Question

I wish to determine if a Point P(x,y,z) is inside a 2D circle in 3D space defined by its center C (cx, cy, cz), radius R, and normal to the plane the circle lies on N.

I know that a point P lying on a 2D circle in 3D space is defined by:

P = R*cos(t)U + Rsin(t)*( N x U ) + C

where U is a unit vector from the center of the circle to any point on the circle. But given a point Q, how do I know if Q is on or inside the circle? What is the appropriate parameter t to choose? And which coordinates do I compare the point Q to see if they are within the circle?

Thanks.

Answer 1

Project P onto the plane containing the circle, call that P’. P will be in the circle if and only if |P – P’| = 0 and |P’ – C| < R.