research-article

Interactive PDE patch-based surface modeling from vertex-frames

Authors:

Alfonso Carriazo,

Andres Iglesias,

Jianjun ZhangAuthors Info & Claims

Engineering with Computers, Volume 38, Issue 5

Pages 4367 - 4385

https://doi.org/10.1007/s00366-022-01602-z

Published: 01 October 2022 Publication History

Abstract

Polygon, subdivision, and NURBS are three mainstream modeling techniques widely applied in commercial software packages. They require heavy manual operations, and involve a lot of design variables leading to big data, high storage costs and slow network transmissions. In this paper, we integrate the strengths of boundary-based surface creation and partial differential equation (PDE)-based geometric modeling to obtain the first analytical

C^{0}

continuous 4-sided PDE patches involving sculpting force-based shape creation and manipulation and use them to develop an interactive modeling technique for easy and quick creation of 3D models with small data from vertex-frames. With this modeling technique, a vertex frame is defined by eight vertices, and a

C^{0}

continuous 4-sided PDE patch is created from the vertex-frame through an analytical solution to a vector-valued second-order PDE subjected to the boundary conditions determined by the eight vertices of a vertex-frame. A user-friendly interface is developed from the obtained analytical solution, which enables users to interactively input and modify vertex-frame models easily and create 3D models in real time. Different surface modeling tasks are carried out to test the developed interactive tool and compare our proposed method with polygon and NURBS modeling and Coons surfaces. The results demonstrate the effectiveness of our proposed method and its advantages in reducing design variables, saving storage costs, and effective shape creation and manipulation.

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Cited By

Wang SYou PWang HZhang HYou LZhang JDing G(2024)PDE parametric modeling with a two-stage MLP for aerodynamic shape optimization of high-speed train headsStructural and Multidisciplinary Optimization10.1007/s00158-024-03886-967:9Online publication date: 4-Oct-2024
https://dl.acm.org/doi/10.1007/s00158-024-03886-9

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Interactive PDE patch-based surface modeling from vertex-frames

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Published In

cover image Engineering with Computers

Engineering with Computers Volume 38, Issue 5

Oct 2022

890 pages

ISSN:0177-0667

EISSN:1435-5663

Issue’s Table of Contents

© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 2022

Accepted: 05 January 2022

Received: 14 January 2021

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Cited By

Wang SYou PWang HZhang HYou LZhang JDing G(2024)PDE parametric modeling with a two-stage MLP for aerodynamic shape optimization of high-speed train headsStructural and Multidisciplinary Optimization10.1007/s00158-024-03886-967:9Online publication date: 4-Oct-2024
https://dl.acm.org/doi/10.1007/s00158-024-03886-9

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