Parametric equation for 3D circle that's off-axis

[rromanowski]

Hi.

I want to know the equation to draw a circle that's a bit tilted. Imagine a 3D circle that's parallel with the Y axis. Now I want to take that circle and have its center cross through the origin still, but I want it to be θ degrees titled from the Y Axis.

I'm using the following equations right now:
x = r * sin(u) * cos(v)
y = r * sin(v)
z = r * cos(u) * cos(v)

where r = radius, u ranges over full circle, v ranges from -pi/2 to pi/2

Thanks,
Ryan

 

[obafgkmrns]

You need to transform your sphere's orientation via multiplication by a direction cosine matrix. Any intro text to mechanics or aero should have a good description. This link also has a decent description: http://www.ece.unb.ca/COBRA/Resources/Kinematics, Rotations and Euler Angles.pdf