Superfície mínima discreta

Abstract

The Minimal Surfaces problem emerged from the study of the Calculus of Variations with the meaning of being a regular surface of smallest area among those that set a specific boundary. This problem was proposed by Lagrange in 1760 and is called the Plateau Problem due to experimental studies of the physicist Joseph Antoine Ferdinand Plateau. This work proposes a numerical solution to a discrete version of the Plateau Problem from the proposed method by Pinkall and Polthier. Of the discrete viewpoint case, surfaces are simplicial complexes with certain restrictions and we use the concepts of Dirichlet Energy over applications that have triangulated surfaces as domain in order to developed a mathematically consistent algorithm to obtain a minimum surface given a boundary.