An Approximately G1 Cubic Surface Interpolant

Abstract

In our earlier work on tangent plane continuous surface interpolation, we observed that many interpolation schemes often produce surfaces with drastic curvature variation. The curvature distributions are extreme enough to render the surfaces undesirable for many practicable applications. In an effort to improve the curvature distributions of surface interpolants, we have developed a surfacing method that (empirically) tends to produce surfaces possessing smoothly varying curvature. The surfaces produced by the method are comprised of cubic triangular parametric patches. An interesting feature of the method is that although the surfaces produced are globally only of class C0, they are “close” to being of class G1 (tangent plane continuous). Moreover, the extent to which they are not of class G1 can be made arbitrarily small using a refinement strategy.