Curve and surface generation by splines

ABSTRACT Polynomial interpolation is frequently unsatisfactory. A function with sharp corners or rapidly changing higher derivatives is less accurately approximated by a higher-order polynomial than by a low-order polynomial. Even some smooth functions can be badly approximated by higher-order polynomials. When approximating functions for interpolation or for data fitting, it is necessary to have classes of functions which enough flexibility to adapt to the given data and can be easily evaluated on a computer. Splines are highly recommended for function approximation or data fitting whenever there is no particular reason for using a single polynomial or other elementary functions. Spline functions have the following properties:. Smooth and flexible,. Easy to store and manipulate on a computer,. Easy to evaluate, along with their derivatives and integrals. Spline functions play an important role in the solution of differential equations, modelling of data, curve and surface design and modelling of objects of complex geometric shape. In this study, Cubic splines are introduced and their properties are developed in section 2. In section 3 describes curves based on parametric cubic spline. In section 4 discusses B-spline curves. In section 5 adresses the design of B-spline surfaces. In parallel, their practical use is demonstrated by many examples using the codes written in C. Keywords: Spline, knot vector, B-spline basis, control points. vui