# Cylinder Equations

• May 15th 2012, 01:47 PM
zekefreed777
Cylinder Equations
This is pretty much my first post here, and I wasn't sure as to where this might belong as it's related to many things at once, but I don't have enough knowledge to be able to pin this down to any particular area.

Pretty much, I was looking for the closest distance between two cylinders with radius r1, r2, length l1, l2.

Basically, in 3D space, each cylinder can be represented by two dots at the center of the two bottom surfaces of the cylinders, plus its radius.

I have to be able to find a way to determine the distance, and judge if they collide or overlap, with a function or functions.

The issue I seem to be having is the fact that I can't seem to be able to make a 3-D set of equations using this data.

I was planning on using the 2*(pi*r^2)+ (2*pi*r)*h equation for surface area, but I have no idea as to how I can apply this equation in 3-D space and try to accommodate a 3-D distance equation, or the square root of (x2-x1)+(y2-y1)+(z2-z1), which is the only thing I have been able to find online.

If you have any recommendations or different equations/methods I can use that maybe easier, please let me know...

• May 15th 2012, 06:44 PM
Prove It
Re: Cylinder Equations
Quote:

Originally Posted by zekefreed777
This is pretty much my first post here, and I wasn't sure as to where this might belong as it's related to many things at once, but I don't have enough knowledge to be able to pin this down to any particular area.

Pretty much, I was looking for the closest distance between two cylinders with radius r1, r2, length l1, l2.

Basically, in 3D space, each cylinder can be represented by two dots at the center of the two bottom surfaces of the cylinders, plus its radius.

I have to be able to find a way to determine the distance, and judge if they collide or overlap, with a function or functions.

The issue I seem to be having is the fact that I can't seem to be able to make a 3-D set of equations using this data.

I was planning on using the 2*(pi*r^2)+ (2*pi*r)*h equation for surface area, but I have no idea as to how I can apply this equation in 3-D space and try to accommodate a 3-D distance equation, or the square root of (x2-x1)+(y2-y1)+(z2-z1), which is the only thing I have been able to find online.

If you have any recommendations or different equations/methods I can use that maybe easier, please let me know...

A cylinder's equation is given by \displaystyle \displaystyle \begin{align*} x^2 + y^2 = r^2 \end{align*} with \displaystyle \displaystyle \begin{align*} z \end{align*} as a free variable.
• May 16th 2012, 03:52 PM
zekefreed777
Re: Cylinder Equations
Thanks for the equation, Prove It.

Can it be expanded into (x-h)^2+(y-k)^2=r^2 for a cylinder with a point not at the origin? I ask just to make sure since this is technically the same equation for a circle in 2-d space, because in essence we are breaking down the cylinder into circular cross-sections, right? My math is a bit rusty...
• May 16th 2012, 04:20 PM
Prove It
Re: Cylinder Equations
Quote:

Originally Posted by zekefreed777
Thanks for the equation, Prove It.

Can it be expanded into (x-h)^2+(y-k)^2=r^2 for a cylinder with a point not at the origin? I ask just to make sure since this is technically the same equation for a circle in 2-d space, because in essence we are breaking down the cylinder into circular cross-sections, right? My math is a bit rusty...

Yes, that is correct :)
• May 17th 2012, 12:51 PM
zekefreed777
Re: Cylinder Equations
I managed to figure it out without using this equation (I think).

Pretty much I was able to see that through the cylinders, I have two different line segments (denoted by the height) and the two different radii along with the points at the top and bottom of the cylinder. The trick is to use the distance formula with x,y,& z and minus both of the radii from that distance to get the closest distances between the surfaces of the cylinders...

Thanks again, Prove It!

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