# Create 3d function with a set of points

by CjStaal
Tags: function, points
 P: 7 I'm creating a computer program and I need to see what's most efficient. I need another program [lol] that I can input 3d points in and have it create the function. the points are this v e t 100 500 3 300 3000 28 500 1000 3 1000 5000 45 1000 10000 330
 Homework Sci Advisor HW Helper Thanks P: 12,974 Cannot be done unless you know what sort of function to expect.
 P: 7 I can get much more points if that's what it needs. Pretty much I need to be able to put in v and e and get t out of it
 P: 7 Create 3d function with a set of points I think matlab can do it http://www.mathworks.fr/matlabcentral/fileexchange/8998
 Homework Sci Advisor HW Helper Thanks P: 12,974 Off your first post - you have a bunch of data points which are from some function f(x,y,z) right? You have asked for a program to recover the equation of f(x,y,z) from the set of ordered triples {(xi,yi,zi)}. The problem is that f(x,y,z) can be anything. Look at the simpler example in 2D ... if I have ordered pairs {(1,1),(2,1),(3,1),...} we could say that the curve is y=1 ... but it could also be y=cos(kx): k=2pi, so which is it? There are an infinite number of possible cosine curves.... then there are other periodic functions ... and, in this case, there are infinite data points. If there were finite data points, then I could also fit polynomials. Then there are all the possible irregular functions, peicewise functions and on and on and on. In 3D f(x,y,z) could even loop back on itself. Programs like matlab have built-in assumptions that they use to do interpolation - they do not, in general, find the equation of the generating function. gridfit, your example, for instance, assumes the data corresponds to a surface z=f(x,y)... and makes assumptions about the nature of the surface. For the 2D case I could use the polyfit function - but I have to also input the order of the polynomial I want to fit.
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,568 Given any finite number of points, there exist an infinite number of functions that give those points. In fact, given n points, there exist an infinite number of polynomials of degree n that give those points.
 P: 7 Well its more t=f(v,e)
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