Theory and practice of geometric and physical modeling

The 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling, which was a federation of the 2009 SIAM Conference on Geometric Design and the 2009 ACM Symposium on Solid and Physical Modeling, was held in San Francisco, USA, from October 5 to October 8, 2009. The goal of the conference was to present theoretically well founded new methods for geometric and physical modeling that have useful practical applications. In response to the call for papers of the conference, 85 papers were submitted on many aspects of geometric and physical modeling, and their application in design, analysis, manufacturing, biomedicine, digital entertainment, and other areas. All papers were assessed by five reviewers, usually a member from the international program committee. A total of 24 papers were selected for plenary presentation and publication as full papers in the proceedings of the conference, published by ACM. Moreover, a total of 18 papers were selected for poster presentation and publication as short papers in the same proceedings. The eight papers published in this special issue have been selected from the 24 full papers in the proceedings. We have made the selection of the papers on the basis of their quality and their suitability for the readership of Computer-Aided Design. The selected papers have been improved and extended with new material. The new versions have once again been assessed, usually by the same reviewers as for the conference, which has led to further improvements. Altogether, this has resulted in a set of highquality and very interesting papers. All papers are on geometric or physical modeling, and present a combination of theory and practice. A geometric constraint on curve networks suitable for smooth interpolation, by T. Hermann, J. Peters and T. Strotman, presents a new result for smooth interpolation of a network of curves. At each vertex of the network where an even number of curves meet, the vertex enclosure constraint must hold. The paper reformulates this algebraic condition in terms of the local geometry of the curve network, i.e. in a geometric constraint that is related to Euler’s theorem on local curvature. This nice theoretical result can be very helpful in practice when modeling free-form surfaces with networks of curves. Parameterization and applications of Catmull–Rom curves, by Cem Yuksel, Scott Schaefer and John Keyser, proves that, in the class of parameterizations ranging from uniform to chordal, centripetal parameterization is the only one for the very popular cubic Catmull–Rom splines that guarantees that there are no cusps or local self-intersections within curve segments. It also gives a bound on the distance between a curve and its control polygon, which canbeused to guaranteeno global self-intersections. Finally, several applications of Catmull–Rom curves are discussed, and the importance of the choice of parameterization in these applications