Curve Fitting:

It is the procedure of construction of a curve passing through a given set of points either with exact fit or best fit criterion (Figure (a)). Curve fitting capture the trend of the data by assigning a single function across the overall range. Interpolation is also to build a curve by piecewise joining of two adjacent points by line entities (linear interpolation) or arc entities (circular interpolation) (Figure (b)).

In several CAD/CAM applications, namely aerofoil cross-section, the displacement curves, in FEM application etc. utilize of interpolation and curve fitting are inevitable. An interpolated shape of aerofoil by using line and arc elements has been illustrated in Figure (c).

(a) Interpolation                                 (b) Curve Fitting

(c)

Figure    

A short overview of curve fitting is presented below. Various curve fitting techniques are available such like Lagrangian interpolation, polynomial fitting; Newton divided difference method and splines etc.

Analytical equation fitting techniques may be broadly classified as exact fit and best fit techniques.