In this paper, we survey the state of the art in collision detection between general geometric models. The set of models include polygonal objects, spline or algebraic surfaces, CSG models, and deformable bodies. We present a number of techniques and systems available for contact determination. We also describe several N-body algorithms to reduce the number of pairwise intersection tests. 1 Introduction The goal of collision detection (also known as interference detection or contact determination) is to automatically report a geometric contact when it is about to occur or has actually occurred. The geometric models may be polygonal objects, splines, or algebraic surfaces. The problem is encountered in computer-aided design and machining (CAD/CAM), robotics and automation, manufacturing, computer graphics, animation and computer simulated environments. Collision detection enables simulationbased design, tolerance verification, engineering analysis, assembly and dis-assembly, motion pla...

This dissertation describes the principles of pen-and-ink illustration, and shows how a great number of them can be implemented as part of an automated rendering system. Illustration techniques in general, and pen-and-ink rendering in particular, offer great potential for creating effective images from CAD models. And with the computer's ability to manipulate increasingly large models, communicating complex information in an effective and comprehensible manner is becoming an important problem. However, this potential remains relatively untapped in the field of computer graphics. After discussing principles of traditional pen-and-ink rendering, this dissertation shows how the traditional graphics pipeline must be modified to support pen-andink rendering. Then, it introduces the new concept of prioritized stroke textures. Prioritized stroke textures form the central mechanism by which strokes are generated so as to both convey a certain texture, such as "bricks", and achieve a target tone simultaneously. Prioritized stroke textures also have the advantages of being resolution dependent

Polygonal models acquired with emerging 3D scanning technology or from large scale CAD applications easily reach sizes of several gigabytes and do not fit in the address space of common 32-bit desktop PCs. In this paper we propose an out-of-core mesh compression technique that converts such gigantic meshes into a streamable, highly compressed representation. During decompression only a small portion of the mesh needs to be kept in memory at any time. As full connectivity information is available along the decompression boundaries, this provides seamless mesh access for incremental in-core processing on gigantic meshes. Decompression speeds are CPU-limited and exceed one million vertices and two million triangles per second on a 1.8 GHz Athlon processor.

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Appeared in Computational Geometry -- Theory and Applications 13, 1999, 65-90. Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, time and space efficiency, and ease-of-use. We focus on topological aspects of polyhedral surfaces and evaluate edge-based representations with respect to our design goals. A design for polyhedral surfaces in a halfedge data structure is developed following the generic programming paradigm known from the Standard Template Library STL for C++. Connections are shown to planar maps and face-based structures. Key words: Library design; Generic programming; Combinatorial data structure; Polyhedral surface; Halfedge data structure 1 Introduction Combinatorial structures, such as planar maps, are fundamental in computational geometry. In order to be useful in practice, a solid library for compu...

A method is presented to broaden implicit surface modeling. The implicit surfaces usually employed in computer graphics are two dimensional manifolds because they are defined by real-valued functions that impose a binary regionalization of space (i.e., an inside and an outside). When tiled, these surfaces yield edges of degree two. The new method allows the definition of implicit surfaces with boundaries (i.e., edges of degree one) and intersections (i.e., edges of degree three or more). These non-manifold implicit surfaces are defined by a multiple regionalization of space. The definition includes a list of those pairs of regions whose separating surface is of interest. Also presented is an implementation that converts a nonmanifold implicit surface definition into a collection of polygons. Although following conventional implicit surface polygonization, there are significant differences that are described in detail. Several example surfaces are defined and polygonized. CR Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling - Curve, Surface, Solid, and Object Representations. Additional Keywords and Phrases: Implicit Surface, NonManifold, Polygonization. 1

this paper has been supported in part by ESPRIT IV LTR Projects No. 21957 (CGAL) and No. 28155 (GALIA), by the USA-Israel Binational Science Foundation, by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), by a Franco-Israeli research grant "factory of the future" (monitored by AFIRST/France and The Israeli Ministry of Science), and by the Hermann Minkowski -- Minerva Center for Geometry at Tel Aviv University

Recently, animations with deforming objects have been frequently used in various computer graphics applications. Metamorphosis (or morphing) of three-dimensional objects is one of the techniques which realizes shape transformation between two or more existing objects. In this paper, we present an efficient framework for metamorphosis between two topologically equivalent, arbitrary meshes with the control of surface correspondences by the user. The basic idea of our method is to partition meshes according to the reference shapes specified by the user, whereby vertex-to-vertex correspondences between the two meshes can be specified. Each of the partitioned meshes is embedded into a polygonal region on the plane with harmonic mapping. Those embedded meshes have the same graph structure as their original meshes. By overlapping those two embedded meshes, we can establish correspondence between them. Based on this correspondence, metamorphosis is achieved by interpolating the corresponding vertices from one mesh 1 to the other. We demonstrate that the minimum control of surface correspondences by the user generates sophisticated results of the interpolation between two meshes.

In this paper an algorithm is proposed that takes as input a generic set of unorganized points, sampled on a real object, and returns a closed interpolating surface. Specifically, this method generates a closed 2-manifold surface made of triangular faces, without limitations on the shape or genus of the original solid. The reconstruction method is based on generation of the Delaunay tetrahedralization of the point set, followed by a sculpturing process constrained to particular criteria. The main applications of this tool are in medical analysis and in reverse engineering areas. It is possible, for example, to reconstruct anatomical parts starting from surveys based on TACs or magnetic resonance.

Many solid modeling construction techniques produce non-manifold r-sets (solids). With each non-manifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each non-manifold edge of N with 2k incident faces will be replicated k times in any manifold model M of that family. Furthermore, some non-manifold vertices of N must also be replicated in M, possibly several times. M can be obtained by defining, in N, a single adjacent face TA(E,F) for each pair (E,F) that combines an edge E and an incident face F. The adjacency relation satisfies TA(E,TA(E,F))=F. The choice of the map A defines which vertices of N must be replicated in M and how many times. The resulting manifold representation of a non-manifold solid may be encoded using simpler and more compact data-structures, especially for triangulated model, and leads to simpler and more efficient algorithms, when it is used instead of a non-manifold repre...