Optimized Design Bézier Surfaces Interpolation Geodesics

Abstract

This paper is concerned with reconstruction of Bézier surfaces through the cubic geodesics. Given n(n=2)regular spatial cubic Bézier curves, polynomial Bézier surfaces are designed to interpolate these curves so that they are isoprametric geodesics of the constructed surfaces. The control points of the interpolation surfaces are represented explicitly, and the surfaces are optimized by two minimization criterions. Computational experiments show the method is feasible.