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Item Fast Dynamic Tessellation of Trimmed NURBS Surfaced1(Blackwell Science Ltd and the Eurographics Association, 1994) Abi-Ezzi, Salim S.; Subramaniam, SrikanthTrimmed NURBS (non-uniform rational B-splines) surfaces are being increasingly used and standardized in geometric modeling applications. Fast graphical processing of trimmed NURBS at interactive speeds is absolutely essential to enable these applications. which poses some unique challenges in software, hardware, and algorithm design. This paper presents a technique that uses graphical compilation to enable fast dynamic tessellation of trimmed NURBS surfaces under highly varying transforms.We use the concept of graphical data compilation. through which we preprocess the NURBS surface into a compact, view-independent form amenable for fast per-frame extraction of triangles. Much of the complexity of processing is absorbed during compilation. Arbitrarily complex trimming regions are broken down into simple regions that are specially designed to facilitate tessellation before rendering. Potentially troublesome cases of degeneracies in the surface are detected and dealt with during compilation. Compilation enables a clean separation of algorithm-intensive and compute-intensive operations, and provides for parallel implementations of the latter. Also, we exercise a classification technique while processing trimming loops. which robustly takes care of geometric ambiguities and deals with special cases while keeping the compilation code simple and concise.Item The Cone of Normals Technique for Fast Processing of Curved Patches(Blackwell Science Ltd and the Eurographics Association, 1993) Shirmun, Leon A.; Abi-Ezzi, Salim S.The cone of normals technique for curved surface patches allows to perform various quick tests at the patch level such as front- or backfacing test, light influence test, and existence of silhouette edges test. For a given patch, a truncated cone of normals is constructed at creation time, which contains all points and all normal directions of the patch. At traversal time, a simple scalar product test determines whether the whole patch is backfacing or frontfacing, so that the costly step of tessellating the patch is avoided in case of patch level face culling. In addition, the technique quickly determines which light sources have no influence on a patch, and which patches have no silhouette edges. The technique can also be used for other surface primitives, such as triangular strips and quadrilateral meshes,