Boundary Curve Based Surface Splines

Abstract

The device of sweeping a cubic polynomial space curve through space while simultaneously deforming it so as to match a second cubic polynomial space curve at the end of the sweep can be generalized so that we can sweep and deform any given initial boundary curve so that it matches any given final boundary curve at the end of the sweeping process. This sweeping can be characterized as forming intermediate curves by interpolating between each corresponding pair of points on the initial and final curves. A. R. Forrest gives a thorough review of this methodology in [For72]; there much of this work is credited to Steven Coons.