Computer Aided Geometric Design

Along with the great progress in 3D data measurement device and the popularization of complex surface modeling, computer aided geometric design and computer graphics has been a research focus in the world over the past 20 years.First section of chapter 1 presents subdivision surface and the its application. Second section introduce our work : we extend method of Nasri[2] to quartic uniform B-spline subdivision and find that it is also established on the any even uniform B-spline subdivision schemes.First section of chapter 2 considers the perturbation idea and application. Second section introduce our work : Based on the perturbation idea, we present an approach for approximating rational surfaces by the interval Bezier surfaces. The method shown in this paper makes the perturbation surfaces having more restrictions than the original surfaces. The applications of this approach are presented. This result can be combined with subdivision method to obtain a piecewise interval polynomial approximation for a rational surface.First section of chapter 3 presents the continuity condition between adjacent surface problems. Second section introduce our work : We presents a practial Gl continuity condition between adjacent NURBS patches along common any degree boundary curve and deduces a specific algorithms for control point and weights of NURBS patches to attain Gl.according to algorithms condition.we can adjust the relative controls points and weights of another patch.