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

by rromanowski
Tags: 3d geometry, circle, equations, sphere
rromanowski is offline
Dec16-11, 12:17 PM
P: 1

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

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obafgkmrns is offline
Dec16-11, 01:48 PM
P: 126
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:

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