A comparison of methods for gradient field estimation on simplicial meshes. (May 2019)

• Record Type: Journal Article
• Authors: Mancinelli, Claudio; Livesu, Marco; Puppo, Enrico
• Is Part Of: Computers & graphics. Volume 80(2019)
• Page Start: 37
• Page End: 50
• Publication Date: 2019-05
• Subjects: Simplicial meshes -- Gradient estimation -- Discrete geometry; Computer graphics -- Periodicals; 006.6
• DOI: 10.1016/j.cag.2019.03.005
• Languages: English
• ISSNs: 0097-8493

Abstract

Highlights: A comparison among four methods for gradient field estimation in 2D and 3D. Hints on what method performs best, both in terms of accuracy and efficiency. A comparison on four alternative methods for gradient field estimation. Three families of simplicial meshes have been considered, both in 2D and 3D. Conclusions suggest implementative hints for both academic and industrial code. Graphical abstract: Abstract: The estimation of the differential properties of a function sampled at the vertices of a discrete domain is at the basis of many applied sciences. In this paper, we focus on the computation of function gradients on triangle and tetrahedral meshes. We study one cell-based method (the standard the facto), plus three vertex-based methods. Comparisons regard accuracy, ability to perform on different domain discretizations, and efficiency. We performed extensive tests and provide an in-depth analysis of our results. Besides some common behaviour, we found that some methods perform better than others, considering both accuracy and efficiency. This directly translates to useful suggestions for the implementation of gradient estimators in research and industrial code.