I have a set of points in space with certain values of a variable, how can i express them as a function?

Question

I have a 3D plot giving me the values of pressure which is the variable in this case. I want to express my field variable in the form of a function.
Please guide me as to what i can do to be able to do this

Answer 1

Well, what kind of a function are you looking for. This is called fitting in statistics. You will fit these data points to any function you want. If it is in 3D, then I am assuming that you have two independent variables and one dependent variable. There are plenty of softwares out there that will do this for you. Some have built-in functions to which you can perform the fitting, others allow you to program your own functions to perform the fitting.

Answer 2

Its an art as well as a science.
If you can draw a smooth line connecting the pressures then you see that there *may* be a continuous algebraic function that satisfies the condition. This does not mean it is a physical law but for the arrangement of the experiment it actually works. Look in a numerical analysis textbook on how interpolation is done using splines and stuff. The good news is that what you are asking for is definitely possible.

MATLAB has utilities for doing this stuff too. You're almost there.

Answer 3

You need to come up with a function of 2 variables f(x,y) that give you pressure. First thing you need is some model of the physical mechanisms in play. Surface fitting is, in general, a high-order b*tch, but there are a few math packages that will do a fairly good job.

Check out some of the math sites on the web.


Doug