Research On Curve Approximation And Surface Reconstruction In CAD

Curve approximation and surface reconstruction are both important topics in the CAD fields. Combing the conventional approximation theorem and geometry modeling technique, curve approximation is widely used in the varied fields, which include the approximation to the curve defined procedurally, polynomial approximation of rational Bezier curves, and degree reduction of NURBS curves etc. surface reconstruction is increasingly important in geometric modeling for generating surfaces from cloud points captured from real objects, often by laser range scanners but also by hand-held digitizers, computer vision techniques, edge detection from medical images, or other technologies. Industrial applications include reverse engineering, product design and the construction of personalized medical applications. In this paper we profoundly research on curve approximation and surface reconstruction. The main contributions are listed as follows:Firstly, the main attention was paid on the curve approximation. There are three main contributions in these fields. (1) We present a novel algorithm to optimally approximate intersection curves of surfaces with C~2 B-spline curves that have approximately only 1/3 of the number of the control points of the B-spline output from the geometry engines. Using the existed curve fitting method, a coarsened curve is constructed to approximate the intersection curve. Then we refine the fitting curve iteratively by local modification where the big error existed. Our algorithm has been integrated into SolidWorks system successfully with very good application performances. (2) With the help of previous work,this paper investigates the affection of reparametrization on the convergence condition for the hybrid polymial approximation.Under some assumptions of the control point weights.we derives some general sufficient conditions for which hybrid polynomial approximation converge to the rational Bezier curves after reparametrization. (3) The C-Bezier curve is introduced to CAD/CAM to deal with circular arcs, cylinders, and cones. It can precisely represent these conic curves in a Bezier-like way. A conjecture in [Chen2003]...