Curves And Surfaces Fitting Based On The Diagonal Linear Differential System With Variable Coefficients

Curves and surfaces fitting is an important problem in computer aided geometric design, there are many methods including Bezier curves and surfaces, B-spline curves and surfaces, NURBS method, subdivision curves and surfaces and so on. However, a large number of practical problem in the natural or engineering fields need to be described in the form of differential equations. Combined with the B-spline curves and surfaces reconstruction methods, this thesis discussed the curves and surfaces fitting methods based on the diagonal linear differential system with variable coefficients.From discrete data points, the main works are as follows. (1) Firstly we introduce the curves fitting algorithms by linear differential system with constant coefficients based the difference schemes. (2) Because the general discrete data points can not be represented by a simple linear differential system with constant coefficient, in order to improve the fitting precision, we propose the curve fitting algorithm by diagonal linear differential system with variable coefficient based on the difference schemes. (3) Since there is no explicit expression of the solution for the general linear ordinary differential system with variable coefficient, it is difficult to achieve the end interpolation conditions. In order to get the end of interpolation, we propose another curve fitting algorithm by special diagonal linear differential system with variable coefficient. In this case, the solution can be represented in exponential matrix form. Combined with the B-spline curve fitting, the new algorithm not only has high fitting accuracy, but also satisfy the end of interpolation. Finally we extend this algorithm to the case of surface fitting, and can obtain satisfactory accuracy.