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91
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.
Virtual Clay: A Realtime Sculpting System with Haptic Toolkits
, 2001
"... In this paper we systematically develop a novel, interactive sculpting framework founded upon subdivision solids and physicsbased modeling. In contrast with popular subdivision surfaces, subdivision solids have the unique advantage offering both the boundary representation and the interior material ..."
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Cited by 54 (9 self)
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In this paper we systematically develop a novel, interactive sculpting framework founded upon subdivision solids and physicsbased modeling. In contrast with popular subdivision surfaces, subdivision solids have the unique advantage offering both the boundary representation and the interior material of a solid object. We unify the geometry of subdivision solids with the principle of physicsbased models and formulate dynamic subdivision solids. Dynamic subdivision solids respond to applied forces in a natural and predictive manner and give the user the illusion of manipulating semielastic virtual clay. We have developed a realtime sculpting system that provides the user with a wide array of intuitive sculpting toolkits. The flexibility of the subdivision solid approach allows users to easily modify the topology of sculpted objects, while the inherent physical properties are exploited to provide a natural interface for direct, forcebased deformation. More importantly, our sculpting sy...
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...
FeatureBased Cellular Texturing for Architectural Models
 In Proceedings of ACM SIGGRAPH 2001, ACM
, 2001
"... Cellular patterns are all around us, in masonry, tiling, shingles, and many other materials. Such patterns, especially in architectural settings, are influenced by geometric features of the underlying shape. Bricks turn corners, stones frame windows and doorways, and patterns on disconnected portion ..."
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Cited by 38 (2 self)
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Cellular patterns are all around us, in masonry, tiling, shingles, and many other materials. Such patterns, especially in architectural settings, are influenced by geometric features of the underlying shape. Bricks turn corners, stones frame windows and doorways, and patterns on disconnected portions of a building align to achieve a particular aesthetic goal. We present a strategy for featurebased cellular texturing, where the resulting texture is derived from both patterns of cells and the geometry to which they are applied. As part of this strategy, we perform texturing operations on features in a welldefined order that simplifies the interdependence between cells of adjacent patterns. Occupancy maps are used to indicate which regions of a feature are already occupied by cells of its neighbors, and which regions remain to be textured. We also introduce the notion of a pattern generator  the cellular texturing analogy of a shader used in local illumination  and show how several can be used together to build complex textures. We present results obtained with an implementation of this strategy and discuss details of some example pattern generators.
Dynamic Sculpting and Animation of Freeform Subdivision Solids
, 2000
"... This paper presents a sculptured solid modeling system founded upon dynamic CatmullClark subdivisionbased solids of arbitrary topology. Our primary contribution is that we integrate the geometry of sculptured freeform solids with the powerful physicsbased modeling framework by augmenting pure ge ..."
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Cited by 25 (5 self)
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This paper presents a sculptured solid modeling system founded upon dynamic CatmullClark subdivisionbased solids of arbitrary topology. Our primary contribution is that we integrate the geometry of sculptured freeform solids with the powerful physicsbased modeling framework by augmenting pure geometric entities with material properties such as mass, damping, and stiffness distributions and with physical behaviors such as elasticity, plasticity, and natural deformation under external forces. Our novel dynamic model of freeform solids frees users from having to deal with lowlevel control point operations and permits them to interact with subdivisionbased virtual clay in a more natural and intuitive fashion via "forces." 1. Introduction To date, the vast majority of popular solid modeling approaches as well as commonlyused solid modeling systems are built upon the following geometric foundations: constructive solid geometry (CSG), boundary representation (Breps), and cell decom...
Automated 3d crack growth simulation
 International Journal for Numerical Methods in Engineering
, 2000
"... Automated simulation of arbitrary, nonplanar, 3D crack growth in reallife engineered structures requires two key components: crack representation and crack growth mechanics. A model environment for representing the evolving 3D crack geometry and for testing various crack growth mechanics is presen ..."
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Cited by 23 (5 self)
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Automated simulation of arbitrary, nonplanar, 3D crack growth in reallife engineered structures requires two key components: crack representation and crack growth mechanics. A model environment for representing the evolving 3D crack geometry and for testing various crack growth mechanics is presented. Reference is made to a specific implementation of the model, called FRANC3D. Computational geometry and topology are used to represent the evolution of crack growth in a structure. Current 3D crack growth mechanics are insufficient; however, the model allows for the implementation of new mechanics. A specific numerical analysis program is not an intrinsic part of the model; i.e., finite and boundary elements are both supported. For demonstration purposes, a 3D hypersingular boundary element code is used for two example simulations. The simulations support the conclusion that automatic propagation of a 3D crack in a reallife structure is feasible. Automated simulation lessens the tedious and timeconsuming operations that are usually associated with crack growth analyses. Specifically, modifications to the geometry of the structure due to crack growth, remeshing of the modified portion of the structure after crack growth, and reapplication of boundary conditions proceeds without user intervention.
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 Multivector Data Structure for Differential Forms and Equations
 Math. Comput. Simulation
, 2000
"... We use tools from algebraic topology to show that a class of structural differential equations may be represented combinatorially and thus by a computer data structure. In particular, every differential kform may be represented by a formal kcochain over a cellular structure that we call a starpl ..."
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Cited by 21 (8 self)
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We use tools from algebraic topology to show that a class of structural differential equations may be represented combinatorially and thus by a computer data structure. In particular, every differential kform may be represented by a formal kcochain over a cellular structure that we call a starplex, and exterior differentiation is equivalent to the coboundary operation on the corresponding kcochain. Furthermore, there is a one to one correspondence between this model and the classical finite cellular model supported by the Generalized Stokes' Theorem, and translation between the two models can be completely automated.