While large investments are made in sophisticated graphics hardware, most realistic rendering is still performed off-line using ray trace or radiosity systems. A coordinated use of hardware-provided bitplanes and rendering pipelines can, however, approximate ray trace quality illumination effects in a user-interactive environment, as well as provide the tools necessary for a user to declutter such a complex scene. A variety of common ray trace and radiosity illumination effects are presented using multi-pass rendering in a pipeline architecture. We provide recursive reflections through the use of secondary viewpoints, and present a method for using a homogeneous 2-D projective image mapping to extend this method for refractive transparent surfaces. This paper then introduces the Dual Z-buffer, or DZ-buffer, an evolutionary hardware extension which, along with current framebuffer functions such as stencil planes and accumulation buffers, provides the hardware platform to render non-refr...

We describe a CSG rendering algorithm that requires no evaluation of the CSG tree beyond normalization and pruning. It renders directly from the normalized CSG tree and primitives described (to the graphics system) by their facetted boundaries. It behaves correctly in the presence of user defined, "near" and "far" clipping planes. It has been implemented on standard graphics workstations using Iris GL 1 and OpenGL 2 graphics libraries. Modestly sized models can be evaluated and rendered at interactive (less than a second per frame) speeds. We have combined the algorithm with an existing B-rep based modeller to provide interactive rendering of incremental updates to large models. 1. Introduction Constructive Solid Geometry (CSG) within an interactive modelling environment provides a simple and intuitive approach to solid modelling. In conventional modelling systems primitives are first positioned, a boolean operation is performed and the results then rendered. Often the corr...

ABSTRACT A convenient interactive design environment requires efficient facilities for shading solid models represented in CSC. Shading techniques based on boundary evaluation or ray casting that require calculations of geometric intersections are too inefficient for interactive graphics when CSC primitives with curved (parametric) surfaces are involved. Projective approaches, where the primitive surfaces are scan-converted using standard hardware-supported graphic functions are preferred. Since not all the points of the faces of a CSC primitive lie on the CSC solid, scan conversion must be combined with a procedure that tests the produced 3D surface-points against the original CSC expression. Point classifications against primitives defined by arbitrary curved boundaries may be performed, without geometric intersections, through depth-comparisons at each pixel. This approach has been implemented for the Pixel-Power machine by researchers at UNC. It deals with complex CSC trees by converting CSC expressions into sum-ofproduct form and repeatedly scan-converting the primitives of each product. The Trickle algorithm, which considerably reduces the number of scan-conversions in the general case has been developed at IBM Research and presented elsewhere. This paper discusses several recent improvements to the original Trickle algorithm. The overall algorithm has been simplified. The " scan-conversion process and the point classification tests have been modified to correctly handle cases where several primitive faces coincide within an arbitrary numerical resolution. These enhancements are not only necessary for on/on cases in regularized Boolean expressions, but also for processing pairs of faces near their common edges. Finally, we point out that a simple two-pass extension of the trickle algorithm using an auxiliary shadow buffer suffices to compute directly from CSC shaded images with shadows. 1

Set membership classification algorithms visit nodes of a CSG tree through a recursive divide-and-conquer process, which stores intermediate results in a stack, whose depth equals the height, H, of the tree. During this process, the candidate sets is usually subdivided into uniform cells, whose interior is disjoint from primitives' boundaries. Cells inside the CSG object are identified by combining the binary results of classifying them against the primitives. In parallel systems, which allocate a different process to each leaf of the tree, and in algorithms that classify large collections of regularly spaced candidate sets (points, pixels, voxels, rays, or cross-sections) against the primitives using forward differences, a separate stack is associated with each candidate or cell. Our new representation for CSG trees, called Blist, distributes the merging operation to the primitives and reduces the storage requirement for each cell to log(H+1) bits. Blist can represent any Boolean expr...

We present algorithms and systems for interactive boundary computation of Boolean combinations of sculptured solids. The algorithm is applicable to all spline solids and computes an accurate boundary representation.To speed up the computation, the algorithm exploits parallelism at all stages. It has been implemented on a multi-processor SGI and takes one second on average per boolean operation to compute the boundary of high degree primitives. The system has also been integrated with an immersive design and manipulation environment. The resulting system is able to interactively evaluate boundaries of the models, display them for model validation and place them at appropriate position using collision detection algorithms.

Methodology is developed to apply ray-representations to geometric analysis of space-filling models of protein structure. The following specific problems are treated. First, we define the ray-representation for fused-sphere models of proteins. Second, using the ray-representation, we treat computation of molecular contact surfaces in solution via Minkowski dilation and erosion. Third, we describe how all points of the molecular contact surface can be tagged according to their chemical properties. Fourth, we show how equivalence set methods can be applied to ray representations of proteins in order to identify internal empty spaces and classify their connectedness to the outside. Fifth, we develop filters to analyze the morphology of interstitial spaces in proteins which connect to the outside. Sixth, we discuss how Boolean algorithms can be used to determine whether water molecules identified in X-ray crystallography are inside, outside, or intersecting the boundary defined by the solv...

The computational requirements of high-quality, real-time rendering exceeds the limits of generally available computing power. However illumination effects, except shadows, are less noticeable on moving pictures. Shadows can be produced with the same techniques used for visibility computations, therefore the basic requirements of real-time rendering are transformations, pre-selection of the part of the scene to be displayed and visibility computations. Transformations scale well, ie, their time requirement grows linearly with the input size. Pre-selection, if implemented by the traditional way of polygon clipping, has a growing rate of N log N in the worst case, where N is the total number of edges in the scene. Visibility computations, exhibiting a quadratic growing rate, are the bottleneck from a theoretical point of view. Three approaches are discussed to speed up visibility computations: (i) reducing the expected running time to O(N log N ) (ii) using approximation algorithms with ...

We present a system for fast and accurate display of CSG (constructive solid geometry) models. Such models have as primitives, polyhedra and solids whose boundaries can be represented using rational spline surfaces. As a part of pre-processing, we compute the Brep (boundary representation) from the CSG tree and represent the resulting solid using trimmed spline surfaces. No assumptions are made on the number of primitives or the degree of the primitives in the CSG tree. Given a trimmed spline model, we tessellate it into polygons as a function of the viewing parameters and render it using visibility culling and coherence between successive frames. The choice of a analytic representation of the model and the trimming curves is fundamental to the fast performance of the system. The system has been used to convert parts of a submarine storage and handling system model represented as more than 2; 000 CSG trees. The B-rep consists of more than 30; 000 trimmed spline surfaces and is displaye...

2.1. Casein kinase 2 functions in eukaryotic cells 2.2. Physiological and evolutionary implications for existence of a bacterial CK2 predecessor