Geometric modeling and processing 2006
The fourth international conference on geometric modeling and processing (GMP2006) was held on July 26-28, 2006, in Pittsburgh, USA. The conference provided a forum for researchers and practitioners to present and discuss new approaches to solving geometric problems using a range of computational techniques. This special issue consists of extended versions of selected papers presented at the conference.
Xu and Zhang derive a sixth-order nonlinear geometric flow and uses this flow in solving surface modeling problems such as surface de-noising, surface blending, N -sided hole filling, and free-form surface design with G 2 continuity at the boundary.
Ju et al. describe a method for computing a family of topology and shape-preserving skeletons of a volumetric model. The family of skeletons is parametrized by two user-specified numbers that determine respectively the size of curve and surface features on the skeleton. The resulting structure is particularly suitable for describing cylindrical and plate-like shapes.
Masuda et al. present a discrete framework for incorporating constraints of form features using a hard constraints approach. Using the Lagrange multiplier method, the authors solve a combination of soft and hard constraints, which are useful for deforming 3D models while preserving form features.
Hanniel and Elber present a new idea of converting the overlap test for multivariate normal cones to the problem of intersecting hyper-planes, which is conceptually much simpler than the original problem. Based on the new test, the authors develop an efficient and robust algorithm for solving a system of multivariate equations.
Varady et al. present a robust solution for automatic creation of a CAD-like surface structure over a polygonal mesh. The consistent topology is assured by applying results from combinatorial Morse theory, while the correct geometric location of curve network is the result of tracing methods. The authors demonstrate the efficiency and high quality of the proposed approach by using examples of representative objects reconstructed by Geomagic systems.
Chen et al. develop algorithms for robustly tracking the intersection curves of two continuously deforming piecewise rational surfaces. The mathematical framework is based on singularity theory, which provides a stable way of detecting the transition points of the topological change of the intersection curves. The whole computation is reduced to solving secondorder differential geometric equations.