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13
Normal Bounds for SubdivisionSurface Interference Detection
 In Proc. of IEEE Scientific Visualization, IEEE
, 2001
"... Subdivision surfaces are an attractive representation when modeling arbitrary topology freeform 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 ..."
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Cited by 19 (2 self)
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Subdivision surfaces are an attractive representation when modeling arbitrary topology freeform 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.
Decomposition Contact Response (DCR) for Explicit Finite Element Dynamics
 INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
, 2005
"... ..."
SubdivisionBased Multilevel Methods for Large Scale Engineering Simulation of Thin Shells
 IN PROCEEDINGS OF ACM SOLID MODELING
, 2002
"... 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 the ..."
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Cited by 14 (2 self)
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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 highresolution simulations (10^5 degrees of freedom or more) become prohibitive. The main
A Cohesive Approach to ThinShell Fracture and Fragmentation
, 2004
"... We develop a finiteelement 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 KirchhoffLove theory. The shell is spatially discretized by means of subdivision shell elements. Fracture is allowe ..."
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Cited by 12 (5 self)
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We develop a finiteelement 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 KirchhoffLove 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 inplane or tearing, shearing, and bending or hinge modes of fracture. In order to follow the propagation and branching of cracks, subdivision shell elements are prefractured 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.
PatientSpecific Vascular NURBS Modeling for Isogeometric Analysis of Blood Flow
 IN PROCEEDINGS OF THE 15TH INTERNATIONAL MESHING ROUNDTABLE
, 2006
"... We describe an approach to construct hexahedral solid NURBS (NonUniform Rational BSplines) meshes for patientspecific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segm ..."
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Cited by 8 (1 self)
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We describe an approach to construct hexahedral solid NURBS (NonUniform Rational BSplines) meshes for patientspecific 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 skeletonbased 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 onetoone 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 patientspecific arterial models are presented.
September 11, 2005 22:5 WSPC/Lecture Notes Series: 9in x 6in main Subdivision on Arbitrary Meshes: Algorithms and Theory
"... 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 ..."
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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
A Survey of SubdivisionBased Tools for Surface Modeling
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 2005
"... Subdivision surfaces have emerged as a powerful representation for surface modeling and design. They address important limitations of traditional splinebased methods, such as the ability to handle arbitrary topologies and to support multiscale editing operations. In this paper we survey existing su ..."
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Subdivision surfaces have emerged as a powerful representation for surface modeling and design. They address important limitations of traditional splinebased methods, such as the ability to handle arbitrary topologies and to support multiscale editing operations. In this paper we survey existing subdivisionbased modeling methods with emphasis on interactive tools for styling and decoration of 3D models.
SUBDIVISION ON ARBITRARY MESHES: ALGORITHMS AND THEORY
"... 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 ..."
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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.
Finite Element Analysis for Linear Elastic Solids Based on Subdivision Schemes ∗
"... Finite element methods are used in various areas ranging from mechanical engineering to computer graphics and biomedical applications. In engineering, a critical point is the gap between CAD and CAE. This gap results from different representations used for geometric design and physical simulation. ..."
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Finite element methods are used in various areas ranging from mechanical engineering to computer graphics and biomedical applications. In engineering, a critical point is the gap between CAD and CAE. This gap results from different representations used for geometric design and physical simulation. We present two different approaches for using subdivision solids as the only representation for modeling, simulation and visualization. This has the advantage that no data must be converted between the CAD and CAE phases. The first approach is based on an adaptive and featurepreserving tetrahedral subdivision scheme. The second approach is based on CatmullClark subdivision solids.
February 7, 2005 2:34 WSPC/Lecture Notes Series: 9in x 6in main Subdivision on Arbitrary Meshes: Algorithms and Theory
"... 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 ..."
Abstract
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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.