Curve fitting

A related topic is regression analysis,[10][11] which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fitted to data observed with random errors.

If the order of the equation is increased to a second degree polynomial, the following results: This will exactly fit a simple curve to three points.

Identical end conditions are frequently used to ensure a smooth transition between polynomial curves contained within a single spline.

There are several reasons given to get an approximate fit when it is possible to simply increase the degree of the polynomial equation and get an exact match.

For example, a first degree polynomial (a line) constrained by only a single point, instead of the usual two, would give an infinite number of solutions.

In agriculture the inverted logistic sigmoid function (S-curve) is used to describe the relation between crop yield and growth factors.

Other types of curves, such as conic sections (circular, elliptical, parabolic, and hyperbolic arcs) or trigonometric functions (such as sine and cosine), may also be used, in certain cases.

For a parametric curve, it is effective to fit each of its coordinates as a separate function of arc length; assuming that data points can be ordered, the chord distance may be used.

[22] Coope[23] approaches the problem of trying to find the best visual fit of circle to a set of 2D data points.

Many statistical packages such as R and numerical software such as the gnuplot, GNU Scientific Library, Igor Pro, MLAB, Maple, MATLAB, TK Solver 6.0, Scilab, Mathematica, GNU Octave, and SciPy include commands for doing curve fitting in a variety of scenarios.

Fitting of a noisy curve by an asymmetrical peak model, with an iterative process ( Gauss–Newton algorithm with variable damping factor α).
Polynomial curves fitting a sine function
Polynomial curves fitting points generated with a sine function. The black dotted line is the "true" data, the red line is a first degree polynomial , the green line is second degree , the orange line is third degree and the blue line is fourth degree.
Relation between wheat yield and soil salinity [ 21 ]
Circle fitting with the Coope method, the points describing a circle arc, centre (1 ; 1), radius 4.
different models of ellipse fitting
Ellipse fitting minimising the algebraic distance (Fitzgibbon method).