INTERPOLATION BY RATIONAL SURFASES OF BEZIER AND NURBS-SURFASES

Abstract

Relevance. Rational Bezier surfases and NURBS-surfases are widely used in modeling curviliniar objects due to the great flexibility and efficiency of the method. Therefore, it is sense to develop an interpolation method by these surfases

Method. The work is devoted to the development of a new approach to interpolation surfases , represented by a set of discret points. The analytical description of the desired surfases is implemented a rational Bezier surfases and a NURBS-surfases.To solve this problem, two approaches are propozed. The first approach is that the weights of the control points are set in advance and then the coordinates of the points of the interpolating rational Bezier surfase as well as the NURBS-surfase are calculated. The second approach is that the coordinates of the control points are set in advance and then the weights of the control points of Bezier surfase as well as the NURBS-surfase are calculated. At the beginning of the process , are set only coordinates, but also parameters are set to a discret points, that is , each poins has the following definition: T(x,y,z,u,v) in the three-dimentional space, where u,v – parameters. To solve the interpolation problem, a system of linear equation is created in with each equation reflects the equality between the analytical formula for a surfase and a given point. Moreover, the number of interpolated points it must be number of control points. Thus, we have a system of N linear equations, where N is the number of control points.

Results. Two methods of interpolation of a points serials by rational Bezier surfases and NURBS-surfases. were developed.

Conclusions. The test cases carried out of using computer programs and calculated of results confirm the validiti of the proposed methods.

Keywords: interpolation, rational Bezier surfases, NURBS-surfases.