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interpolate data points of a curve

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I am looking for a method to interpolate data points on a non liner curve.

 

The method I am trying to emulate in MATLAB is y1 = interp1(x,y,x1)

 

Essentially I am trying to supply my interpolate function two components of a curve (x & y).  The x1 one value is an independent variable such as time. 

 

Are there any built in features that would allow me to do this?  


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