Efficient contact determination between geometric models

http://archive.org/details/efficientcontact00linmN

Intersecting biquadratic Bézier surface patches

International audienceWe present three symbolic–numeric techniques for computing the in- tersection and self–intersection curve(s) of two Bézier surface patches of bidegree (2,2). In particular, we discuss algorithms, implementation, illustrative examples and provide a comparison of the methods

Intersecting biquadratic Bézier surface patches

International audienceWe present three symbolic–numeric techniques for computing the in- tersection and self–intersection curve(s) of two Bézier surface patches of bidegree (2,2). In particular, we discuss algorithms, implementation, illustrative examples and provide a comparison of the methods

Theory and algorithms for swept manifold intersections

Recent developments in such fields as computer aided geometric design, geometric modeling, and computational topology have generated a spate of interest towards geometric objects called swept volumes. Besides their great applicability in various practical areas, the mere geometry and topology of these entities make them a perfect testbed for novel approaches aimed at analyzing and representing geometric objects. The structure of swept volumes reveals that it is also important to focus on a little simpler, although a very similar type of objects - swept manifolds. In particular, effective computability of swept manifold intersections is of major concern. The main goal of this dissertation is to conduct a study of swept manifolds and, based on the findings, develop methods for computing swept surface intersections. The twofold nature of this goal prompted a division of the work into two distinct parts. At first, a theoretical analysis of swept manifolds is performed, providing a better insight into the topological structure of swept manifolds and unveiling several important properties. In the course of the investigation, several subclasses of swept manifolds are introduced; in particular, attention is focused on regular and critical swept manifolds. Because of the high applicability, additional effort is put into analysis of two-dimensional swept manifolds - swept surfaces. Some of the valuable properties exhibited by such surfaces are generalized to higher dimensions by introducing yet another class of swept manifolds - recursive swept manifolds. In the second part of this work, algorithms for finding swept surface intersections are developed. The need for such algorithms is necessitated by a specific structure of swept surfaces that precludes direct employment of existing intersection methods. The new algorithms are designed by utilizing the underlying ideas of existing intersection techniques and making necessary technical modifications. Such modifications are achieved by employing properties of swept surfaces obtained in the course of the theoretical study. The intersection problems is also considered from a little different prospective. A novel, homology based approach to local characterization of intersections of submanifolds and s-subvarieties of a Euclidean space is presented. It provides a method for distinguishing between transverse and tangential intersection points and determining, in some cases, whether the intersection point belongs to a boundary. At the end, several possible applications of the obtained results are described, including virtual sculpting and modeling of heterogeneous materials

Detection and Resolution of Interpenetrations of Woven Tows

Woven composite tows can be approximated by creating surfaces using the Virtual Textile Morphology Suite (VTMS) developed at the Air Force Research Lab (AFRL). These surfaces have interpenetrations between tow surface meshes which must be resolved in order to have strict, compatible mesh between all domains. A compatible mesh is desirable to reduce the complexity of the model and allow for a wider range of FEA tools to be used for analysis. To detect these interpenetrations, the surfaces were approximated using Non-Uniform Rational B-Spline (NURBS) surfaces with the SISL library from SINTEF. The interpenetration regions were then identified by B-Spline curves which, when included during the mesh generation process, allowed the surface interpenetrations to be removed and replaced with a compatible mesh between tows. The meshes are strictly tied together to investigate the effects of removing the thin slices of matrix from between tows in close proximity. These resulting meshes were subjected to a simple in-plane loading and compared to another method for removing interpenetrations that shrinks the tow cross-sections until they no longer penetrate. The predicted stresses show that the new method can create small regions of high magnitude stress in the tow local to the edge of the connected region between tows, and that high mesh refinement around these regions can increase the magnitude of these stress concentrations. In regions away from the boundary of the connected regions, both models predict similar stress responses. Also, the analysis predicts less matrix volume at high von Mises stress due to the lack of matrix between tows in the NURBS method meshes. While the analysis shows evidence of singularities, the size of the concentrations and the similar overall response as the previous method show that the new method has some merit, particularly when considering the potential use cases for compatible, connected regions between tow meshes