What is the spline?

Spline is a type of polynomial function in parts. In mathematics, Spline is often used in the type of interpolation known as spline interpolation. Spline curves are also used in computer graphics and computer -supported design (CAD) for approximate complex shapes.

Interpolation is used if there is a set of discrete data points and it is necessary to estimate additional points of the same data type from the points. Polynomial interpolations are commonly used for a small number of data points; It is a method that corresponds to the polynomic function of the order of the order to the data points N + 1. However, when the number of points increases, polynomial interpolations often do not match the data well. In these cases, Spline interpolation is often used instead. This is why Spline is more of a piece of functions than smooth curves. Commonly used interpolation techniques include linear, quadratic and cubic interpolation.

Interpolation of linear spline simply fits into a line over every consecutive pair of data points. Each line of line can have a similar or very different slope from the second part depending on the data distribution. To find the value of Y on the Cardesian coordinate system for a given value of X between two data points, the slope between the points is multiplied by the distance between the value of the value of the value of the Y value and the value of x for the point of the left. This number is then added to the Y to the left of the desired location to obtain the approximation of the value y between two points.

interpolation of quadratic spline is closer to the data between consecutive points of a quadratic polynomial. A number of methods of solving simultaneous equations can be used to find coefficients of these quadratic equations. Linear algebra techniques or solutions using computer software are some of the more common techniques used. The interpolated value y to the quadratic spline is found by the general quadratic equation, y = a*x _{2 + B*x + C, with previously determined coefficients A, B and C.}

Cubic spline interpolation uses cubic or third order, a polynomial function to zoom in to the data between consecutive points. This type of spline is usually calculated using computer software or graphics calculator. A special type of interpolation of cubic spline, called interpolation of Splied or Complete Spline, uses the slopes given at the ends of the curve to help calculate the function.