On a linear programming approach to the discrete Willmore boundary value problem and generalizations

We consider the problem of finding (possibly non connected) discrete surfaces spanning a finite set of discrete boundary curves in the three-dimensional space and minimizing (globally) a discrete energy involving mean curvature. Although we consider a fairly general class of energies, our main focus is on the Willmore energy, i.e. the total squared mean curvature. Most works in the literature have been devoted to the approximation of a surface evolving by the Willmore flow and, in particular, to the approximation of the so-called Willmore surfaces, i.e., the critical points of the Willmore energy. Our purpose is to address the delicate task of approximating global minimizers of the energy under boundary constraints. The main contribution of this work is to translate the nonlinear boundary value problem into an integer linear program, using a natural formulation involving pairs of elementary triangles chosen in a pre-specified dictionary and allowing self-intersection. The reason fo...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Thomas Schoenemann, Simon Masnou, Daniel Cremers
• Keywords: CORR 2011, Education, Integer Linear, Integer Linear Program, Linear Program