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A Decomposition-based Representation for 3D Simplicial Complexes
[article]
2006
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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We present a thorough comparison with existing representations for 3D simplicial complexes. ...
We define a new representation for non-manifold 3D shapes described by three-dimensional simplicial complexes, that we call the Double-Level Decomposition (DLD) data structure. ...
Decomposition of 3D simplicial complex In this Section, we present an algorithm for computing the IQM decomposition of a 3D simplicial complex. ...
doi:10.2312/sgp/sgp06/101-110
fatcat:vtb3trtqxjhf7njjomghhyfymu
A Decomposition-based Approach to Modeling and Understanding Arbitrary Shapes
[article]
2011
Smart Tools and Applications in Graphics
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Here, we consider a representation for arbitrary shapes, that we call Manifold-Connected Decomposition (MC-decomposition), which is based on a unique decomposition of the shape into nearly manifold parts ...
We present efficient and powerful two-level representations for non-manifold shapes based on the MC-decomposition and on an efficient and compact data structure for encoding the underlying components. ...
There are few representations for describing arbitrary shapes discretized as 3D simplicial complexes. ...
doi:10.2312/localchapterevents/italchap/italianchapconf2011/053-060
dblp:conf/egItaly/CaninoF11
fatcat:aaj6jk7uevc4pdfravrgntbm2i
Computing and Visualizing a Graph-Based Decomposition for Non-manifold Shapes
[chapter]
2009
Lecture Notes in Computer Science
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We describe an algorithm for computing the decomposition and its associated graph representation. ...
Here, we consider a decomposition of a non-manifold shape into components which are almost manifolds, and we present a novel graph representation which highlights the non-manifold singularities shared ...
In Section 4, we present the decomposition for non-manifold shapes discretized through simplicial 3-complexes, i.e., the MC-decomposition, and a graph-based representation for the MC-decomposition. ...
doi:10.1007/978-3-642-02124-4_7
fatcat:2khqhahby5h3xnaegp6l2gqwaq
Shape Representations Based on Simplicial and Cell Complexes
[article]
2007
Eurographics State of the Art Reports
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In this state-of-the-art report, we review, analyze and compare data structures for simplicial and cell complexes. ...
We also discuss a decomposition approach to modeling non-manifold shapes, which has led to powerful and scalable representations. ...
The Double-Level Decomposition (DLD) data structure [HVD06] is a representation for a simplicial 3complex based on its IQM decomposition. ...
doi:10.2312/egst.20071055
fatcat:lntqzl2ymzge7fwbty4hh52smq
Algebraic Topological Analysis of Time-Sequence of Digital Images
[chapter]
2005
Lecture Notes in Computer Science
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Considering AT-models for all the 2D digital images in a time sequence, it is possible to get an AT-model for the 3D digital image consisting in concatenating the successive 2D digital images in the sequence ...
Our answer is based on an algebraictopological coding, called AT-model, for a nD (n = 2, 3) digital binaryvalued image I consisting simply in taking I together with an algebraic object depending on it. ...
K(I) is called a simplicial representation of I and is defined as a subcomplex of the infinite simplicial complex K obtained by the decomposition of the 3D euclidean space into unit cubes (which vertices ...
doi:10.1007/11555964_18
fatcat:yl4cteadzjfdlph4tzfe6m2wza
Modeling with Simplicial Diffeomorphisms
[article]
2005
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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The framework is based on dynamic, adaptive simplicial decompositions of the embedding space and conforming piecewise diffeomorphisms. ...
In this paper we introduce a new framework for geometric modeling that combines implicit and parametric surface representations with volumetric warpings. ...
This framework is based on adaptive simplicial decompositions of the embedding space and conforming piecewise diffeomorphisms. ...
doi:10.2312/sgp/sgp05/159-160
fatcat:ghddox5izbg6zcnx2sne2mlgm4
Face Recognition Using Simplicial Complexes
[chapter]
2010
Lecture Notes in Computer Science
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The resulting data are represented by simplicial complexes. This representation can capture topological and geometric information at a specified resolution with a small number of control points. ...
The paper presents a novel method for 3D facial shape recognition. Our inputs are 3D facial shapes which are reconstructed from point clouds, and then filtered using PCA. ...
Experimental results have shown that our method for 3D facial shape representation and recognition is feasible and effective. ...
doi:10.1007/978-3-642-15992-3_3
fatcat:t3qmpeherrffjh3refu2kdwv5q
Getting Topological Information for a 80-Adjacency Doxel-Based 4D Volume through a Polytopal Cell Complex
[chapter]
2009
Lecture Notes in Computer Science
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Given an 80-adjacency doxel-based digital four-dimensional hypervolume V , we construct here an associated oriented 4-dimensional polytopal cell complex K(V ), having the same integer homological information ...
This is the first step toward the construction of an algebraic-topological representation (AT-model) for V , which suitably codifies it mainly in terms of its homological information. ...
