A Novel Triangle-based Method for Scattered Data Interpolation

Local numerical methods for scattered data interpolation often require a smart subdivision of the domain in geometrical polyhedral structures. In particular triangulations in the plane (2D) and tetrahedrizations in the space (3D) are widely used to define interpolation models. In this paper we give a short survey on the main methods for the scattered data problem and we recall preliminaries on triangulations and their related properties. Finally, combining two well-known ideas we present a new triangle-based interpolation method and show its application to a case study.