Abstract:We explore for designing an algorithm to construct NURBS surfaces with approximate minimal area which interpolate given boundaries, and hence supply a gap that the current NURBS system is unable to design minimal NURBS surface effectively which is urgently required for engineering. Applying multifold techniques of NURBS surfaces such as knot-inserting, Hybrid polynomial approximations, etc., one can convert a NURBS surface into Bézier patches which are relatively simple to get minimal surfaces; then by using iterative method of optimizing the control points of each sub-surface and updating the whole surface continuously, one can obtain approximate minimal Bézier patches with high-precision successfully. In the end, one could choose the corresponding iterated approximation algorithms according to various requirements of different users, to compute the NURBS surfaces with approximate minimal area which satisfy boundary position constraints.

Abstract:This paper investigates the relationship between the hybrid polynomial approximation and the Hermite polynomial approximation for rational surfaces. Under some assumptions of the control point weights, the paper derives the general necessary and sufficient conditions for which both the hybrid polynomial approximation and the Hermite polynomial approximation converge to the rational surface.