Interpolation of Surfaces over Scattered Data

We investigate the performance of DEI, an approach [2] that computes off-mesh approximations of PDE solutions, and can also be used as a technique for scattered data interpolation and surface representation. For the general case of unstructured meshes, we found it necessary to modify the original DEI. The resulting method, ADEI, adjusts the parameter of the interpolant, obtaining better performance. Finally, we measure ADEI’s performance using different sets of scattered data and test functions and compare ADEI against two methods from the collection of ACM algorithms: Algorithms 752 [10] and 790 [11]. The results show that ADEI is better than, if not comparable to, the best of the compared scattered data interpolation techniques.