用表面有限元法求测地线距离近似的p-拉普拉斯

IF 1.3 4区 计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Hannah Potgieter, Razvan C. Fetecau, Steven J. Ruuth
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引用次数: 0

摘要

我们使用具有大p值的p-拉普拉斯算子来近似地表特征的测地线距离。这与Fayolle和Belyaev(2018)使用p-拉普拉斯算子求解距离表面问题的计算结果不同。与其他流行的基于pde的距离函数近似方法相比,我们的方法似乎提供了一些明显的优势。我们采用了一种曲面有限元格式,并证明了对真测地线距离函数的数值收敛性。我们检查我们的数值结果是否符合三角不等式,并检查对几何噪声(如顶点扰动)的鲁棒性。我们还将我们的方法与Crane等人(2017)的热法和Mitchell等人(1987)的经典多面体法进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Geodesic distance approximation using a surface finite element method for the p-Laplacian
We use the p-Laplacian with large p-values in order to approximate geodesic distances to features on surfaces. This differs from Fayolle and Belyaev's (2018) computational results using the p-Laplacian for the distance-to-surface problem. Our approach appears to offer some distinct advantages over other popular PDE-based distance function approximation methods. We employ a surface finite element scheme and demonstrate numerical convergence to the true geodesic distance functions. We check that our numerical results adhere to the triangle inequality and examine robustness against geometric noise such as vertex perturbations. We also present comparisons of our method with the heat method from Crane et al. (2017) and the classical polyhedral method from Mitchell et al. (1987).
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来源期刊
Computer Aided Geometric Design
Computer Aided Geometric Design 工程技术-计算机:软件工程
CiteScore
3.50
自引率
13.30%
发文量
57
审稿时长
60 days
期刊介绍: The journal Computer Aided Geometric Design is for researchers, scholars, and software developers dealing with mathematical and computational methods for the description of geometric objects as they arise in areas ranging from CAD/CAM to robotics and scientific visualization. The journal publishes original research papers, survey papers and with quick editorial decisions short communications of at most 3 pages. The primary objects of interest are curves, surfaces, and volumes such as splines (NURBS), meshes, subdivision surfaces as well as algorithms to generate, analyze, and manipulate them. This journal will report on new developments in CAGD and its applications, including but not restricted to the following: -Mathematical and Geometric Foundations- Curve, Surface, and Volume generation- CAGD applications in Numerical Analysis, Computational Geometry, Computer Graphics, or Computer Vision- Industrial, medical, and scientific applications. The aim is to collect and disseminate information on computer aided design in one journal. To provide the user community with methods and algorithms for representing curves and surfaces. To illustrate computer aided geometric design by means of interesting applications. To combine curve and surface methods with computer graphics. To explain scientific phenomena by means of computer graphics. To concentrate on the interaction between theory and application. To expose unsolved problems of the practice. To develop new methods in computer aided geometry.
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