Cubic spline interpolation Online

Cubic spline interpolation

Performs and visualizes a cubic spline interpolation for a given set of points. 

https://tools.timodenk.com/cubic-spline-interpolation

Example

-1.5 -1.2

-.2 0

1 0.5

5 1

10 1.2

15 2

20 1

Points

$$P_0(-1.5|-1.2);P_1(-0.2|0);P_2(1|0.5);P_3(5|1);P_4(10|1.2);P_5(15|2);P_6(20|1)$$

Equation

$$f(x)=\{\begin{array}{ll}-7.5160\cdot {10}^{-2}\cdot x^3-3.3822\cdot {10}^{-1}\cdot x^2+5.4277\cdot {10}^{-1}\cdot x+1.2148\cdot {10}^{-1},& \text{if }x\in [-1.5,-0.2],\\ 6.9014\cdot {10}^{-2}\cdot x^3-2.5172\cdot {10}^{-1}\cdot x^2+5.6007\cdot {10}^{-1}\cdot x+1.2263\cdot {10}^{-1},& \text{if }x\in (-0.2,1],\\ 2.5014\cdot {10}^{-3}\cdot x^3-5.2179\cdot {10}^{-2}\cdot x^2+3.6053\cdot {10}^{-1}\cdot x+1.8915\cdot {10}^{-1},& \text{if }x\in (1,5],\\ 3.4778\cdot {10}^{-3}\cdot x^3-6.6825\cdot {10}^{-2}\cdot x^2+4.3376\cdot {10}^{-1}\cdot x+6.7099\cdot {10}^{-2},& \text{if }x\in (5,10],\\ -6.7257\cdot {10}^{-3}\cdot x^3+2.3928\cdot {10}^{-1}\cdot x^2-2.6273\cdot x+1.0271\cdot {10}^1,& \text{if }x\in (10,15],\\ 4.2251\cdot {10}^{-3}\cdot x^3-2.5351\cdot {10}^{-1}\cdot x^2+4.7645\cdot x-2.6689\cdot {10}^1,& \text{if }x\in (15,20].\end{array}$$

By default, the algorithm calculates a "natural" spline. Details about the mathematical background of this tool and boundary conditions can be found here.

x-value

Graph

–o+←↓↑→

P0

P1

P2

P3

P4

P5

P6

 keep aspect ratio

LaTeX

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See also

Linear interpolation · Quadratic interpolation · Polynomial interpolation

Additional information

Cubic spline interpolation is a mathematical method commonly used to construct new points within the boundaries of a set of known points. These new points are function values of an interpolation function (referred to as spline), which itself consists of multiple cubic piecewise polynomials. Read more

Source code

JavaScript source code (cubic-spline-interpolation.js)