We present a paradigm and toolkit for rapid prototyping of interactive, animated 3D graphics programs. The paradigm has its roots in declarative programming, emphasizing immutable values, first class functions, and relations, applying these concepts to a broad range of types, including points, vectors, planes, colors, transforms, geometry, and sound. The narrow role of modifiable state in this paradigm allows applications to be run in a collaborative setting (multi-user and multi-computer) without modification.

Abstract 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.

Abstract 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,

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.

Abstract 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.

Modeling clip gives an application the ability to remove sections of an object in order to view internal detail. The clipping volume defied by modeling clip can be concave and disjoint, and is composed of a set of volumes that are specified in modeling coordinates. The modeling clip functionality has been included in the PHIGS specification [4], Some interesting peculiarities arise from the fact that most graphics pipelines (such as PHIGS) are algebraically based and that modeling clip regions are specified in modeling coordinates. One such peculiarity occurs when the transformation relating the coordinate system of the clip region to world coordinates is singular. A study on the algorithmic and architectural issues of implementing modeling clip is presented. The resulting algorithm to implement the modeling clip mechanism represents the clip volume as a pipeline of filters with each filter representing one of the sub-volumes. The method handles all of the sixteen possible set combinations between two regions in space. The effects of transformations on modeling clip have been examined, and has resulted in identifying when modeling clip can be efficiently performed in device coordinates as well as the cases when it can not. When handling singular modeling transformations, it is shown that it i

No abstract available.

Abstract 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.