VISUALLY SMOOTH COMPOSITE SURFACES FOR AN UNEVENLY SPACED 3D DATA ARRAY

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.