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Hy, In math classes, I've learned that given some points in 2D space: a(1,2), b(7,3), c(8,5),...

You can find an equation that goes through these points (using interpolation).

Now I was wondering if the same is possible for 3D points? Could a(x,y,z), b(x',y',z'), c(x",y",z"),... result me in a 3D surface, like for example x²+y²+z² = 1 (a sphere)?

Thanks for the help

genz
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    It seems that you want to reconstruct an implicit surface from a point cloud. This is a rather difficult problem that has been attacked in several papers. Even the 2d parametric curve reconstruction problem is hard, though better understood. – lhf May 03 '13 at 16:13
  • You could use a method similar to one dimensional LaGrange interpolation, by setting up for each point $P_k$ in the set of $n$ planar points of the interpolation "input set" a function $f_k$ which is $1$ at $P_k$ and zero at all the other $P_j,j \neq k$. – coffeemath May 03 '13 at 16:27

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