Interpolation

Interpolation guarantees that the fitted curve will pass through each and every data point.

Lagrangian interpolation

Interpolating the data set with a polynomial. The order of the polynomial is determined by the number of points in the data set. The Lagrangian interpolating polynomial exhibits more oscillatory behavior as the degree increases. FindGraph limits the use of Lagrangian interpolation to data sets with 18 points or less.

Linear

Interpolating the range between data points (Xi,Yi) and (Xi+1,Yi+1) by a straight line. The interpolation function tooks two inputs. The simplest form of interpolation.

Cubic

Interpolating the range between data points by 3rd order polynomials. The interpolation functions took four inputs, including the point (Xi-1,Yi-1) before (Xi,Yi) and the point (Xi+2,Yi+2) after (Xi+1,Yi+1)

Cubic Spline

Interpolating the range between data points by 3rd order polynomials. Cubic spline curve fitting ensures that each spline is equal to the data points, the 1st derivatives are continuous at the knots, and the 2nd derivatives are continuous at the knots.

As against interpolation Regression curve fits and Linear Regression discover the best model to describe your data.


There are different ways to connect consequent points:

Y = f(X) X increases.
X = f(Y) Y increases.
f(X, Y) Sequence number, i.e. parameter Z increases.
R = f(fi) In Polar coordinates angle fi increases. First we sort normalized data.