Approximation of sweep surfaces by tensor product B-splines

Tensor product B-spline approximations to surfaces generated by sweeping a (possibly deforming) B-spline cross-section curve along a Bspline axis curve are discussed. A general form for the tensor product B-spline approximation for sweeps is derived and expressed in terms of the approximation of a set of offset curves of the axis curve. The actual algorithm used to generate the approximation depends on the nature of the desired deformation and change in orientation that the crosssection undergoes as it is swept along the axis. Several algorithms for generating tensor product B-spline approximations to sweep surfaces are presented.