Fairing Spatial B-Spline Curves

Abstract

Three-dimensional curves are playing an increasing role in ship-hull modeling and many other areas of computer-aided design (CAD). The problem of evaluating and improving the fairness of such a curve is considered and three solutions (algorithms) are proposed representing all major methodologies currently pursued by CAD researchers: local fairing by knot removal, and local/global fairing based on "energy" minimization. The performance of the algorithms is studied for both cubic and quintic B-splines using realistic test cases. Finally, a comparison with existing techniques is presented and some visualization tools for spatial-curve fairing are briefly discussed.