Integrated Homotopy Sweep Technique for Computer-Aided Geometric Design

Abstract

A homotopy sweep technique is proposed for use in CAGD. The technique integrates the sweep technique and the homotopy model through sharing of a common parameter which controls the sweeping as well as the homotopic deformation of the cross sectional shape. The deformation is determined by two functions, a blending function which controls the smooth transition of one contour to the other, and a scaling function which shapes the outline of the sweep object. The sufficient conditions for the homotopy sweep surface patches to meet with first order geometry continuity are discussed. The technique provides a convenient and intuitive control of the shape of the cross section between two defined contours, and allows generalized cylinders to be modelled with lesser user input.