Advantages of Interval Modification of NURBS Curves in Modeling Uncertain Boundary Shape in Boundary Value Problems

摘要

In this paper, the advantages of interval modification of NURBS curves for modeling uncertainly defined boundary shapes in boundary value problems, are presented. The different interval techniques for modeling the uncertainty of linear as well as curvilinear shapes are considered. The uncertainty of the boundary shape is defined using interval coordinates of control points. The knots and weights in the proposed interval modification of NURBS curves are defined exactly. Such a definition allows for modification of the uncertainly defined shape without any change of interval values. The interval NURBS curves are compared with other interval techniques. The correctness of modeling the shape uncertainty is confirmed by solving the problem using the interval parametric integral equations system method. Such solutions (obtained using a program implemented by authors) confirm the advantages of using interval NURBS curves for modeling the boundary shape uncertainty. The shape approximation is improved using less number of interval input data and the obtained solutions are correct and less over-estimated.