The Approximate Calculation Of NURBS And Study On Effects Of Weights

Non-Uniform Rational B-spline(NURBS) is the significant standard of describing and processing geometry problem on curve and surface in Computer Aided Geometry Design (CAGD). Because of the fine characteristics of NURBS, it already has become the only international standard that applies mathematics to describe the products. Now it has extensively been applied to CAD/CAM and the study field of Computer Graphics.The algorithm on length of NURBS curve and area of NURBS surface is discussed in this dissertation. And effects of weights on NURBS curve are studied. The principle content studied in this dissertation includes:1. An adaptive subdivision algorithm is adopted to compute the approximating lengths of NURBS curve. Based on the theory, three kinds of different calculating methods are put forward. These methods are all suitable for NURBS curve of arbitrary degree under three-dimensional space, and according to approximating precision in advance, automatically disperse curve to compute length. And this dissertation has improved the existing approach of computing approximating error.2. Based on the approximating subdivision algorithm of NURBS curve, three approximate calculating methods are brought forward. These three methods are employed to estimate areas, volumes of revolution, first moments of area, whose regions bounded by NURBS curve of any degree under three-dimensional space.3. Depended on the approximating subdivision algorithm of curve, the subdivision algorithm of NURBS surface has further proposed. And it draws the approximate calculating method of NURBS surface areas.4. It systemically summarizes the physics and geometry of weights of control points, and investigates the modification of weights of NURBS curve how to affect shape and length of NURBS curve. Analyzing the experimental datum by regression, it draws the different influences of the modification of the weights of two kinds of control points on length of NURBS curve.5. Finally, adopted the application framework based on " Document/View", Approximation Computing System of NURBS Curve and Surface is implemented by utilizing Visual C++6.0, OpenGL supported by WindowsXR And numerical tests on the above algorithms have finished under this system.