How do I convert from Cartesian to conical coordinates?

I have some polygons I would like to map onto the face of a cone.

I can see from this page that I can convert the points of the polygon to cylindrical coordinates, which is almost what I want.

How do I go about modifying the formulas to work for conical coordinates?

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1 Answer

Presumably you already have the formulas for converting from conical to rectangular coordinates as listed on the Wikipedia page for conical coordinates. You'll need to solve for r, μ, and ν in terms of x, y, and z to get your answer. I can't see offhand the easiest way to find a general formula, but if you're trying to find it for particular values of r, μ, and ν, it shouldn't be too hard.

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