Efficient rendering of trimmed nurbs surfaces

Abstract

An algorithm for the interactive display of trimmed nurbs surfaces is presented. The algorithm converts the nurbs surfaces to Bézier surfaces, and nurbs trimming curves to Bézier curves. It tessellates each trimmed Bézier surface into triangles, and renders them using the triangle rendering capabilities common in current graphics systems. It makes use of tight bounds for the uniform tessellation of Bézier surfaces into cells and it traces the trimming curves to compute the trimmed regions of each cell. This operation is based on the tracing of trimming curves, intersection computation with the cells, and triangulation of the cells. The resulting technique also makes use of spatial and temporal coherence between successive frames for cell computation and triangulation. Polygonization anomalies such as cracks and angularities are avoided as well. The algorithm can display trimmed models described using thousands of Bézier surfaces at interactive frame rates on high end graphics systems.