# Calculating circle geometry in 3D

• Aug 1st 2012, 07:18 AM
shaunc
Calculating circle geometry in 3D
Hi,

It's my first post here, but I've been having a maths problem...

I have a circle in 3D space, and know 3 coordinates on the circle, as well as it's radius (all marked on the drawing in red).

What I need to work out is the angle of the circle's plane - basically the azimuth and elevation angles (marked as purple).

• Aug 1st 2012, 09:36 AM
a tutor
Re: Calculating circle geometry in 3D
Do you know how to work out a vector normal to the plane containing your three points?

Say it was <3,4,12>

You can use the first two components to work out the rotation in the XY plane.

Then take the length of the projection onto the XY plane, (5 in my example) and use this and the third component to get your other angle.
• Aug 1st 2012, 11:20 AM
shaunc
Re: Calculating circle geometry in 3D

I'm not sure that I explained myself very well in the post above. I'm not trying to find the angles of a specific point - the 3 points on the circle's perimeter have actually been calculated from azimuth and height angles.

What I need to do is to work out the plane of the circle calculated from these points, and the rotation of this plane. The angles in the diagram are supposed to be perpendicular to the circle's plane.
• Aug 1st 2012, 11:45 AM
a tutor
Re: Calculating circle geometry in 3D
Quote:

Originally Posted by shaunc
I'm not trying to find the angles of a specific point

I realise that.

Since your plane passes through the origin you only need two of your points.

The normal to the plane is $\begin{vmatrix} i & j & k \\x_1& y_1 & z_1 \\x_2 & y_2 & z_2 \end{vmatrix}$
• Aug 4th 2012, 07:14 AM
shaunc
Re: Calculating circle geometry in 3D
Great, I've got it. Thank you for your help.