Local Convex Hulls for the 4-Polytopal Cell Complex In this section we show a simplicial decomposition of the elementary hypercube Q 4 . ...
doi:10.1007/978-3-642-10268-4_33
fatcat:x24kxpdn45enloptcnpr6uluxy
Data Structures for Simplicial Complexes: An Analysis And A Comparison
[article]
2005
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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In this paper, we review, analyze and compare representations for simplicial complexes. ...
We classify such representations, based on the dimension of the complexes they can encode, into dimension-independent structures, and data structures for three- and for two-dimensional simplicial complexes ...
Usually, this leads to more compact representations. Edge-based data structures are specific for two-dimensional complexes embedded in the 3D Euclidean space. ...
doi:10.2312/sgp/sgp05/119-128
fatcat:omstnsk72rai3luciyzubb4s6a
On Curved Simplicial Elements and Best Quadratic Spline Approximation for Hierarchical Data Representation
2010
Dagstuhl Publications
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We present a method for hierarchical data approximation using curved quadratic simplicial elements for domain decomposition. ...
Curved simplicial elements make possible a better representation of curved geometry, domain boundaries, and discontinuities than simplicial elements with non-curved edges and faces. ...
We thank the members of the Visualization and Computer Graphics Research Group at the Institute for Data Analysis and Visualization (IDAV)) at the University of California, Davis. ...
doi:10.4230/dfu.sciviz.2010.45
dblp:conf/dagstuhl/Hamann10
fatcat:ygkwgvkoavam5oi4xekp6zq5e4
A Compact Topological DBMS Data Structure For 3D Topography
[chapter]
2007
Lecture Notes in Geoinformation and Cartography
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Based on earlier results (i.e. the full decomposition of space, the use of a TEN structure and applying Poincaré simplicial homology as mathematical foundation) a simplicial complex-based TEN structure ...
The described data structure is developed as a DBMS data structure and the usage of views, function based indexes and 3D R-trees result in a compact topological 3D data structure. ...
Based on earlier results (i.e. the full decomposition of space, the use of a TEN structure and applying Poincaré simplicial homology as mathematical foundation) a simplicial complex-based TEN structure ...
doi:10.1007/978-3-540-72385-1_27
fatcat:3tswnfta4fhytfy7w36aufm2tq
Diamond Hierarchies of Arbitrary Dimension
2009
Computer graphics forum (Print)
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Thus, efficient representations have been proposed in 2D and 3D based on a clustering of the simplices sharing a common longest edge in what is called a diamond. ...
Nested simplicial meshes generated by the simplicial bisection decomposition proposed by Maubach [Mau95] have been widely used in 2D and 3D as multi-resolution models of terrains and three-dimensional ...
Acknowledgments We would like to thank the anonymous reviewers for their many helpful suggestions. This work has been partially supported by the National Science Foundation under grant CCF-0541032. ...
doi:10.1111/j.1467-8659.2009.01506.x
fatcat:vypuu7kt45b27paoqohgn3fgq4
Non-manifold Multi-tessellation: From Meshes to Iconic Representations of Objects
[chapter]
2001
Lecture Notes in Computer Science
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This paper describes preliminary research work aimed at obtaining a multi-level iconic representation of 3D objects from geometric meshes. ...
The multi-level iconic model, called Non-manifold Multi-Tessellation, incorporates decompositions of an object into parts at different levels of abstraction, and permits to refine an iconic representation ...
Related Work There exists a large body of literature on the segmentation and representation of objects based on part decomposition (see, e.g., [1] for a fairly complete set of references. ...
doi:10.1007/3-540-45129-3_60
fatcat:y2pfl2anznesdofynzqx5jcnvy
The Stellar tree: a Compact Representation for Simplicial Complexes and Beyond
[article]
2019
arXiv
pre-print
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2017 pre-print arXiv:1707.02211v1 fatcat:ronrd2adbrb6lkdejohe43naaaOther Versions
We introduce the Stellar decomposition, a model for efficient topological data structures over a broad range of simplicial and cell complexes. ...
Stellar trees are competitive with state-of-the-art topological data structures for manifold simplicial complexes and offer significant improvements for cell complexes and non-manifold simplicial complexes ...
requirements for a top CP cell in a Stellar decomposition representation. ...
arXiv:1707.02211v2
fatcat:lpcblumrpfdvfof6bqyeh33nfa
APPLICATION OF 3D SPATIO-TEMPORAL DATA MODELING, MANAGEMENT, AND ANALYSIS IN DB4GEO
2016
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences
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However, the modeling, management and analysis of 3D geo-objects with changing shape and attributes in time still is a challenge for geospatial database architectures. ...
In this article we describe the application of concepts for the modeling, management and analysis of 2.5D and 3D spatial plus 1D temporal objects implemented in DB4GeO, our service-oriented geospatial ...
ACKNOWLEDGEMENTS The funding of this work within different DFG and BMBF grants and the researchers group FOR-1546 by the German Research Foundation (DFG) is acknowledged. ...
doi:10.5194/isprs-annals-iv-2-w1-163-2016
fatcat:5gbpfxw7abhqfc4yzysaxh7ema
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