Subdivision surfaces are an attractive representation when modeling arbitrary topology free-form surfaces and show great promise for applications in engineering design [5, 6] and computer animation [10]. Interference detection is a critical tool in many of these applications. In this paper we derive normal bounds for subdivision surfaces and use these to develop an efficient algorithm for (self-) interference detection.

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This paper presents a multilevel algorithm to accelerate the numerical solution of thin shell finite element problems described by subdivision surfaces. Subdivision surfaces have become a widely used geometric representation for general curved three dimensional boundary models and thin shells as they provide a compact and robust framework for modeling 3D geometry. More recently, the shape functions used in the subdivision surfaces framework have been proposed as candidates for use as finite element basis functions in the analysis and simulation of the mechanical deformation of thin shell structures. When coupled with standard solvers, however, such simulations do not scale well. Run time costs associated with high-resolution simulations (10^5 degrees of freedom or more) become prohibitive. The main

We develop a finite-element method for the simulation of dynamic shell fracture and fragmentation based on cohesive models of fracture. We assume the shells to be thin and to obey the Kirchhoff-Love theory. The shell is spatially discretized by means of subdivision shell elements. Fracture is allowed only along element edges and is assumed to be governed by a cohesive law. When coupled to the shell kinematics, the cohesive model accounts both for in-plane or tearing, shearing, and bending or hinge modes of fracture. In order to follow the propagation and branching of cracks, subdivision shell elements are pre-fractured ab initio. Prior to crack nucleation, crack opening is constrained by means of a penalty method in implicit calculations, or by a projection or displacement averaging method in explicit calculations.

We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input imaging data. Then, luminal surfaces are extracted by isocontouring the preprocessed data, followed by the extraction of vascular skeleton via Voronoi and Delaunay diagrams. Next, the skeleton-based sweeping method is used to construct hexahedral control meshes. Templates are designed for various branching configurations to decompose the geometry into mapped meshable patches. Each patch is then meshed using one-to-one sweeping techniques, and boundary vertices are projected to the luminal surface. Finally, hexahedral solid NURBS are constructed and used in isogeometric analysis of blood flow. Piecewise linear hexahedral meshes can also be obtained using this approach. Examples of patient-specific arterial models are presented. Key words: Patient-specific vascular models, hexahedral mesh, skeleton-based sweeping, NURBS, isogeometric analysis, blood flow. 1

Subdivision surfaces have become a standard geometric modeling tool for a variety of applications. This survey is an introduction to subdivision algorithms for arbitrary meshes and related mathematical theory; we review the most important subdivision schemes the theory of smoothness of subidivision surfaces, and known facts about approximation properties of subdivision bases. 1

Subdivision surfaces have emerged as a powerful representation for surface modeling and design. They address important limitations of traditional spline-based methods, such as the ability to handle arbitrary topologies and to support multiscale editing operations. In this paper we survey existing subdivision-based modeling methods with emphasis on interactive tools for styling and decoration of 3D models.

Subdivision surfaces have become a standard geometric modeling tool for a variety of applications. This survey is an introduction to subdivision algorithms for arbitrary meshes and related mathematical theory; we review the most important subdivision schemes, the theory of smoothness of subdivision surfaces, and known facts about approximation properties of subdivision bases. 1.