Animation of deformable objects built with simplex meshes

In this paper, we had generated the animation of deformable objects and these has been built with simplex meshes. A deformable object is a kind of object which is reshaped according to the Newton's second law of motion in a mechanical system composed of springs, masses, and dampers. To perform the animation, we need first to resolve numerically the law of motion. In this work, we present a comparison among four different numerical methods: finite differences, Euler, Heun, and fourth order Runge-Kutta. From our results and for our application, the best method is the simplest: finite differences. The simplex meshes allow to generate the whole animation from simple local deformations. We show four application examples: the animation of a sphere deformed to get a cube, the animation of a ball bounced against a wall, a ball compressed by two walls, and a ball deformed in a point.