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December 26th, 2012, 02:32 AM  #1 
Newbie Joined: Dec 2012 Posts: 2 Thanks: 0  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. Thanks. 
December 26th, 2012, 04:57 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Equation of a cylinder in 3 dimensional space.
It's easiest if the cylinder is axisaligned; if not, I usually change the coordinates so that it is. Once this is so, you can check the zcoordinate 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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cylinder, dimensional, equation, space 
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