A Heat Method for Generalized Signed Distance

Author:

Feng Nicole1ORCID,Crane Keenan1ORCID

Affiliation:

1. Carnegie Mellon University, Pittsburgh, United States of America

Abstract

We introduce a method for approximating the signed distance function (SDF) of geometry corrupted by holes, noise, or self-intersections. The method implicitly defines a completed version of the shape, rather than explicitly repairing the given input. Our starting point is a modified version of the heat method for geodesic distance, which diffuses normal vectors rather than a scalar distribution. This formulation provides robustness akin to generalized winding numbers (GWN) , but provides distance function rather than just an inside/outside classification. Our formulation also offers several features not common to classic distance algorithms, such as the ability to simultaneously fit multiple level sets, a notion of distance for geometry that does not topologically bound any region, and the ability to mix and match signed and unsigned distance. The method can be applied in any dimension and to any spatial discretization, including triangle meshes, tet meshes, point clouds, polygonal meshes, voxelized surfaces, and regular grids. We evaluate the method on several challenging examples, implementing normal offsets and other morphological operations directly on imperfect curve and surface data. In many cases we also obtain an inside/outside classification dramatically more robust than the one obtained provided by GWN.

Funder

National Science Foundation

Publisher

Association for Computing Machinery (ACM)

Reference81 articles.

1. Properties of Laplace Operators for Tetrahedral Meshes

2. P. Alliez, D. Cohen-Steiner, Y. Tong, and M. Desbrun. 2007. Voronoi-Based Variational Reconstruction of Unoriented Point Sets. In Proceedings of the Fifth Eurographics Symposium on Geometry Processing (Barcelona, Spain) (SGP '07). Eurographics Association, Goslar, DEU, 39--48.

3. Matan Atzmon and Yaron Lipman. 2019. SAL: Sign Agnostic Learning of Shapes from Raw Data. CoRR abs/1911.10414 (2019). arXiv:1911.10414 http://arxiv.org/abs/1911.10414

4. Signed Distance Computation Using the Angle Weighted Pseudonormal

5. Robust generation of signed distance fields from triangle meshes

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3