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December 26th, 2012, 03:32 AM   #1
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Equation of a cylinder in 3 dimensional space.

Hi Friends,

Please, I like to know the equation of a cylinder with a given radius, r and a given height, h in 3 dimensional space(x,y,z).

We need this in other to verify whether a given point, say (1,2,3) is in the cylinder or not.

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December 26th, 2012, 05:57 AM   #2
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Re: Equation of a cylinder in 3 dimensional space.

It's easiest if the cylinder is axis-aligned; if not, I usually change the coordinates so that it is. Once this is so, you can check the z-coordinate directly: is it between z_0 and z_0 + h? If not, the point is outside the cylinder. Otherwise, check (x - x_0)^2 + (y - y_0)^2; if between 0 and r^2, it's in the cylinder, otherwise outside.
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