# Offsetting a function by a sphere

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I gave a function in 3d, that I need to offset a bit towards its normal. I need to define the function so I can control a homebrew CNC milling machine along it, to create a parabolic mirror. The cutting head is round. The function goal is a 3D parabola, but for starters I will solve the 2d version. (x - h)^2 = 4p(y - k) http://en.wikipedia.org/wiki/Parabola I first guessed that I could use the circle equation: (x-a)^2+(y-b)^2=r^2 I would then isolate y in the circle equation and insert it into the parabola function. And then find what possible values for X would be possible, leaving with a and b as my new function. But Im not sure this is correct. I guess I am missing the "along the normal" restriction somewhere. It started as a subquestion in another thread, but I guess its a new problem of its own. At the end I hope to end up with a function on the form f(x,y)=??? I hope you can give me some pointers, Thanx in advance. /TAX

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