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Bubble Mesh: Automated Triangular Meshing of NonManifold Geometry by Sphere Packing
 ACM SYMPOSIUM ON SOLID MODELING AND APPLICATIONS
, 1995
"... This paper presents a new computational method for fully automated triangular mesh generation, consistently applicable to wireframe, surface, solid, and nonmanifold geometries. The method, called bubble meshing, is based on the observation that a pattern of tightly packed spheres mimics a Voronoi d ..."
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Cited by 61 (11 self)
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This paper presents a new computational method for fully automated triangular mesh generation, consistently applicable to wireframe, surface, solid, and nonmanifold geometries. The method, called bubble meshing, is based on the observation that a pattern of tightly packed spheres mimics a Voronoi diagram, from which a set of wellshaped Delaunay triangles and tetrahedra can be created by connecting the centers of the spheres. Given a domain geometry and a nodespacing function, spheres are packed on geometric entities, namely, vertices, edges, faces, and volumes, in ascending order of dimension. Once the domain is filled with spheres, mesh nodes are placed at the centers of these spheres and are then connected by constrained Delaunay triangulation and tetrahedrization. To obtain a closely packed configuration of spheres, the authors devised a technique for physically based mesh relaxation with adaptive population control. The process of mesh relaxation significantly reduces the number of illshaped triangles and tetrahedra.
Polygonization of NonManifold Implicit Surfaces
, 1995
"... A method is presented to broaden implicit surface modeling. The implicit surfaces usually employed in computer graphics are two dimensional manifolds because they are defined by realvalued functions that impose a binary regionalization of space (i.e., an inside and an outside). When tiled, these su ..."
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Cited by 50 (0 self)
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A method is presented to broaden implicit surface modeling. The implicit surfaces usually employed in computer graphics are two dimensional manifolds because they are defined by realvalued functions that impose a binary regionalization of space (i.e., an inside and an outside). When tiled, these surfaces yield edges of degree two. The new method allows the definition of implicit surfaces with boundaries (i.e., edges of degree one) and intersections (i.e., edges of degree three or more). These nonmanifold implicit surfaces are defined by a multiple regionalization of space. The definition includes a list of those pairs of regions whose separating surface is of interest. Also presented is an implementation that converts a nonmanifold implicit surface definition into a collection of polygons. Although following conventional implicit surface polygonization, there are significant differences that are described in detail. Several example surfaces are defined and polygonized. CR Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling  Curve, Surface, Solid, and Object Representations. Additional Keywords and Phrases: Implicit Surface, NonManifold, Polygonization. 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 40 (20 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...
Grow & Fold: Compression of Tetrahedral Meshes
, 1998
"... Standard representations of irregular finite element meshes combine vertex data (sample coordinates and node values) and connectivity (tetrahedronvertex incidence). Connectivity specifies how the samples should be interpolated. It may be encoded for each tetrahedron as four vertexreferences, which ..."
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Cited by 33 (7 self)
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Standard representations of irregular finite element meshes combine vertex data (sample coordinates and node values) and connectivity (tetrahedronvertex incidence). Connectivity specifies how the samples should be interpolated. It may be encoded for each tetrahedron as four vertexreferences, which together occupy 128 bits. Our `Grow&Fold' format reduces the connectivity storage down to 7 bits per tetrahedron: 3 of these are used to encode the presence of children in a tetrahedron spanning tree; the other 4 constrain sequences of `folding' operations, so that they produce the connectivity graph of the original mesh. Additional bits must be used for each handle in the mesh and for each topological `lock' in the tree. However, as our experiments with a prototype implementation show, the increase of the storage cost due to this extra information is typically no more than 12%. By storing vertex data in an order defined by the tree, we avoid the need to store tetrahedronvertex reference...
