Linear algebraic representation for topological structures

DiCarlo, Antonio; Paoluzzi, Alberto; Shapiro, Vadim

doi:10.1016/j.cad.2013.08.044

Cited by 25 publications

(41 citation statements)

References 9 publications

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“…The Linear Algebraic Representation (LAR) scheme [14], uses Combinatorial Cellular Complexes (CCC) as its mathematical domain [5], and various compressed representations of sparse matrices [11] as its codomain.…”

Section: Linear Algebraic Representationmentioning

confidence: 99%

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CAD models from medical images using LAR

Paoluzzi¹,

DiCarlo²,

Furiani³

et al. 2016

Computer-Aided Design and Applications

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This paper points out the main design goals of a novel representation scheme of geometric-topological data, named Linear Algebraic Representation (LAR), characterized by a wide domain, encompassing 2D and 3D meshes, manifold and non-manifold geometric and solid models, and high-resolution 3D images. To demonstrate its simplicity and effectiveness for dealing with huge amounts of geometric data, we apply LAR to the extraction of a clean solid model of the hepatic portal vein subsystem from micro-CT scans of a pig liver

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Section: Linear Algebraic Representationmentioning

confidence: 99%

“…As a contribution to these efforts, we present here a novel representation scheme [14] which unifies the treatment of images, meshes and polyhedral data, and requires the minimum amount of storage for a complete representation of their topology and geometry.…”

Section: Introductionmentioning

confidence: 99%

CAD models from medical images using LAR

Paoluzzi¹,

DiCarlo²,

Furiani³

et al. 2016

Computer-Aided Design and Applications

Self Cite

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“…A linear algebraic mesh representation that bears some similarity to our approach is presented in a technical note by DiCarlo et al [DPS14]. They store characteristic matrices that map each k-face (see Section 3) to the unordered vertices as a binary compressed sparse row (CSR) matrix.…”

Section: Array-based Volumetric Mesh Data Structuresmentioning

confidence: 99%

Ternary Sparse Matrix Representation for Volumetric Mesh Subdivision and Processing on GPUs

Mueller-Roemer

Altenhofen

Sourander

2017

Computer Graphics Forum

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In this paper, we present a novel volumetric mesh representation suited for parallel computing on modern GPU architectures. The data structure is based on a compact, ternary sparse matrix storage of boundary operators. Boundary operators correspond to the first‐order top‐down relations of k‐faces to their (k − 1)‐face facets. The compact, ternary matrix storage format is based on compressed sparse row matrices with signed indices and allows for efficient parallel computation of indirect and bottom‐up relations. This representation is then used in the implementation of several parallel volumetric mesh algorithms including Laplacian smoothing and volumetric Catmull‐Clark subdivision. We compare these algorithms with their counterparts based on OpenVolumeMesh and achieve speedups from 3× to 531×, for sufficiently large meshes, while reducing memory consumption by up to 36%.

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“…Three structures were selected: the coupling-entity [21,22], the radial-edge [14], and the partial-entity [10]. There are also new data structures for non-manifold modelling developed recently [23][24][25][26] but they are based on the older data structures [4,10,14,21,27,28] or else a direct comparison is difficult: they introduce many construction entities stored explicitly, like regions, shells, faces, edges, vertices, loops, disks, etc.-while there are only edges and vertices in the DHE models, similar to the feather introduced in the coupling-entity data structure.…”

Section: Comparisons With the Dhementioning

confidence: 99%

The Dual Half-Edge—A Topological Primal/Dual Data Structure and Construction Operators for Modelling and Manipulating Cell Complexes

Bogusławski

Gold

2016

IJGI

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Abstract:There is an increasing need for building models that permit interior navigation, e.g., for escape route analysis. This paper presents a non-manifold Computer-Aided Design (CAD) data structure, the dual half-edge based on the Poincaré duality that expresses both the geometric representations of individual rooms and their topological relationships. Volumes and faces are expressed as vertices and edges respectively in the dual space, permitting a model just based on the storage of primal and dual vertices and edges. Attributes may be attached to all of these entities permitting, for example, shortest path queries between specified rooms, or to the exterior. Storage costs are shown to be comparable to other non-manifold models, and construction with local Euler-type operators is demonstrated with two large university buildings. This is intended to enhance current developments in 3D Geographic Information Systems for interior and exterior city modelling.Keywords: three-dimensional modelling; solid modelling; data structures; Euler operators GIS HistoryThis paper presents a detailed technical description and properties of the dual half-edge (DHE) topological data structure and its application in the Geographic Information Sciences (GIS), particularly in building interior modelling. It includes associated navigation and construction operators necessary for a convenient usage of DHE. Previous papers describing DHE [1][2][3] reported on the importance of the primal/dual approach, some applications, model representation and preliminary development, but with only a brief discussion of technical details and properties. DHE is compared with some other similar data structures.Early 2D GIS data structures were designed for polygon (choropleth) maps, where the objective was to combine the sets of individual digitized polygon boundaries to form a network. Various approaches were attempted, but finally an arc-based structure predominated, where an "arc" consisted of an intermediate set of digitized points between the "nodes" at boundary junctions. This was closely related to the winged-edge structure [4], with pointers to the four adjacent arcs and the two bounding polygons. The winged-edge structure was developed by Baumgart [4] and provided a way to connect

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Linear algebraic representation for topological structures

Cited by 25 publications

References 9 publications

CAD models from medical images using LAR

CAD models from medical images using LAR

Ternary Sparse Matrix Representation for Volumetric Mesh Subdivision and Processing on GPUs

The Dual Half-Edge—A Topological Primal/Dual Data Structure and Construction Operators for Modelling and Manipulating Cell Complexes

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