New Cubic Timmer Triangular Patches With C¹ and G¹ Continuity

Abstract

In this study, a new cubic Timmer triangular patch is constructed by extending the univariate cubic Timmer basis functions. The best scheme that lies towards the control polygon is cubic Timmer curve and surface compared to the other methods. From the best of our knowledge, nobody has extended the univariate cubic Timmer basis to the bivariate triangular patch. The construction of the proposed cubic Timmer triangular patch is based on the main idea of the cubic Ball and cubic Bezier triangular patches construction. Some properties of the new cubic Timmer triangular patch are investigated. Furthermore, the composite cubic Timmer triangular patches with parametric continuity (C1) and geometric continuity (G1) are discussed. Simple error analysis between the triangular patches and one test function is provided for each continuity type. Numerical and graphical results are presented by using Mathematica and MATLAB.