Optimizing 2-D Triangulations by the Steepest Descent Method

2-D triangulations are useful for building 3-D models or constructing meshes for finite element methods in scientific computing. This paper suggests a new objective function in optimizing the shape of elements. Our new objective function provides a criterion for evaluating the uniformity of a given triangulation. The criterion can be used to optimize triangulations by the steepest descent method. Furthermore, this paper outlines a new strategy of step-size controlling to guarantee that non self-intersections exist within the triangulations. Computational experiments show that the new optimization method is stable and well performed.