Physics-based simulations of deforming tetrahedral meshes are widely used to animate detailed embedded geometry. Unfortunately most practitioners still use linear interpolation (or other low-order schemes) on tetrahedra, which can produce undesirable visual artifacts, e.g., faceting and shading artifacts, that necessitate increasing the simulation's spatial resolution and, unfortunately, cost.
In this paper, we propose Phong Deformation, a simple, robust and practical vertex-based quadratic interpolation scheme that, while still only C0 continuous like linear interpolation, greatly reduces visual artifacts for embedded geometry. The method first averages element-based linear deformation models to vertices, then barycentrically interpolates the vertex models while also averaging with the traditional linear interpolation model. The method is a fast, robust, and easily implemented replacement for linear interpolation that produces visually better results for embedded deformation with irregular tetrahedral meshes.
Doug L. James