A New Unified Model of Univariate and Bivariate Bases for Curves, Rectangular Surfaces and Triangular surfaces

In this paper, a new basis for polynomial curve modeling is presented with its linear computation. This new proposed curve can be formed by the convex combination of its blending functions and related control points. Moreover, several important geometric properties for this curve are identified, for examples, a partition of unity, convex hull property and symmetry. Later the recursive algorithm, coefficient matrix representation, the derivatives and the relationships between Bezier curve and this proposed curve are defined. Finally, a new proposed rectangular and triangular basis functions are also presented with their surface definitions.