### MULTIPLE SOLUTIONS OF INTERPOLATION WITH SECOND AND THIRD DEGREE BÉZIER POLYNOMIALS

Nicolae URSU-FISCHER, Diana Ioana POPESCU, Ioan RADU, Iuliana Fabiola MOHOLEA

#### Abstract

In this paper we study the problem of interpolation with Bézier functions, considering different conditions regarding the number of interpolation points, the degree of parametric interpolation parametric curves and the derivatives of these functions in the common points. The mathematical background about Bézier functions is presented, also some essential issues and the interpolation conditions that are required. The following three issues are studied and solved: interpolation with a second-degree Bézier function passing through three points, interpolation with multiple second-degree Bezier functions having the equal first-order derivatives in common points and, finally, interpolation with a third-degree Bézier function passing through four points. All deduced mathematical relations were programmed in C and various examples were presented in the paper. The work ends with a series of very useful conclusions.

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