research-article

Topologically Clean Distance Fields

Authors:

Attila Gyulassy,

Mark Duchaineau,

Vijay Natarajan,

Valerio Pascucci,

Eduardo Bringa,

Andrew Higginbotham,

Bernd HamannAuthors Info & Claims

IEEE Transactions on Visualization and Computer Graphics, Volume 13, Issue 6

Pages 1432 - 1439

https://doi.org/10.1109/TVCG.2007.70603

Published: 01 November 2007 Publication History

Abstract

Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields containing a minimal number of topological features, and we use them to identify features of the material. We focus on distance fields defined on a volumetric domain considering the distance to a given surface embedded within the domain. Topological features of the field are characterized by its critical points. Our first methodbegins with a distance field that is computed using a standard approach, and simplifies this field using ideas from Morse theory. We present a procedure for identifying and extracting a feature set through analysis of the MS complex, and apply it to find the invariants in the clean distance field. Our second method proceeds by advancing a front, beginning at the surface, and locally controlling the creation of new critical points. We demonstrate the value of topologically clean distance fields for the analysis of filament structures in porous solids. Our methods produce a curved skeleton representation of the filaments that helps material scientists to perform a detailed qualitative and quantitative analysis of pores, and hence infer important material properties. Furthermore, we provide a set of criteria for finding the “difference” between two skeletal structures, and use this to examine how the structure of the porous solid changes over several timesteps in the simulation of the particle impact.

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Cited By

Song YFellegara RIuricich FDe Floriani L(2024)Parallel Topology-aware Mesh Simplification on Terrain TreesACM Transactions on Spatial Algorithms and Systems10.1145/365260210:2(1-39)Online publication date: 13-Mar-2024
https://dl.acm.org/doi/10.1145/3652602
Kissi MPont MLevine JTierny J(2024)A Practical Solver for Scalar Data Topological SimplificationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2024.345634531:1(97-107)Online publication date: 10-Sep-2024
https://dl.acm.org/doi/10.1109/TVCG.2024.3456345
Sisouk KDelon JTierny J(2024)Wasserstein Dictionaries of Persistence DiagramsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.333026230:2(1638-1651)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3330262
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Index Terms

Topologically Clean Distance Fields
1. Computing methodologies
2. Human-centered computing
  1. Human computer interaction (HCI)
    1. Interactive systems and tools

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cover image IEEE Transactions on Visualization and Computer Graphics

IEEE Transactions on Visualization and Computer Graphics Volume 13, Issue 6

November 2007

662 pages

ISSN:1077-2626

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Copyright © 2007.

Publisher

IEEE Educational Activities Department

United States

Publication History

Published: 01 November 2007

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Cited By

Song YFellegara RIuricich FDe Floriani L(2024)Parallel Topology-aware Mesh Simplification on Terrain TreesACM Transactions on Spatial Algorithms and Systems10.1145/365260210:2(1-39)Online publication date: 13-Mar-2024
https://dl.acm.org/doi/10.1145/3652602
Kissi MPont MLevine JTierny J(2024)A Practical Solver for Scalar Data Topological SimplificationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2024.345634531:1(97-107)Online publication date: 10-Sep-2024
https://dl.acm.org/doi/10.1109/TVCG.2024.3456345
Sisouk KDelon JTierny J(2024)Wasserstein Dictionaries of Persistence DiagramsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.333026230:2(1638-1651)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3330262
Maack RLukasczyk JTierny JHagen HMaciejewski RGarth C(2024)Parallel Computation of Piecewise Linear Morse-Smale SegmentationsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.326198130:4(1942-1955)Online publication date: 1-Apr-2024
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Guillou PVidal JTierny J(2024)Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data – An Algorithm and a BenchmarkIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.323800830:4(1897-1915)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3238008
Subhash VPandey KNatarajan V(2023)A GPU Parallel Algorithm for Computing Morse-Smale ComplexesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.317476929:9(3873-3887)Online publication date: 1-Sep-2023
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Iuricich F(2022)Persistence Cycles for Visual Exploration of Persistent HomologyIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.311066328:12(4966-4979)Online publication date: 1-Dec-2022
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Song YFellegara RIuricich FDe Floriani L(2021)Efficient topology-aware simplification of large triangulated terrainsProceedings of the 29th International Conference on Advances in Geographic Information Systems10.1145/3474717.3484261(576-587)Online publication date: 2-Nov-2021
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Petruzza SGyulassy ALeventhal SBaglino JCzabaj MSpear APascucci V(2019)High-throughput feature extraction for measuring attributes of deforming open-cell foamsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2019.293462026:1(140-150)Online publication date: 25-Nov-2019
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