Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents an...

Crown simulation based on basis spline (b-spline) interpolation is a compatible method to simulate tree polymorphism at present. However, there are two problems when it simulates the crown: first problem that derivative value top point needs be given manually, and second type of collected equidistantly. To solve above realize convenient accurate simulation, this study took Chinese fir as object...

In this paper a numerical technique based on the B-spline method is presented for the solution of Fredholm integro-differential equations. To illustrate the efficiency of the method some examples are introduced and the results are compared with the exact solution.  

In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline-based interpolation method for spectral codes is presented. The theory links the order of the interpolation method with its spectral properties. In this way many properties like order of continuity, order of convergence, and magnitude of errors can be exp...

In this paper, we purposed a new method in modeling the uncertainty data based on the theory of fuzzy sets and the interpolation B-spline model curve. The uncertainty data firstly defined by using fuzzy number concept and fuzzy relation by defined them in real data form. The existed coefficient control of interpolation B-spline basis function is substituted with the fuzzy data points(FDPs) whic...

The interpolation of a sequence of points is an important task in Engineering. In this work, three different interpolation methods are studied and expanded. The first method is the conventional interpolation Spline. The second method is a subdivision based geometric algorithm. The third method interpolates a given set of points with additional point normal constraints. The last two methods were...

We introduce the B-spline interpolation problem corresponding to a C∗-valued sesquilinear form on Hilbert C∗-module and study its basic properties as well uniqueness of solution. first in case when is self-dual. Passing setting W∗-modules, we present our main result by characterizing spline for extended has Finally, solutions C∗-modules over C∗-ideals W∗-algebras are extensively discussed.