Cubic Trigonometric Triangular Spline with Rational Basis Functions in 3-Dimensional Space

Abstract

Digitization of an object from visual to data point will help researchers manipulate the data for further use – particularly in reconstructing a surface. Currently, surface reconstruction focuses on non-rectangular topologies such as triangular surface because of its ability to generate smooth complex surface. The use of trigonometric function to generate a triangular surface are able to offer smooth surface with flexibility because it has the advantages of derivation and cyclability. There are studies that provides trigonometric basis functions for curves and surfaces with certain range of shape parameters. This study proposed four univariate trigonometric basis function and extending it to ten trigonometric basis functions over triangular domain with smaller set of shape parameter values. The basis is proven suitable for curve and surface design because it possesses blossoms which exist if and only if the space 〖DT〗_(λ,μ) is an EC-space on [0,π/2]. In addition, the properties of the basis are shown. Curve and surfaces are illustrated in this study using the proposed basis functions.