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Has files: true × Start date: 1990 × Author: Abi-Ezzi, Salim S. ×

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Now showing 1 - 4 of 4
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    Tessellation of Curved Surfaces under Highly Varying Transformations
    (Eurographics Association, 1991) Abi-Ezzi, Salim S.; Shirman, Leon A.
    We pursue the problem of step size determination for tessellating arbitrary degree polynomial and rational Bezier patches, under highly varying modeling and viewing transformations, to within post-viewing size and/or deviation thresholds specified in display coordinates. The technique involves the computation of derivative bounds of surfaces in modeling coordinates, and the mapping of these bounds into world coordinates (or lighting coordinates), where tessellation takes place by using norms of modeling transformations. A key result of this work is a closed form expression for the maximum scale a perspective transformation is capable of at an arbitrary point in space. This result allows the mapping of thresholds from DC into WC (LC). In practice, while the step size determination needs to take place during every traversal, the costly operations of finding derivative bounds, computing norms of modeling transformations, and factoring viewing transformations take place at creation time.
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    Factoring a Homogeneous Transformation for a more Efficient Graphics Pipeline
    (Eurographics Association, 1990) Abi-Ezzi, Salim S.; Wozny, Michael J.
    We identify an intermediate coordinate system situated between world coordinates and display coordinates, which exhibits unique features for lighting calculations and for clipping in homogeneous coordinates. Our key contribution is an algorithm for extracting such a coordinate system from a homogeneous viewing transformation that relates WC to DC. The algorithm is based on factoring the transformation into a product of a Euclidean factor and a sparse (computationally cheap) but non- Euclidean factor. A particularly strong application of the proposed technique is the graphical processing of curved surface primitives, such as what is needed in the PHIGS PLUS viewing pipeline. Furthermore, in PHIGS PLUS the graphical data is retained by the graphics system, therefore, it is possible to perform the factoring of the viewing transformation at creation time, and to take advantage of this factored form at traversal time.
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    Fast Dynamic Tessellation of Trimmed NURBS Surfaced1
    (Blackwell Science Ltd and the Eurographics Association, 1994) Abi-Ezzi, Salim S.; Subramaniam, Srikanth
    Trimmed 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.
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    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,