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175
Static analysis yields efficient exact integer arithmetic for computational geometry
 ACM Trans. Graph
, 1996
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Implicitization using Moving Curves and Surfaces
, 1995
"... This paper presents a radically new approach to the century old problem of computing the implicit equation of a parametric surface. For surfaces without base points, the new method expresses the implicit equation in a determinant which is one fourth the size of the conventional expression based on D ..."
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Cited by 66 (4 self)
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This paper presents a radically new approach to the century old problem of computing the implicit equation of a parametric surface. For surfaces without base points, the new method expresses the implicit equation in a determinant which is one fourth the size of the conventional expression based on Dixon's resultant. If base points do exist, previous implicitization methods either fail or become much more complicated, while the new method actually simplifies.
Using Generic Programming for Designing a Data Structure for Polyhedral Surfaces
 Comput. Geom. Theory Appl
, 1999
"... Appeared in Computational Geometry  Theory and Applications 13, 1999, 6590. Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, ..."
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Cited by 50 (4 self)
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Appeared in Computational Geometry  Theory and Applications 13, 1999, 6590. Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedral surfaces and evaluate edgebased representations with respect to our design goals. A design for polyhedral surfaces in a halfedge data structure is developed following the generic programming paradigm known from the Standard Template Library STL for C++. Connections are shown to planar maps and facebased structures. Key words: Library design; Generic programming; Combinatorial data structure; Polyhedral surface; Halfedge data structure 1 Introduction Combinatorial structures, such as planar maps, are fundamental in computational geometry. In order to be useful in practice, a solid library for compu...
Converting bases with the Gröbner walk
 Journal of Symbolic Computation
, 1997
"... We present an algorithm which converts a given Gröbner basis of a polynomial ideal I to a Gröbner basis of I with respect to another term order. The conversion is done in several steps following a path in the Gröbner fan of I. Each conversion step is based on the computation of a Gröbner basis of a ..."
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Cited by 45 (1 self)
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We present an algorithm which converts a given Gröbner basis of a polynomial ideal I to a Gröbner basis of I with respect to another term order. The conversion is done in several steps following a path in the Gröbner fan of I. Each conversion step is based on the computation of a Gröbner basis of a toric degeneration of I. c ○ 1997 Academic Press Limited 1.
Matchmaker: Manifold BReps for nonmanifold rsets
 Proceedings of the ACM Symposium on Solid Modeling
, 1999
"... Many solid modeling construction techniques produce nonmanifold rsets (solids). With each nonmanifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each nonmanifold edge of N with 2k incident faces will be ..."
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Cited by 41 (19 self)
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Many solid modeling construction techniques produce nonmanifold rsets (solids). With each nonmanifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each nonmanifold edge of N with 2k incident faces will be replicated k times in any manifold model M of that family. Furthermore, some nonmanifold vertices of N must also be replicated in M, possibly several times. M can be obtained by defining, in N, a single adjacent face TA(E,F) for each pair (E,F) that combines an edge E and an incident face F. The adjacency relation satisfies TA(E,TA(E,F))=F. The choice of the map A defines which vertices of N must be replicated in M and how many times. The resulting manifold representation of a nonmanifold solid may be encoded using simpler and more compact datastructures, especially for triangulated model, and leads to simpler and more efficient algorithms, when it is used instead of a nonmanifold repre...
Interactive Boolean Operations for Conceptual Design of 3D Solids
, 1997
"... Interactive modeling of 3D solids is an important and difficult problem in computer graphics. The Constructive Solid Geometry (CSG) modeling scheme is highly attractive for interactive design, due to its support for hierarchical modeling and Boolean operations. Unfortunately, current algorithms for ..."
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Cited by 41 (1 self)
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Interactive modeling of 3D solids is an important and difficult problem in computer graphics. The Constructive Solid Geometry (CSG) modeling scheme is highly attractive for interactive design, due to its support for hierarchical modeling and Boolean operations. Unfortunately, current algorithms for interactive display of CSG models require expensive specialpurpose hardware that is not easily available. In this paper we present a method for interactive display of CSG models using standard, widely available graphics hardware. The method enables the user to interactively modify the affine transformations associated with CSG subobjects. The application we focus upon is that of conceptual design, a stage in the design process in which rapid, interactive visualization of the model and highlevel design operations are of crucial importance, while the objects are relatively simple. The method converts the CSG graph to a novel Convex Differences Aggregate(CDA) representation. The CDA utili...
Approximate Boolean Operations on Freeform Solids
, 2001
"... In this paper we describe a method for computing approximate results of boolean operations (union, intersection, difference) applied to freeform solids bounded by multiresolution subdivision surfaces. ..."
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Cited by 41 (5 self)
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In this paper we describe a method for computing approximate results of boolean operations (union, intersection, difference) applied to freeform solids bounded by multiresolution subdivision surfaces.
Preventing SelfIntersection under FreeForm Deformation
 IEEE Transactions on Visualization and Computer Graphics
, 2001
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Designing a Data Structure for Polyhedral Surfaces
 In Proc. 14th Annu. ACM Sympos. Comput. Geom
, 1998
"... Design solutions for a program library are presented for combinatorial data structures in computational geometry, such as planar maps and polyhedral surfaces. Design issues considered are genericity, flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedr ..."
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Cited by 34 (2 self)
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Design solutions for a program library are presented for combinatorial data structures in computational geometry, such as planar maps and polyhedral surfaces. Design issues considered are genericity, flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedral surfaces. Edgebased representations for polyhedrons are evaluated with respect to the design goals. A design for polyhedral surfaces in a halfedge data structure is developed following the generic programming paradigm known from the Standard Template Library STL for C++. Connections are shown to planar maps and facebased structures managing holes in facets. 1 Introduction Combinatorial structures, such as planar maps, are fundamental in computational geometry. In order to use computational geometry in practice, a solid library must provide generic and flexible solutions as one of its fundamental cornerstones. Other design criteria are time and space efficiency. Easeofuse is necessar...