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Suppose I have the set of points

x1 = c(0,3,6) 
x2 = c(0,3,6)

and I want to interpolate the function 

y <- function(x){x[1]^2 + x[2]^2}

On set the set of points such that

x1 + x2 <= 6. That is...

z = 
    x1  x2
    0   0 
    0   3
    3   0
    6   0
    0   6

In reality, I do not know the function, but I know it's evaluation on each point of z.

The interpolation will fill in the gaps for any point in this set. For example, using the linear interpolation, I could evaluate it on anything in the rectangle 

x1 + x2<=6
wolfsatthedoor
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    I'm having difficulty understanding what you mean by "interpolate" when you have an analytic expression that gives exact values. – IRTFM May 03 '17 at 22:47
  • @42 In reality I don't, I only have evaluations of the function at the triangular grid points above. – wolfsatthedoor May 03 '17 at 22:53

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