Precise Fitting of Rational Bezier Surfaces onto Free Surfaces.

For computer-aided geometric design or for computer-aided geometric display, parametric curve segments and surface patches such as the Bezier form or B-spline form have been frequently used. It is very convenient if we can use the same parametric representations for the approximation of algebraic curves or surfaces, such as circles, ellipses, spheres and tori. Then we can perform unified treatment for all free-form and nonfree-form curves and surfaces. For the design, machining and inspection of accurate geometry such as precision machine parts, it is very important to know the qualitative and quantitative error of approximation from exact geometry. But up to the present, little work has been done on this error estimation. In this report, we treated the method of optimum fitting of rational cubic Bezier curves and rational bicubic Bezier surfaces onto algebraic and free curves and surfaces, and numerically examined the magnitudes of approximation errors.