#
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.
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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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