In this paper, we describe an efficient image-based approach to computing and shading visual hulls from silhouette image data. Our algorithm takes advantage of epipolar geometry and incremental computation to achieve a constant rendering cost per rendered pixel. It does not suffer from the computation complexity, limited resolution, or quantization artifacts of previous volumetric approaches. We demonstrate the use of this algorithm in a real-time virtualized reality application running off a small number of video streams.

. We present new algorithms for creating and rendering visual hulls in real-time. Unlike voxel or sampled approaches, we compute an exact polyhedral representation for the visual hull directly from the silhouettes. This representation has a number of advantages: 1) it is a view-independent representation, 2) it is well-suited to rendering with graphics hardware, and 3) it can be computed very quickly. We render these visual hulls with a view-dependent texturing strategy, which takes into account visibility information that is computed during the creation of the visual hull. We demonstrate these algorithms in a system that asynchronously renders dynamically created visual hulls in real-time. Our system outperforms similar systems of comparable computational power. 1

A new approach to ray tracing is introduced. The definition of a "ray" is extended into a cone by including information on the spread angle and the virtual origin. The advan-tages of this approach, which tries to model light propagation with more fidelity, include a better method of anti-aliasing, a way of calculating fuzzy shadows and dull reflections, a method of calculating the correct level of detail in a procedural model and texture map, and finally, a procedure for faster intersection calculation.

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...

this paper, we present a system that exploits object-space, rayspace, image-space and temporal coherence to accelerate ray tracing. Our system uses per-surface interpolants to approximate radiance, while conservatively bounding error. The techniques we introduce in this paper should enhance both interactive and batch ray tracers.

Sphere tracing is a new technique for rendering implicit surfaces using geometric distance. Distance-based models are common in computer-aided geometric design and in the modeling of articulated figures. Given a function returning the distance to an object, sphere tracing marches along the ray toward its first intersection in steps guaranteed not to penetrate the implicit surface. Sphere tracing is particularly adept at rendering pathological surfaces. Creased and rough implicit surfaces are defined by functions with discontinuous or undefined derivatives. Current root finding techniques such as L-G surfaces and interval analysis require periodic evaluation of the derivative, and their behavior is dependent on the behavior of the derivative. Sphere tracing requires only a bound on the magnitude of the derivative, robustly avoiding problems Manuscript, July 1994. Recommended for publication: The Visual Computer. 5-70 where the derivative jumps or vanishes. This robustness and scope ...

We present an algebraic framework, called Constructive Volume Geometry (CVG), for modelling complex spatial objects using combinational operations. By utilising scalar fields as fundamental building blocks, CVG provides high-level algebraic representations of objects that are defined mathematically or built upon sampled or simulated datasets. It models amorphous phenomena as well as solid objects, and describes the interior as well as the exterior of objects. We also describe a hierarchical representation scheme for CVG, and a direct rendering method with a new approach for consistent sampling. The work has demonstrated the feasibility of combining a variety of graphics data types in a coherent modelling scheme.

Interactive modeling of 3-D solids is an important and difficult problem in computer graphics. The Constructive Solid Geometry (CSG) modeling scheme is highly attractive for interactive design, due to its support for hierarchical modeling and Boolean operations. Unfortunately, current algorithms for interactive display of CSG models require expensive special-purpose hardware that is not easily available. In this paper we present a method for interactive display of CSG models using standard, widely available graphics hardware. The method enables the user to interactively modify the affine transformations associated with CSG sub-objects. The application we focus upon is that of conceptual design, a stage in the design process in which rapid, interactive visualization of the model and high-level design operations are of crucial importance, while the objects are relatively simple. The method converts the CSG graph to a novel Convex Differences Aggregate(CDA) representation. The CDA utili...

The recurrent iterated function system and the L-system are two powerful linear fractal models. The main drawback of recurrent iterated function systems is a difficulty in modeling whereas the main drawback of L-systems is inefficient geometry specification. Iterative and recursive structures extend the object instancing paradigm, allowing it to model linear fractals. Instancing models render faster and are more intuitive to the computer graphics community. A preliminary section briefly introduces the object instancing paradigm and illustrates its ability to model linear fractals. Two main sections summarize recurrent iterated function systems and L-systems, and provide methods with examples for converting such models to the object instancing paradigm. Finally, a short epilogue describes a particular use of color in the instancing paradigm and the conclusion outlines directions for further research.

Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSG-based algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of set-membership classification by traversing the tree associated with the solid. These algorithms usually generate intermediate results that do not contribute to the final result, and hence may be regarded as redundant and a source of inefficiency. To reduce such inefficiencies, we associate with each primitive A in a tree S an active zone 2 that represents the region of space where changes to A affect the solid represented by S, and we use a representation of 2 instead of S for set-membership classification. In the paper we develop a mathematical theory of active zones, prove that they correspond to the intersection of certain nodes of the original trees, and show how they lead to efficient new algorithms for boundary evaluation, for detecting and eliminating redundant nodes in CSG trees, for interference (null-set) detection, and for graphic shading.