Reparameterization of piecewise rational Bezier curves and its applications
A piecewise rational Bezier curve is formed by several rational Bezier curve segments. It can be represented by a rational B-spline curve where the multiplicity of each interior knot equals degree. Although the curve segments are C-1 continuous in three dimensions, they may be C-0 continuous in four dimensions. In this case, the multiplicity of each interior knot cannot be reduced and the B-spline basis function becomes C-0 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 C-0 continuity. This paper presents a reparameterization method for reducing the multiplicity of each interior knot to make the curve segments C-1 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.
reparameterization piecewise rational bezier curve rational b-spline curve skinning ruled