C¹ Positive Surface over Positive Scattered Data Sites.

Abstract

The aim of this paper is to develop a local positivity preserving scheme when the data amassed from different sources is positioned at sparse points. The proposed algorithm first triangulates the irregular data using Delauny triangulation method, therewith interpolates each boundary and radial curve of the triangle by C¹ rational trigonometric cubic function. Half of the parameters in the description of the interpolant are constrained to keep up the positive shape of data while the remaining half are set free for users' requirement. Orthogonality of trigonometric function assures much smoother surface as compared to polynomial functions. The proposed scheme can be of great use in areas of surface reconstruction and deformation, signal processing, CAD/CAM design, solving differential equations, and image restoration.