Approximate Simulation of Elastic Membranes by Triangulated Spring Meshes

Abstract

Spring meshes have been used to model elastic material in computer graphics, with skin, textiles, and soft tissue being typical applications. A spring mesh is a system of vertices and edges, possibly with highly irregular geometry, in which each edge is a spring, and springs are connected by “pin-joints” (“gimbal-joints” in three dimensions) at the vertices. This method is computationally attractive, compared to some alternatives. Given a specified set of elastic material properties, however, the question of whether a particular spring mesh accurately simulates those properties has been largely ignored in the literature. Additionally, previous reports on the technique are silent on the subject of assigning stiffness to the various springs. This paper shows that assigning the same stiffness to all springs fails to simulate a uniform elastic membrane, for equilibrium calculations. A formula for spring stiffness that provides a more accurate simulation is then derived. In its simplest form, this formula specifies that stiffness varies as triangle area over edge length squared. Its accuracy is demonstrated on test and practical mesh examples. It is also shown that, in general, an exact simulation is not possible.