Minimum Distance Between Two Biquadratic NURBS Surfaces

NURBS surfaces are first subdivided into a set of identical rational Bézier patches by inserting multiple knots at the crossing points of patch boundaries. From the theorem of positivity and convexity of biquadratic Bézier patches, parallel planes tangent to each pair of relevant patches at the extreme point with minimum or maximum z coordinate are constructed, the minimum distance between these planes gives the required answer.