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A Decomposition-based Representation for 3D Simplicial Complexes [article]

Annie Hui, Lucas Vaczlavik, Leila De Floriani
2006 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
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]

David Canino, Leila De Floriani
2011 Smart Tools and Applications in Graphics  
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]

Leila De Floriani, Daniele Panozzo, Annie Hui
2009 Lecture Notes in Computer Science  
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]

L. De Floriani, A. Hui
2007 Eurographics State of the Art Reports  
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]

Rocio Gonzalez–Diaz, Belen Medrano, Pedro Real, Javier Sánchez–Peláez
2005 Lecture Notes in Computer Science  
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]

Luiz Velho
2005 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
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]

Chengming Zou, Edwin R. Hancock
2010 Lecture Notes in Computer Science  
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]

Ana Pacheco, Pedro Real
2009 Lecture Notes in Computer Science  
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]

Leila De Floriani, Annie Hui
2005 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
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

Bernd Hamann, Marc Herbstritt
2010 Dagstuhl Publications  
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]

Friso Penninga, Peter van Oosterom
2007 Lecture Notes in Geoinformation and Cartography  
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

Kenneth Weiss, Leila De Floriani
2009 Computer graphics forum (Print)  
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]

Leila De Floriani, Paola Magillo, Franco Morando, Enrico Puppo
2001 Lecture Notes in Computer Science  
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]

Riccardo Fellegara and Kenneth Weiss and Leila De Floriani
2019 arXiv   pre-print
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

P. V. Kuper, M. Breunig, M. Al-Doori, A. Thomsen
2016 ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
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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