Research On Approximation And Interpolation In Curves And Surfaces Modeling

In the engineering design and the scientific research, must to assign the data point frequently to carry on the interpolation and approximation. The interpolation and approximation are in the science computation most basic and one of most important research questions, has the especially important theory significance and the application value. Although this aspect has many effective methods still had the insufficient existence. In order to solve the actual problem need, the new theory method appears unceasingly. The present paper discussion is based on the curve and the surface interpolation and approximation problems, propose some new theory methods.In the second chapter, the paper discussed the spline function partition structure, elaborated the spline function computational method. Regarding the B-spline basis function, has given based on the Hermite interpolation thought structure method. This B-spline basis function structure method, the different existing B-spline basis function definition or the computational method, have the theory and the application significance. In addition, based on the linear functional expression, discussed the spline function to approach the nature superiorly.By using quadratic B-splines, returned to give back to the time series partial interpolation model in the second chapter, the interpolation curve is C~1 continuous. Because the given method is the local interpolation model, the merit is this method has done not need to solve the system of linear equations, and then expanded the B-spline application. This method applies in the stock index analysis; the experimental result indicated the method is effective. Regarding the three dimensional data, gave quadratic tensor product B-splines local interpolation surface to accumulate the numerical procedure.In the third chapter, we propose a new method with piecewise cubic Hermite interpolation curve fitting statistics histogram. First selects the Hermite interpolation curve according to the statistical histogram characteristic the interpolation spot which and may adjust in the interpolation place derivative value, then basis area restraint determination adjustment value, thus obtains the fitted curve. The obtained fitted curve and the statistical histogram have the area equal restraint, and the fitted curve is the C~1 continuous smooth curve. This method gives a simple use.Fourth chapter has given approximate interpolation method based on the radial basis function. Because the scattered data correspondence radial basis function interpolation system of equations often is a morbid state, uses the Gaussian function, has given the multi-dimensional data radial basis function approximate interpolation expression, avoided the shortcoming of having to solve the system of equations by the existing radial basis function interpolation. The given approximate interpolation type to be possible to approach the single variable or the multivariable continuous function by any precision. The value example has confirmed the method is effective.Fifth chapter discusses the question the Box spline function to use in the computer assistance geometry design. Elaborated the Box spline expression, regarding the multi-dimensional spline, discussed the Box spline multinomial nature, the differential nature, the convexity, the subdivision properties, as well as the Box spline and the tensor product B-spline relations.