# Simple circles

1. Jul 25, 2006

### kevdoig

I have a point a 3D space (say 0,0,0), a radius of the circle(say 2m), and know a single point that lies on the circle at a certain x co-ordinate, and have the corresponding y coordinate for the point on the circle. How can I calculate the Z co-ordinate for this point given the above parameters?

I am trying to generate a 3D pipe and have the centre of the pipe at (0,0,0), and know the the x distance along the pipe and the height of the pipe at any given point, but not its depth (which i need to calculate), if this helps explain.

2. Jul 25, 2006

### benorin

Assuming that the point you named in 3D space (0,0,0) is the center of the circle of radius 2m, and that you know that $$( x_0 ,y_0,z)$$ is a point on the circle and z (the Z coordinate) is unknown: then to determine z know the the distance between the center of the circle (0,0,0) and any point on it, say $$( x_0 ,y_0,z)$$ , is equal to the radius 2m, hence

$$\sqrt{x_0^2+y_0^2+z^2}=2m$$

which gives

$$z=\sqrt{(2m)^2-x_0^2-y_0^2}$$

for the Z coordinate.

3. Jul 25, 2006

### kevdoig

cheers, solved it 5 mins after posting, using a similar method, think long nights with early mornings make me a little slow!