Reparameterization of piecewise rational Bezier curves and its applications

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. 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.