REVIEW OF GEOMETRIC CONTINUITY, WITH APPLICATION TO THE CONSTRUCTION OF G² CONTINUOUS CURVES

Abstract

Geometric continuity is a relatively new research area, and the concept causes considerable confusion for those not familiar with it. We give a brief summary of the different types of geometric continuity, and discuss three different, but equivalent, approaches for constructing Bézier curves. The continuity of composite Bézier curves are investigated, and we show that certain restrictions on the control points of the curves will ensure that they connect with a specific type and degree of continuity. We then use these results to construct C² and G² piecewise-cubic curves in three dimensions, since such curves are frequently used in computer aided design.