# Changing center point of a cylinder

1. Apr 23, 2014

### mpittma1

1. The problem statement, all variables and given/known data
How could I express a parametric formula for a right circular cylinder centered at (-2, 10, 3)?
with radius 3 and length 12

2. Relevant equations
Parametric equations for a right circular cylinder are:

x=rcosΘ
y=rsinθ
z = h

3. The attempt at a solution

Not sure how to start this...

2. Apr 23, 2014

### Simon Bridge

Well, if you have an equation y=f(x), you will find that equation y=f(x-a) is just f(x) shifted to the right by a units.

It is a coordinate translation.
Your problem is the same thing.

3. Apr 23, 2014

### mpittma1

Thats what i thought, the main problem is that this is an assignment using maple, where i have to graph the right circular cylinder with its center at that point.

when ever i try doing that it doesn't move the center to that point...

4. Apr 23, 2014

### Simon Bridge

Please show the adjusted equation followed by the maple code/instructions you are using to draw it.

5. Apr 23, 2014

### mpittma1

i posted the same question with the attached maple file here:

Last edited: Apr 23, 2014
6. Apr 23, 2014

### Simon Bridge

7. Apr 23, 2014

### mpittma1

Wasn't requiring anything, was trying to make it easier for you to just download the whole maple file.

unfortunately my colleges server just went down so I cant use maple for the rest of the night....

What i was doing before it crashed though, was I found the null space of the plane 2x-10y-3z=0

and then using that as a basis i made it into an orthonormal basis by using the Gram Schmidt command in maple, then found the third basis that is perpendicular to both w1 and w2 by taking the cross product of w1 and w2.

then using the parametric equation for the cylinder with radius 3 and length 12

{x = rcostheta
C1= {y = rsintheta
{z = s 0<theat<2pi & 0<s<12

then defined a transition matrix P = <w1 w2 w3>

then found the parametric equations for the cylinder by using

C2 = P.C1

then from that i graphed the image and began messing around with placing the center (-2, 10, 3) into the original C1 parametric equation as you suggested in your first response.

It was looking like i was getting close until the stupid program froze up on me..

8. Apr 23, 2014

### Simon Bridge

That sounds way too complicated-a method to possibly get the right equation.
Even if it is supposed to work, you are too likely to misplace something.
Why not just apply the transformation directly to the coordinates?

i.e.
for the origin centered cylinder, the x values will vary between x=-r and x=r - which centers the x values at x=0

for the cylinder you want, what will the values of x vary between in order to get the same radius, but centered on x=-2? How does that suggest you should modify the equation?

9. Apr 23, 2014

### LCKurtz

If you let $cyl:=[3\cos\theta,3\sin\theta,z]:$ and $v:=[-2,10,3]$, all you have to do is a plot3d of cyl+v.

10. Apr 23, 2014

### mpittma1

I see what your saying, but its a tilted cylinder that previous to this question i had to use transition matrices to find its parametric equation.

would your suggestion work for such a "titlted" cylinder?

11. Apr 23, 2014

### LCKurtz

If you are responding to me you should quote me so I know that. If you can plot your tilted cylinder at the origin, adding v to it will move it wherever you want it.

12. Apr 23, 2014

### mpittma1

Ok, so what you saying is i take system of parametric equations (C2) that make the titled cylinder and simply add the new center point, v, to it?

13. Apr 24, 2014

### LCKurtz

I haven't checked anything about your tilted cylinder. What I am saying is if you have figured out how to plot it at the origin then, yes, just add v to it to move it. It's just a translation.

14. Apr 24, 2014

### mpittma1

i understand, dont know why i didnt think of that lol

thanks a lot!

15. Apr 24, 2014

### Simon Bridge

The cylinder is being rotated as well as translated?!
That information was not in the problem statement.

Thanks to mpittma1 - I was trying not to be so direct :)