Subdivision And Application Of NURBS Curve Based On Coefficient Matrix

Subdivision schemes have important applications in curves and surfaces modeling and engineering designing. Applying subdivision schemes to geometric modeling may overcome the limitations of parametric schemes. Subdivision is efficient to design, represent and approach arbitrarily topological curves and surfaces. Because subdivision schemes have the advantages of discrete-to-discrete, simple rules, efficiency and convenient modification, which have already been widely used in 3D geometric modeling, computer animation and multiresolution analysis. NURBS may represent curves and surfaces accurately by uniform algebraic expression. Therefore, it is important to solve the problem of NURBS curves and surfaces subdivision for geometric modeling. For the accuracy of engineering, analyzing the error of NURBS curves subdivision is needed. This thesis studies subdivision schemes and applications of NURBS curves based on coefficient matrix, and point projection clipping circular algorithm is used to analyze the error of NURBS curves subdivision. The main results are as follow:(1) It studies the subdivision expression of NURBS curves based on NURBS coefficient matrix, with which 2-band subdivision scheme of quadratic NURBS curves, 3-band subdivision scheme of quadratic NURBS curves and 2-band subdivision scheme of cubic NURBS curves are obtained. Consequently, it can subdivide higher degree NURBS curves with multi-band.(2) It discusses NURBS point projection, and researches B-spline curves product and clipping circular algorithm in detail. Analyzing the error of NURBS curves subdivision with clipping circular algorithm of point projection and examples are given.(3) Through the nine vertex representation of circle and ellipse, combined with the characteristics of rotary surfaces, it obtains quadratic NURBS surfaces subdivision based on NURBS curves subdivision, and achieves subdivision of hyperboloid of one sheet, hyperboloid of two sheets, elliptic paraboloid and triaxial ellipsoid and so on.'NURBS curves and surfaces subdivision'software platform is constructed by MATLAB R2009a, examples used in the thesis are generated by this software platform.