Implementation-friendly Geometric Algorithms for Provable Surface and Volume Meshing

用于可证明表面和体积网格划分的易于实施的几何算法

基本信息

项目摘要

Intellectual Merit:Numerous applications in science and engineering require meshing a surface or a volume into a triangulation. The problem arises at the micro-level in molecular modeling and at the macro-level in automotive designs, in the scientific study of natural phenomena and in the engineering of man-made machine tools and appliances. As varied the applications are, so are the types of their inputs. Almost no provable algorithm exists for many of these input domains. As a result, many of the commercial products catering to the huge needs for quality meshing rely on heuristics which often produce poor meshes. This research will fill the gap between the need for quality meshing of a variety of input domains and the algorithm and software that can achieve it with guaranteed correctness. To this end, this research will consider inputs as varied as implicit, parametric, point-sampled, polyhedral, piecewise smooth surfaces as well as volumes enclosed by them. Each of these inputs poses difficulties that are unique to its kind. The project will focus on the design and analysis of the provable meshing algorithms and software systems based on them for these input domains.Broader Impact:The developed tools in this project will enable meshing complicated geometry with guarantees and enhance further analysis using them. This will impact a variety of areas in science and engineering including physics, biology, environmental science, computer aided designs, manufacturing, health care, entertainment and so on.The development will influence the research in the areas of computational geometry, computational topology, geometric modeling, computer graphics and visualization. Course notes, seminars and software systems developed through the project will enable educators and students to attack meshing problems in a formal setting with guaranteed correctness.
智力优势:在科学和工程中的许多应用都需要将一个表面或一个体积网格化成一个三角形。这个问题出现在微观层面的分子建模和宏观层面的汽车设计、自然现象的科学研究以及人造机床和设备的工程中。随着应用程序的多样化,它们的输入类型也多种多样。对于这些输入域,几乎没有可证明的算法存在。因此,许多满足高质量网格划分需求的商业产品依赖于启发式算法,而启发式算法往往产生较差的网格。本研究将填补各种输入域的高质量网格划分需求与能够保证其正确性的算法和软件之间的空白。为此,本研究将考虑各种各样的输入,如隐式、参数化、点采样、多面体、分段光滑表面以及由它们包围的体积。每一种输入都有其独特的困难。该项目将侧重于设计和分析可证明的网格算法和基于这些输入域的软件系统。更广泛的影响:在这个项目中开发的工具将使网格复杂的几何保证和加强进一步的分析使用它们。这将影响科学和工程的各个领域,包括物理学、生物学、环境科学、计算机辅助设计、制造业、医疗保健、娱乐等。这一发展将影响计算几何、计算拓扑、几何建模、计算机图形学和可视化等领域的研究。通过该项目开发的课程笔记、研讨会和软件系统将使教育工作者和学生能够在保证正确性的正式环境中解决网格问题。

项目成果

期刊论文数量(0)
专著数量(0)
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会议论文数量(0)
专利数量(0)

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Tamal Dey其他文献

Predicting the optimum harvesting dates for different exotic apple varieties grown under North Western Himalayan regions through acoustic and machine vision techniques.
  • DOI:
    10.1016/j.fochx.2023.100754
  • 发表时间:
    2023-10-30
  • 期刊:
  • 影响因子:
    6.1
  • 作者:
    Nazrana Rafique Wani;Syed Zameer Hussain;Gopinath Bej;Bazila Naseer;Mushtaq Beigh;Ufaq Fayaz;Tamal Dey;Abhra Pal;Amitava Akuli;Alokesh Ghosh;B.S. Dhekale;Fehim J. Wani
  • 通讯作者:
    Fehim J. Wani
Emergence of an unconventional Enterobacter cloacae-derived Iturin A C-15 as a potential therapeutic agent against methicillin-resistant Staphylococcus aureus
  • DOI:
    10.1007/s00203-024-04226-7
  • 发表时间:
    2024-12-30
  • 期刊:
  • 影响因子:
    2.600
  • 作者:
    Dipro Mukherjee;Samya Sen;Aniket Jana;Surojit Ghosh;Moumita Jash;Monika Singh;Satyajit Ghosh;Nabanita Mukherjee;Rajsekhar Roy;Tamal Dey;Shankar Manoharan;Surajit Ghosh;Jayita Sarkar
  • 通讯作者:
    Jayita Sarkar

Tamal Dey的其他文献

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{{ truncateString('Tamal Dey', 18)}}的其他基金

Collaborative Research: Multiparameter Topological Data Analysis
合作研究:多参数拓扑数据分析
  • 批准号:
    2301360
  • 财政年份:
    2023
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
AF: Small: Expanding the Reach of Topological Data Analysis
AF:小:扩大拓扑数据分析的范围
  • 批准号:
    2049010
  • 财政年份:
    2020
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
AF: Small: Expanding the Reach of Topological Data Analysis
AF:小:扩大拓扑数据分析的范围
  • 批准号:
    2007961
  • 财政年份:
    2020
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
AF: Small: Topological Data Analysis for Big and High Dimensional Data
AF:小:大维和高维数据的拓扑数据分析
  • 批准号:
    1318595
  • 财政年份:
    2013
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
AF: Medium: Collaborative Research: Optimality in Homology - Algorithms and Applications
AF:媒介:协作研究:同调中的最优性 - 算法和应用
  • 批准号:
    1064416
  • 财政年份:
    2011
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
AF: Small: Analyzing Spaces and Scalar Fields via Point Clouds
AF:小:通过点云分析空间和标量场
  • 批准号:
    1116258
  • 财政年份:
    2011
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
MCS: Reconstructing and Inferring Topology and Geometry from Point Cloud Data
MCS:从点云数据重建和推断拓扑和几何形状
  • 批准号:
    0915996
  • 财政年份:
    2009
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Inferring Topology and Geometry for Dynamic Shapes
推断动态形状的拓扑和几何形状
  • 批准号:
    0830467
  • 财政年份:
    2008
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Collaborative Research: Non-smoothness in Meshing and Reconstruction
协作研究:网格划分和重构中的非平滑性
  • 批准号:
    0635008
  • 财政年份:
    2006
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
Postdoctoral: Sampling Based Geometric Modeling
博士后:基于采样的几何建模
  • 批准号:
    0102280
  • 财政年份:
    2001
  • 资助金额:
    --
  • 项目类别:
    Standard Grant

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