Transformation of a Dynamic B-spline Curve Into Piecewise Power Basis Representation

Abstract

In the fields of computer aided geometric design and computer graphics, B-spline curves and surfaces are often adopted as a geometric modelling tool and their evaluation is frequently required for a various geometric processing. In this paper, we present a new algorithm to convert Bspline curves into piecewise polynomials in power form. The proposed algorithm considers recursive B-spline basis function to be a pile of linear functions and collects all the necessary linear functions in each knot span. Then, algorithm computes the power form representation of B-spline basis functions and the required transformation of B-spline curve is obtained through the linear combination of B-splines in power form and the corresponding control points in each knot span.