Why use spline interpolation

The spline functions S x satisfying this type of boundary condition are called periodic splines. There are several methods that can be used to find the spline function S x according to its corresponding conditions.

Since there are 4n coefficients to determine with 4n conditions, we can easily plug the values we know into the 4n conditions and then solve the system of equations. Note that all the equations are linear with respect to the coefficients, so this is workable and computers can do it quite well. The algorithm given in Spline interpolation is also a method by solving the system of equations to obtain the cubic function in the symmetrical form.

The other method used quite often is Cubic Hermite spline , this gives us the spline in Hermite form. Hello, in my experience for approximating multi-variable curves calculate a spline for each variable, each with respect to a single parametric variable. Hi Timo, thanks for your work. You indicate to use the mathjs library to eliminate the round-off errors in javascript.

Bignumber effectively eliminates these errors. Hey Vincent, thanks for your nice comment! Back then I did not know about these things. Awesome job! I am trying to print that matrix you provided above.

Is there a way that it does provide it so that I can take a look at it? Dear Timo, I liked your description, thanks for writing it nicely. But, I think you do not need 16 equations for the example you have used with 5 data points.

You only need 3 equations — equations for the second derivatives of the spline. This way you can work with a N-2 x N-2 only, which is good for optimal performance. Save my name, email, and website in this browser for the next time I comment. Leave this field empty. Boundary Conditions In order to be able to solve the system of equations, two more pieces of information are required. Intuitively, the result looks best compared to the other methods.

The consistent change of steepness results in a slightly shifted maximum next to the second rightmost point, compared to the natural spline. Quadratic Spline The quadratic boundary condition defines the first and the last polynomial to be quadratic which makes this method the simplest one. The first and the last polynomial are not cubic but quadratic parabola pieces; colored in red. For the given set of data, this does not result in a counter-intuitive shape of the interpolation function.

Row 9 to The first derivative of two adjacent polynomials is equal in the point where they touch. Row 12 to The second derivative of two adjacent polynomials is equal in the point where they touch. Row 15 and The boundary condition natural spline. Outside of these bounds the polynomial function values do not match the points. Online Tool The cubic spline interpolation tool on tools. Timo Denk 73 Posts.

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