Efficient Rendering of Trimmed NURBS Surfaces

Subodh Kumar                      Dinesh Manocha
Department of Computer Science    Department of Computer Science
University of North Carolina      University of North Carolina
Chapel Hill NC 27599              Chapel Hill NC 27599

We present an algorithm for interactive display of trimmed NURBS surfaces. The algorithm converts the NURBS surfaces to Bézier surfaces and NURBS trimming curves into 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 uniform tessellation of Bézier surfaces into cells and traces the trimming curves to compute the trimmed regions of each cell. This is based on tracing 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 like cracks and angularities are avoided as well. The algorithm can display trimmed models described using thousands of Bézier surfaces at interactive frame rates on the high end graphics systems.

Additional Keywords and Phrases:

NURBS, trimming curves, Bézier surface, CSG, Boundary Representation, Trimming Curves, Tessellation.

Supported by DARPA ISTO Order No. A410, ONR Contract N00014-94-1-0738, NSF Grant No. MIP-9306208, Junior Faculty Award, University Research Award, NSF Grant CCR-9319957, ARPA Contract DABT63-93-C-0048 and NSF/ARPA Science and Technology Center for Computer Graphics and Scientific Visualization, and NSF Prime Contract No. 8920219.

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