Boolean operations on 3D selective Nef complexes: Data structure, algorithms, and implementation
 IN PROC. 11TH ANNU. EURO. SYMPOS. ALG., VOLUME 2832 OF LNCS
, 2003
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Modeling and Designing Functionally Graded Material Components for Fabrication with Local Composition Control
, 1999
"... Solid Freeform Fabrication #SFF# processes have demonstrated the ability to produce parts with locally controlled composition. In the limit, processes such as 3D Printing can create parts with composition control on a length scale of 100 #m. To exploit this potential, new methods to model, exchange, ..."
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Cited by 28 (4 self)
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Solid Freeform Fabrication #SFF# processes have demonstrated the ability to produce parts with locally controlled composition. In the limit, processes such as 3D Printing can create parts with composition control on a length scale of 100 #m. To exploit this potential, new methods to model, exchange, and process parts with local composition control need to be developed. An approach to modeling a part's geometry, topology, and composition is presented. This approach is based on subdividing the solid model into subregions and associating analytic composition blending functions with each region. These blending functions de#ne the composition throughout the model as mixtures of the primary materials available to the SFF machine. Design tools basedupon distance functions are also introduced, such as the speci#cation of composition as a function of the distance from the surface of a part. Finally, the role of design rules restricting maximum and minimum concentrations is discussed. Introduc...
Polyhedral Perturbations That Preserve Topological Form
 COMPUTER AIDED GEOMETRIC DESIGN
, 1995
"... The idea, that we are willing to accept variation in an object but that we insist it should retain its original topological form, has powerful intuitive appeal, and the concept appears in many applied fields. Some of the most important of these are tolerancing and metrology, solid modeling, engineer ..."
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Cited by 27 (18 self)
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The idea, that we are willing to accept variation in an object but that we insist it should retain its original topological form, has powerful intuitive appeal, and the concept appears in many applied fields. Some of the most important of these are tolerancing and metrology, solid modeling, engineering design, finite element analysis, surface reconstruction, computer graphics, path planning in robotics, fairing procedures, image analysis, and medical imaging. In this paper we focus on the field of tolerancing and metrology. The requirement that two objects or sets should have the same topological form requires a precise definition. We specify "same topological form " to mean that there exists a "space homeomorphism" from IR 3 onto IR 3 that carries a nominal object S onto another design object. In general, establishing the existence of such space homeomorphisms can be considerably more difficult than demonstrating classical topological equivalence by a homeomorphism. In the special case when the boundary of S is a polyhedral twosphere in R 3, one of the authors has previously given a simple sufficient condition for the existence of a space homeomorphism mapping S onto another design object. This paper presents
Nonmanifold Modeling: An Approach Based on Spatial Subdivision
, 1997
"... This paper deals with the problem of creating and maintaining a spatial ..."
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Cited by 22 (7 self)
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This paper deals with the problem of creating and maintaining a spatial
A MultiResolution Topological Representation for NonManifold Meshes
 IN 7TH ACM SYMPOSIUM ON SOLID MODELING AND APPLICATIONS
, 2004
"... We address the problem of representing and processing 3D objects, described through simplicial meshes, which consist of parts of mixed dimensions, and with a nonmanifold topology, at different levels of detail. First, we describe a multiresolution model, that we call a Nonmanifold MultiTessel ..."
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Cited by 19 (10 self)
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We address the problem of representing and processing 3D objects, described through simplicial meshes, which consist of parts of mixed dimensions, and with a nonmanifold topology, at different levels of detail. First, we describe a multiresolution model, that we call a Nonmanifold MultiTessellation (NMT), and we consider the selective refinement query, which is at the heart of several analysis operations on multiresolution meshes. Next, we focus on a specific instance of a NMT, generated by simplifying simplicial meshes based on vertexpair contraction, and we describe a compact data structure for encoding such a model. We also propose a new data structure for twodimensional simplicial meshes, capable of representing both connectivity and adjacency information with a small memory overhead, which is used to describe the mesh extracted from an NMT through selective refinement. Finally, we present algorithms to efficiently perform updates on such a data structure.