Projecting Tetrahedra with a Simplified Basis Graph

The basis graph with five vertices has been commonly used in the GPU-accelerated Project Tetrahedra algorithm because of the inability to create or delete vertices within a vertex program and the fixed topological constraints of submitted vertices. However, it is so complicated that projecting a tetrahedron need to render four triangles. In this paper, we present a novel algorithm with a simplified four-vertex basis graph which decomposes a tetrahedral silhouette into two triangles. In contrast with previous algorithms, our algorithm can reduce the vertices and the triangles to be rendered and computational overhead on vertex processors, and therefore can remarkably improve the interactive rendering performance. Experimental results demonstrate that our algorithm can sort and render up to 2.30 - 6.16 Mtets/sec for a frame buffer resolution in 512 times 512.