Visually smooth composite surfaces for an unevenly spaced 3D data array

Abstract

Ferguson's composite surfaces, which are widely used in automatic surface fitting from an array of 3D points, are second-order continuous (C2), but they suffer from local flatness and bulges when the physical spacing of data points becomes uneven. This paper presents a method of constructing a G1 composite surface which is free from any local flatness and bulges even with a very uneven spacing of data points. The proposed surface interpolation scheme consists of (1) construction of chord-length spline mesh curves from the input data, (2) conversion of each cubic curve segment to a sextic Bezier curve, (3) determination of ''off-boundary'' control points by using a G1 condition, and (4) determination of ''internal'' control points. The surface interpolation scheme proposed in the paper has some nice features, for example: (a) it is a completely local scheme, (b) isoparametric curves of the entire surface are smooth across patch boundaries, and (c) the surface patches are all (nonrational) Bezier patches.