Reparameterization of piecewise rational Bezier curves and its applications

Abstract

. Although the curve segments are C1 continuous in three dimensions, they may be C0 continuous in four dimensions. In this case, the multiplicity of each interior knot cannot be reduced and the B-spline basis function becomes C0 continuous. Using a surface generation method, such as skinning these kinds of rational B-spline curves to construct an interpolatory surface, may generate surfaces with C0 continuity. This paper presents a reparameterization method for reducing the multiplicity of each interior knot to make the curve segments C1 continuous in four dimensions. The reparameterized rational B-spline curve has the same shape and degree as before and also has a standard form. Some applications in skinned surface and ruled surface generation based on the reparameterized curves are shown.