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108
Progressive Simplicial Complexes
, 1997
"... In this paper, we introduce the progressive simplicial complex (PSC) representation, a new format for storing and transmitting triangulated geometric models. Like the earlier progressive mesh (PM) representation, it captures a given model as a coarse base model together with a sequence of refinement ..."
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Cited by 169 (2 self)
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In this paper, we introduce the progressive simplicial complex (PSC) representation, a new format for storing and transmitting triangulated geometric models. Like the earlier progressive mesh (PM) representation, it captures a given model as a coarse base model together with a sequence of refinement transformations that progressively recover detail. The PSC representation makes use of a more general refinement transformation, allowing the given model to be an arbitrary triangulation (e.g. any dimension, non-orientable, non-manifold, non-regular), and the base model to always consist of a single vertex. Indeed, the sequence of refinement transformations encodes both the geometry and the topology of the model in a unified multiresolution framework. The PSC representation retains the advantages of PM's. It defines a continuous sequence of approximating models for runtime level-of-detail control, allows smooth transitions between any pair of models in the sequence, supports progressive transmission, and offers a space-efficient representation. Moreover, by allowing changes to topology, the PSC sequence of approximations achieves better fidelity than the corresponding PM sequence.
Parallel Algorithm Oriented Mesh Database
- Int. J. Numer. Meth. Engng
, 2001
"... In this paper, we present a new point of view for efficiently managing general parallel mesh representations. Taking as a starting point the Algorithm Oriented Mesh Database (AOMD) of [12] we extend the concepts to a parallel mesh representation. The important aspects of parallel adaptivity and dyna ..."
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Cited by 41 (7 self)
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In this paper, we present a new point of view for efficiently managing general parallel mesh representations. Taking as a starting point the Algorithm Oriented Mesh Database (AOMD) of [12] we extend the concepts to a parallel mesh representation. The important aspects of parallel adaptivity and dynamic load balancing are discussed. We finally show how AOMD can be effectively interfaced with mesh adaptive partial differential equation solvers. Results of the calculation of an elasticity problem and of a transient fluid dynamics problem involving thousands of mesh refinements, and load balancings are finally presented.
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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Compact representations of simplicial meshes in two and three dimensions
- International Journal of Computational Geometry and Applications
, 2003
"... We describe data structures for representing simplicial meshes compactly while supporting online queries and updates efficiently. Our data structure requires about a factor of five less memory than the most efficient standard data structures for triangular or tetrahedral meshes, while efficiently su ..."
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Cited by 25 (6 self)
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We describe data structures for representing simplicial meshes compactly while supporting online queries and updates efficiently. Our data structure requires about a factor of five less memory than the most efficient standard data structures for triangular or tetrahedral meshes, while efficiently supporting traversal among simplices, storing data on simplices, and insertion and deletion of simplices. Our implementation of the data structures uses about 5 bytes/triangle in two dimensions (2D) and 7.5 bytes/tetrahedron in three dimensions (3D). We use the data structures to implement 2D and 3D incremental algorithms for generating a Delaunay mesh. The 3D algorithm can generate 100 Million tetrahedrons with 1 Gbyte of memory, including the space for the coordinates and all data used by the algorithm. The runtime of the algorithm is as fast as Shewchuk’s Pyramid code, the most efficient we know of, and uses a factor of 3.5 less memory overall. 1
A Point-Placement Strategy for Conforming Delaunay Tetrahedralization
- Proceedings of the Eleventh Annual Symposium on Discrete Algorithms
, 2000
"... A strategy is presented to find a set of points which yields a Conforming Delaunay tetrahedralization of a three-dimensional Piecewise-Linear Complex (PLC). This algorithm is novel because it imposes no angle restrictions on the input PLC. In the process, an algorithm is described that computes a ..."
