Gradient field estimation on triangle meshes

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 meshes. We study one face-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 behaviour that is common to all methods, in our study we found that, considering both accuracy and efficiency, some methods are preferable to others. This directly translates to useful suggestions for the implementation of gradient estimators in research and industrial code