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<p><strong>Guest editors Jarek R. Rossignac of IBM's T.J. Watson Research Center and Christoph M. Hoffmann of Purdue University</strong> pulled together a collection of articles on solid modeling, drawing on presentations at an internationally known solid modeling symposium. The original plan was to publish a special section in the March 1996 issue of <it>IEEE Computer Graphics and Applications</it>. Following discussions among the guest editors, <it>CG&A</it>, and <it>IEEE Transactions on Visualization and Computer Graphics</it> Editor-in-Chief Arie Kaufman of SUNY at Stony Brook and Associate Editor-in-Chief Greg Nielson of Arizona State University, the decision was to publish the solid modeling section in <it>TVCG</it>. The articles accepted after the <it>TVCG</it> review process appear in the March issue. The following abstracts explain the articles in the solid modeling section of that issue.</p><p><b>"A Road Map to Solid Modeling," Christoph M. Hoffman and Jaroslaw R. Rossignac</b></p><p>The guest editors of this special issue provide the background of solid modeling, beginning with some mathematical foundations. They review the major representation schemata of solids, then characterize major layers of abstraction in a typical solid modeling system. The lowest level of abstraction comprises a substratum of basic service algorithms. At an intermediate level of abstraction are algorithms for larger, more conceptual operations. A yet higher level of abstraction presents a function view that typically targets solid design. The guest editors look at some applications and user interaction concepts. To conclude, they briefly explore trends in the field.</p><p><b>"Volume-Preserving Free-Form Solids," Ari Rappoport, Alla Sheffer, and Michel Bercovier</b></p><p>Important trends in geometric modeling include the reliance on solid models rather than surface-based models and the enhancement of the expressive power of models by using free-form objects in addition to the usual geometric primitives and by incorporating physical principles. Another trend is the emphasis on interactive performance.</p><p>The authors integrate all of these requirements in a single geometric primitive by endowing the trivariate tensor product free-form solid with several important physical properties, including volume and internal deformation energy. They present a novel method for modeling an object composed of several tensor-product solids while preserving the desired volume of each primitive and ensuring high-order continuity constraints between the primitives. The method uses the Uzawa algorithm for nonlinear optimization, with objective functions based on deformation energy or least squares.</p><p><b>"Function Representation for Sweeping by a Moving Solid," A. Sourin and A. Pasko</b></p><p>The authors study a function representation of point sets swept by moving solids. The original solid generator is defined by an inequality greater than or equal to zero, based on Cartesian coordinates and time. This definition allows the inclusion of solids that change their shapes in time. Constructive solids can also be used as generators when described by R-functions. The trajectory of the generator can be defined in parametric form as movement of its local coordinate system. The authors did this with superposition of time-dependent affine transformations. To get the function representation of the swept solid, they applied the concept of envelopes. They reduced the problem of swept solid description to a global extremum search by time.</p><p><b>"An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids," Evan C. Sherbrooke, Nicholas M. Patrikalakis, and Erik Brisson</b></p><p>The authors develop an algorithm for determining the Medial Axis Transform (MAT) for general 3D polyhedral solids of arbitrary genus without cavities, with nonconvex vertices and edges. The algorithm is based on a classification scheme that relates different pieces of the medial axis to one another even in the presence of degenerate medial axis points. The authors address representation of the medial axis and associated radius function, and give pseudocode for the algorithm along with recommended optimizations. Examples illustrate the algorithm's computational properties for convex and nonconvex 3D polyhedral solids with polyhedral holes.</p><p><b>"Shape Description by Medial Surface Construction," Damian J. Sheehy, Cecil G. Armstrong, and Desmond J. Robinson</b></p><p>The medial surface is a skeletal abstraction of a solid that provides useful shape information. The authors define the medial surface and its associated topological entities and present an algorithm for computing the medial surface of a large class of B-rep solids. The algorithm is based on the domain Delaunay triangulation of a relatively sparse distribution of points generated on the object's boundary. This strategy is adaptive, in that the boundary point set is refined to guarantee a correct topological representation of the medial surface.</p><p><b>"Solving Geometric Constraints by Homotopy," H. Lamure and D. Michelucci</b></p><p>Geometric modeling by constraints yields systems of equations classically solved by Newton-Raphson's iteration, from a starting guess interactively provided by the designer. However, this method might fail to converge or might converge to an unwanted solution after "chaotic" behavior. This article claims that, in such cases, the homotopic method is much more satisfactory.</p><p><b>"A Fast Method for Estimating Discrete Field Values in Early Engineering Design," Jovan Zagajac</b></p><p>The author describes a fast method of computing estimates of field values at a few critical points. The method is based on an old technique—integrated partial differential equations through stochastic sampling—accelerated through the use of ray representations. In the preprocessing stage, the domain is coherently sampled to produce a ray-rep. The second stage involves the usual stochastic sampling of the field, now enhanced by exploiting the semi-discrete character of ray-reps. The method is relatively insensitive to the complexity of the shape being analyzed and has adjustable precision. Its mechanics and advantages are illustrated using Laplace's equation as an example.</p>

N. K. Hays, "Abstracts for Solid Modeling Articles in March 1996 TVCG," in IEEE Computer Graphics and Applications, vol. 16, no. , pp. 16-17, 1996.
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