Applications of rational B-splines in computer-aided geometric design.

摘要

The advantages of non-uniform rational B-splines over their non-rational counterparts has led to their widespread use in commercial and private CAD/CAM systems. While surface representation using rational B-splines has been limited mainly to standard shapes such as cylinders, spheres, torii, and surfaces of revolution, surface manipulation has been even more limited to simple Bezier patches.; To complement curve and surface construction features, a surface modeler needs other applications to make it a more versatile system. Some of these applications include trimming and extending curves and surfaces, creating transition surfaces between non-intersecting surfaces, and blending surfaces that meet at corners. Considering the fact that work on free-form surface design using rational B-splines is fairly limited, and the fact that conic sections are an essential curve form in surface design, there is a definite need for algorithms that facilitate the representation and manipulation of rational B-spline curves and surfaces.; This dissertation focuses on two applications required in a CAD/CAM system based upon the rational B-spline mathematical form: extending curves and surfaces and creating transition curves and surfaces between non-intersecting geometry. The study takes a geometric approach with emphasis on continuity conditions between the original and newly created geometry and on ease of implementation in a practical CAD/CAM system. This work introduces capabilities not known to exist presently in a commercial CAD/CAM system based upon the rational B-spline mathematical form.