Summary. We present a tetrahedral mesh improvement schedule that usually creates meshes whose worst tetrahedra have a level of quality substantially better than those produced by any previous method for tetrahedral mesh generation or "mesh clean-up." Our goal is to aggressively optimize the worst tetrahedra, with speed a secondary consideration. Mesh optimization methods often get stuck in bad local optima (poor-quality meshes) because their repertoire of mesh transformations is weak. We employ a broader palette of operations than any previous mesh improvement software. Alongside the best traditional topological and smoothing operations, we introduce a topological transformation that inserts a new vertex (sometimes deleting others at the same time). We describe a schedule for applying and composing these operations that rarely gets stuck in a bad optimum. We demonstrate that all three techniques-smoothing, vertex insertion, and traditional transformations-are substantially more effective than any two alone. Our implementation usually improves meshes so that all dihedral angles are between 31• and 149• , or (with a different objective function) between 23• and 136• .

We describe a structure- from-motion

This paper presents a method for animating fluid using unstructured tetrahedral meshes that change at each time step. We show that meshes that conform well to changing boundaries and that focus computation in the visually important parts of the domain can be generated quickly and reliably using existing techniques. We also describe a new approach to two-way coupling of fluid and rigid bodies that, while general, benefits from remeshing. Overall, the method provides a flexible environment for creating complex scenes involving fluid animation.

This paper presents a method for animating fluid using unstructured tetrahedral meshes that change at each time step. We show that meshes that conform well to changing boundaries and that focus computation in the visually important parts of the domain can be generated quickly and reliably using existing techniques. We also describe a new approach to two-way coupling of fluid and rigid bodies that, while general, benefits from remeshing. Overall, the method provides a flexible environment for creating complex scenes involving fluid animation.

Figure 1: An elastoplastic substance slowly drips from a horizontal surface. A dynamic meshing algorithm refines the drop while maintaining high-quality tetrahedra. At the narrowest part of the tendril, the mesher creates small, anisotropic tetrahedra where the strain gradient is anisotropic, so that a modest number are adequate. Work hardening causes the tendril to become brittle, whereupon it fractures. At right, we animate a fine triangulated surface embedded in the mesh. AbstractWe propose a finite element simulation method that addresses the full range of material behavior, from purely elastic to highly plastic, for physical domains that are substantially reshaped by plastic flow, fracture, or large elastic deformations. To mitigate artificial plasticity, we maintain a simulation mesh in both the current state and the rest shape, and store plastic offsets only to represent the nonembeddable portion of the plastic deformation. To maintain high element quality in a tetrahedral mesh undergoing gross changes, we use a dynamic meshing algorithm that attempts to replace as few tetrahedra as possible, and thereby limits the visual artifacts and artificial diffusion that would otherwise be introduced by repeatedly remeshing the domain from scratch. Our dynamic mesher also locally refines and coarsens a mesh, and even creates anisotropic tetrahedra, wherever a simulation requests it. We illustrate these features with animations of elastic and plastic behavior, extreme deformations, and fracture.