.ThermoSysPro.Functions.TableSplineInterpolation

Information

ThermoSysPro Version 3.1

Computes 2-dimensional spline interpolation based on function SplineInterpolation. The resulting 2-dimensional spline will be continuous and have continuous first derivatives.

Implementation

It uses a cardinal spline interpolation algorithm. Cardinal splines are a sub-set of cubic Hermite splines where each piece is a third-degree polynomial specified in Hermite form: i.e specified by its values and the first derivatives at the end points of the reference interval.

The derivatives are calculated based on the non-uniform cardinal grid approach, see function SplineInterpolation for futher details.

Inputs

• TabP: vecor containing p-table values
• TabX: Vector containing x-table values
• TabY: Vector containing y-table values
• P: The p-value that the spline should be evaluated at
• X: The x-value that the spline should be evaluated at
• t: Cardinal spline shape parameter. t = 0.5 is default and is generally a good choice. A value close to 1 will yield a stiff spline, t=0 corresponds to a Catmull-Rom spline and  t < 0 corresponds to a more “loose” spline. From testing, t=0.5  seems to be a good choice in general and is therefore chosen as a default value. A value of t = 1 corresponds to that the derivative in all data points is zero, which may result in strange curves . See Examples > TestSplineInterpolation for a demonstration.

Output

• Y: Interpolated value evaluated at P,X

Extrapolation

Linear extrapolation is employed if the reference value is not contained in the reference value table.

Example

• TabX = {1,2,3,4};
• TabP = {1,2,3,4};
• TabY =  [2,2,2,2;2,2,1,2;2,2,2,2;1,2,1,2];

TabY respresents the value table, and TabX and TabP represent the reference tables.

The example was called for X = linspace(0,0.1,5) and P = linspace(0.1,0.1,4)

The black dots represent the data points, and the red lines represent the interpolation result.

References

http://people.cs.clemson.edu/~dhouse/courses/405/notes/splines.pdf

Interface

function TableSplineInterpolation
  input Real TabP[:] "1st reference table";
  input Real TabX[:] "2nd reference table";
  input Real TabY[:, :] "Results table";
  input Real P "1st reference value";
  input Real X "2nd reference value";
  input Real t = 0.5 "Stiffness parameter";
  output Real Y "Interpolated result";
end TableSplineInterpolation;

Revisions