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Cited by 23 (0 self)
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A strategy is presented to find a set of points which yields a Conforming Delaunay tetrahedralization of a three-dimensional Piecewise-Linear Complex (PLC). This algorithm is novel because it imposes no angle restrictions on the input PLC. In the process, an algorithm is described that computes a planar conforming Delaunay triangulation of a Planar StraightLine Graph (PSLG) such that each triangle has a bounded circumradius, which may be of independent interest. 1 Introduction In many two- and three-dimensional geometric modeling problems, notably the numerical approximation of the solution to a Partial Differential Equation with a Finite-Element type method [SF73], it is very desirable to obtain a triangulation (tetrahedralization) that respects the domain of interest. The task of forming such decompositions, along with ensuring that the elements of the decompositions satisfy application-specific quality requirements, is sometimes referred to as unstructured mesh generation. Se...
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
Design Automation for Customized Apparel Products
"... This paper presents solution techniques for a three-dimensional Automatic Made-to-Measure (AMM) scheme for apparel products. Freeform surface is adopted to represent the complex geometry models of apparel products. When designing the complex surface of an apparel product, abstractions are stored in ..."
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Cited by 14 (6 self)
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This paper presents solution techniques for a three-dimensional Automatic Made-to-Measure (AMM) scheme for apparel products. Freeform surface is adopted to represent the complex geometry models of apparel products. When designing the complex surface of an apparel product, abstractions are stored in conjunction with the models using a non-manifold data structure. Apparel products are essentially designed with reference to human body features, and thus share a common set of features as the human model. Therefore, the parametric feature-based modeling enables the automatic generation of fitted garments on differing body shapes. In our approach, different apparel products are each represented by a specific feature template preserving its individual characteristics and styling. When the specific feature template is encoded as the equivalent human body feature template, it automates the generation of made-to-measure apparel products. The encoding process is performed in 3D, which fundamentally solves the fitting problems of the 2D tailoring and pattern-making process. This paper gives an integrated solution scheme all above problems. In detail, a non-manifold data structure, a constructive design method, four freeform modification tools, and a detail template encoding/decoding method are developed for the design automation of customized apparel products.
Generating Topological Information from a "Bucket of Facets"
"... The STL de facto data exchange standard for Solid Freeform Fabrication represents CAD models as a collection of unordered triangular planar facets. No topological connectivity information is provided; hence the term "bucket of facets." Such topological information can, however, be quite us ..."
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Cited by 14 (0 self)
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The STL de facto data exchange standard for Solid Freeform Fabrication represents CAD models as a collection of unordered triangular planar facets. No topological connectivity information is provided; hence the term "bucket of facets." Such topological information can, however, be quite useful for performing model validity checking and speeding subsequent processing operations such as model slicing. This paper discusses model topology and how to derive it given a collection of unordered triangular facets which represent a valid model. 1 Introduction Computer Aided Design (CAD) model data is frequently passed to various Solid Freeform Fabrication processes using the STL polygonal facet representation [1]. Facet models represent solid objects by spatial boundaries which are defined by a set of planar faces. This is a special case of the more general Boundary Representation which does not require object boundaries be planar [2]. In general, the term facet is used to denote any constrain...
Out-of-Core Build of a Topological Data Structure from Polygon Soup
- In Proc. Symposium on Solid Modeling and Applications
, 2001
"... Many solid modeling applications require information not only about the geometry of an object but also about its topology. Most interchange formats do not provide this information, which the application must then derive as it builds its own topological data structure from unordered, "polygon so ..."
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Cited by 14 (1 self)
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Many solid modeling applications require information not only about the geometry of an object but also about its topology. Most interchange formats do not provide this information, which the application must then derive as it builds its own topological data structure from unordered, "polygon soup" input. For very large data sets, the topological data structure itself can be bigger than core memory, so that a naive algorithm for building it that doesn't take virtual memory access patterns into account can become prohibitively slow due to thrashing. In this paper, we describe a new out-of-core algorithm that can build a topological data structure efficiently from very large data sets, improving performance by two orders of magnitude over a naive approach.
