementation.