Constrained Adaptive B-spline Curve Fitting On Surface

Curve fitting of scattered data is always an important part of approximation theory. It is of great significance and extensive applications in many fields. B-spline method play an important part in Computer Aided Geometry Design (CAGD). Some analysis and discussion on the method of B-spline curve fitting of scattered data are presented in this thesis.Chapter 1 introduces the method to approximate a set of points by a smooth curve when designing curves on surface, and several methods are presented.B-spline curves and their main properties are described in chapter 2.In chapter 3, constrained curve fitting method on surface is discussed, which is motivated by an insight that properly selected points using discrete curvature called dominant points. A smooth curve constrained on surface can be fitted with this dominant points. A method called parameter modification which can play an important role in producing better curve approxima-tion is discussed. Through this method, dominant points can be inserted in the properly position to make a better approximation. Numerical experiments illustrate the effectiveness of our algo-rithm.A weighted least squares method for scattered data fitting is described in chapter 4. Nu-merical experiments illustrate the effectiveness of this algorithm.Finally, a summary of this thesis is given and several problems which need to be solved are proposed.