Is the reference point (x, y) above or below the non-linear equation?

Question

BACKGROUND

In short, I have a series of 3 to 10 data points that will be used to represent a curve. For example:

• $X=0, Y=10$
• $X=4, Y=7$
• $X=9, Y=12$
• $X=16, Y=10$

What I am trying to do is determine whether or not a reference point is above or below the curve.

My gut feeling is that for people in the know, this is a relatively straight forward problem to solve. Unfortunately, my area of expertise is programming... not mathematics :(

Any guidance you can provide would be greatly appreciated.

ADDITIONAL NOTES

If it helps, I have access to the Math.NET library.

Answer 1

From what I understand you want to create a curve that passes through the points {(0,0),(4,7),(9,12),(16,10)}. This is called interpolation. This website might help in implementing it using math.net: https://numerics.mathdotnet.com/

Information from the graph you arrive at using interpolation is not reliable beyond the points you did the interpolation with.

Answer 2

Fit a spline to the data points:

http://en.wikipedia.org/wiki/Spline_(mathematics)

http://www.extremeoptimization.com/QuickStart/CSharp/CubicSplines.aspx