利用积分曲线的等价类生成和优化四边形布局:有边界曲面的理论和应用

IF 1.5 4区 工程技术 Q3 MECHANICS
Kendrick M. Shepherd, X. Gu, R. Hiemstra, T. Hughes
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引用次数: 6

摘要

从表面三角形中提取四边形布局是纹理映射、传统分析中的半结构四边形网格划分和等几何分析中的样条重构的重要步骤。目前的方法很难产生高质量的布局,在奇异节点之间具有适当的连通性(对于样条表示称为“异常点”),而不诉诸混合整数优化或手动约束处方。第一种方法在计算上很昂贵,而且没有保证,而第二种方法很费力,而且容易出错。在这项工作中,我们严格描述了四边形布局中的曲线直至同伦类型,并使用该信息快速定义奇异节点之间的高质量连接约束。数学理论伴随着适当的计算算法。在美国陆军DEVCOM通用车体车辆和1996年道奇霓虹灯双线性四边形有限元网格(带有一些线性三角形)的部分上,证明了所提出方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Quadrilateral layout generation and optimization using equivalence classes of integral curves: theory and application to surfaces with boundaries
Extracting quadrilateral layouts from surface triangulations is an important step in texture mapping, semi-structured quadrilateral meshing for traditional analysis and spline reconstruction for isogeometric analysis. Current methods struggle to yield high-quality layouts with appropriate connectivity between singular nodes (known as “extraordinary points” for spline representations) without resorting to either mixed-integer optimization or manual constraint prescription. The first of these is computationally expensive and comes with no guarantees, while the second is laborious and error-prone. In this work, we rigorously characterize curves in a quadrilateral layout up to homotopy type and use this information to quickly define high-quality connectivity constraints between singular nodes. The mathematical theory is accompanied by appropriate computational algorithms. The efficacy of the proposed method is demonstrated in generating quadrilateral layouts on the United States Army’s DEVCOM Generic Hull vehicle and parts of a bilinear quadrilateral finite element mesh (with some linear triangles) of a 1996 Dodge Neon.
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来源期刊
Journal of Mechanics
Journal of Mechanics 物理-力学
CiteScore
3.20
自引率
11.80%
发文量
20
审稿时长
6 months
期刊介绍: The objective of the Journal of Mechanics is to provide an international forum to foster exchange of ideas among mechanics communities in different parts of world. The Journal of Mechanics publishes original research in all fields of theoretical and applied mechanics. The Journal especially welcomes papers that are related to recent technological advances. The contributions, which may be analytical, experimental or numerical, should be of significance to the progress of mechanics. Papers which are merely illustrations of established principles and procedures will generally not be accepted. Reports that are of technical interest are published as short articles. Review articles are published only by invitation.
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