Anisotropic Sampling for Differential Point Rendering of Implicit Surfaces

In this paper, we propose a solution to adapt the differential point rendering technique developed by Kalaiah and Varshney to implicit surfaces. Differential point rendering was initially designed for parametric surfaces as a twostage sampling process that strongly relies on an adjacency relationship for the samples, which does not naturally exist for implicit surfaces. This fact made it particularly challenging to adapt the technique to implicit surfaces. To overcome this difficulty, we extended the particle sampling technique developed by Witkin and Heckbert in order to locally account for the principal directions of curvatures of the implicit surface. The final result of our process is a curvature driven anisotropic sampling where each sample ”rules” a rectangular or elliptical surrounding domain and is oriented according to the directions of maximal and minimal curvatures. As in the differential point rendering technique, these samples can then be efficiently rendered using a specific shader on a programmable GPU.