SPLINE INTERPOLATION WITH THIRD-DEGREE BÉZIER FUNCTIONS

The Bezier, B-spline and NURBS curves and surfaces were extensively studied in the literature and used in the shapes design of different products, initially for cars. From the mathematical point of view, in most cases the problems linked to interpolations and approximations with curves and surfaces have been solved.  Our research team has studied and solved the spline interpolation problem using third-degree Bezier curves between the interpolation points. An efficient algorithm has been set up following the mathematical model which solves the problem. It has been programmed in the C language and used to solve different numerical examples, with results illustrated by diagrams. It can be observed that there exist multiple variants of interpolation curves due to the imposed interpolation problem specificity: there exist more unknowns than equations (possible conditions to be imposed), that’s why one has to start with some initial values for a pair of selected unknowns.