矩形曲面参数化

IF 9.5 1区 计算机科学 Q1 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Etienne Corman, Keenan Crane
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引用次数: 0

摘要

本文描述了一种曲面参数化的计算方法,该方法将平面上的无限小的轴向正方形映射到表面上的无限小矩形。从物理模拟到几何建模再到计算制造,这种矩形参数化需要广泛的任务。我们的主要贡献是在网格细化的限制下,构造完全正交和精确可积的框架域的新策略。与过去实现可积性的策略相比,我们获得的映射失真较小,并且更好地保留了目标场方向。该方法支持用户定义的畸变测量、尖锐特征对齐、规定或自动锥体奇点,以及对边界行为的直接控制(例如,尺寸或纵横比)。通过量化和等高线化这些地图,我们获得了高质量的各向异性四边形网格,即使没有基于元素的优化。根据经验,我们在元素质量,精度和端到端仿真任务的渐近收敛率方面优于最先进的研究和商业网格生成算法,与广泛使用的自动重拓扑ZBrush包具有竞争力,并为专门为数字制造量身定制的方法提供优质的切比雪夫网。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Rectangular Surface Parameterization
This paper describes a method for computing surface parameterizations that map infinitesimal axis-aligned squares in the plane to infinitesimal rectangles on the surface. Such rectangular parameterizations are needed for a broad range of tasks, from physical simulation to geometric modeling to computational fabrication. Our main contribution is a novel strategy for constructing frame fields that are perfectly orthogonal and exactly integrable, in the limit of mesh refinement. In contrast to past strategies for achieving integrability, we obtain maps that are less distorted and better preserve target field directions. The method supports user-defined distortion measures, sharp feature alignment, prescribed or automatic cone singularities, and direct control over boundary behavior (e.g., sizing or aspect ratio). By quantizing and contouring these maps we obtain high-quality anisotropic quad meshes, even without element-based optimization. Empirically, we outperform state-of-the-art research and commercial mesh generation algorithms in terms of element quality, accuracy, and asymptotic convergence rate in end-to-end simulation tasks, are competitive with the widely-used ZBrush package for automatic retopology, and provide Chebyshev nets of superior quality to methods specifically tailored to digital fabrication.
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来源期刊
ACM Transactions on Graphics
ACM Transactions on Graphics 工程技术-计算机:软件工程
CiteScore
14.30
自引率
25.80%
发文量
193
审稿时长
12 months
期刊介绍: ACM Transactions on Graphics (TOG) is a peer-reviewed scientific journal that aims to disseminate the latest findings of note in the field of computer graphics. It has been published since 1982 by the Association for Computing Machinery. Starting in 2003, all papers accepted for presentation at the annual SIGGRAPH conference are printed in a special summer issue of the journal.
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