PCO: Precision-Controllable Offset Surfaces with Sharp Features

IF 7.8 1区 计算机科学 Q1 COMPUTER SCIENCE, SOFTWARE ENGINEERING ACM Transactions on Graphics Pub Date : 2024-11-19 DOI:10.1145/3687920
Lei Wang, Xudong Wang, Pengfei Wang, Shuangmin Chen, Shiqing Xin, Jiong Guo, Wenping Wang, Changhe Tu
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Abstract

Surface offsetting is a crucial operation in digital geometry processing and computer-aided design, where an offset is defined as an iso-value surface of the distance field. A challenge emerges as even smooth surfaces can exhibit sharp features in their offsets due to the non-differentiable characteristics of the underlying distance field. Prevailing approaches to the offsetting problem involve approximating the distance field and then extracting the iso-surface. However, even with dual contouring (DC), there is a risk of degrading sharp feature points/lines due to the inaccurate discretization of the distance field. This issue is exacerbated when the input is a piecewise-linear triangle mesh. This study is inspired by the observation that a triangle-based distance field, unlike the complex distance field rooted at the entire surface, remains smooth across the entire 3D space except at the triangle itself. With a polygonal surface comprising n triangles, the final distance field for accommodating the offset surface is determined by minimizing these n triangle-based distance fields. In implementation, our approach starts by tetrahedralizing the space around the offset surface, enabling a tetrahedron-wise linear approximation for each triangle-based distance field. The final offset surface within a tetrahedral range can be traced by slicing the tetrahedron with planes. As illustrated in the teaser figure, a key advantage of our algorithm is its ability to precisely preserve sharp features. Furthermore, this paper addresses the problem of simplifying the offset surface's complexity while preserving sharp features, formulating it as a maximal-clique problem.
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PCO: 具有锐利特征的精密可控偏移表面
曲面偏移是数字几何处理和计算机辅助设计中的一项重要操作,偏移被定义为距离场的等值曲面。由于底层距离场的不可分特性,即使是光滑的表面也会在偏移中表现出尖锐的特征,这就给我们带来了挑战。解决偏移问题的主流方法是近似距离场,然后提取等值面。然而,即使采用双等高线(DC),由于距离场的离散化不准确,也存在锐利特征点/线退化的风险。当输入是片状线性三角形网格时,这一问题会更加严重。与植根于整个表面的复杂距离场不同,基于三角形的距离场在整个三维空间中(除三角形本身外)保持平滑。对于由 n 个三角形组成的多边形表面,通过最小化这 n 个基于三角形的距离场,就能确定用于容纳偏移表面的最终距离场。在实施过程中,我们首先对偏移表面周围的空间进行四面体化,从而对每个三角形距离场进行四面体线性近似。通过对四面体进行平面切分,可以追踪到四面体范围内的最终偏移表面。如预告图所示,我们算法的一个关键优势是能够精确保留尖锐特征。此外,本文还解决了在保留尖锐特征的同时简化偏移曲面复杂性的问题,并将其表述为一个最大角问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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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