Fast Dynamic Tessellation of Trimmed NURBS Surfaced1

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.     

The scaling behavior of viewing transformations

Using formal analysis of parallel and perspective viewing transformation behavior, closed-form form expressions are obtained for immediate evaluation of maximum, minimum, and average scales at a given point in space. While these are constant for parallel transformations, they vary from point to point for perspective transformations. The average scale of a transformation is expressed in ways useful for heuristic computations. The expressions indicate how transformations perform in general without providing guarantees. It is shown that these results apply to the dynamic tessellation of curved surfaces. The maximum scale of a transformation across a bounded region can guarantee that one will meet postviewing approximation thresholds specified in display coordinates, based on derivative bounds precomputed in modeling coordinates     

An Implementer's View of PHIGS

The Programmer's Hierarchical Interactive Graphics System (PHIGS) specifies an interface for programming device-independent computer graphics applications. After a brief review of PHIGS concepts, an experimental environment used to study and evaluate the proposed standard is presented. The basic structure and distribution of function in this PHIGS implementation is discussed. We describe the architecture of a device-independent environment designed to realize the performance essential to the adequate functioning of a PHIGS implementation. The results presented emphasize the PHIGS output model. Full utilization of workstation processing capabilities, minimization of host/workstation interaction and efficient data management are key to our implementation.     

The Priority Tree, a HL/HSR Approach for PHIGS

The Programmer's Hierarchical Interactive Grahics System (PHIGS) specifies an interface for programming device-independent computer graphics applications. PHIGS provides a powerful data grouping mechanism, called the PHIGS structure, that may be used to model the geometry of 3D objects. Hidden Line/Hidden Surface Removal (HL/HSR) is a required process to produce realistic solid views of the modeled objects. Modeling clip is an essential process for viewing a clipped portion of the modeled objects. A technique is presented that provides HL/HSR and modeling clip as added utilities to PHIGS. The technique is based on the Binary Space Partitioning (BSP) tree (sometimes called priority tree), and involves a back to front sorting of the primitives of a PHIGS structure network to another PHIGS structure. Modeling clip is achieved by limiting the sorting to those primitives in a specified clip ping region of the object space. The resulting structure when displayed on a raster device produces a realistic view of the possibly clipped object that was originally modeled by the PHIGS structure network.     

The Cone of Normals Technique for Fast Processing of Curved Patches

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,