3D Box Circle intersection

4
votes

I've got a circle defined by a center (x,y,z), a radius and an orientation vector that specifies which way the circle is facing. I need to test whether such a circle intersects with an axis-aligned bounding box. To clarify, by intersects, I mean if any points within the area described by the circle are within the bounding box, then that constitutes an "intersection."

This is not for a game and I'd rather not approximate the circle in some way. It should be OK though to treat the circle as cylinder with a very small height if that makes this any more tractable.

thanks.

Nick

1
3dintersection
Did you Google for "box circle intersection"? - Oliver Charlesworth
Not sure what do you mean by "bounding box". A "bounding box" is typically not intersected ... - Dr. belisarius
All the box-circle google hits are for 2D, not a 3D "circle" oriented along a vector. - Nick Collier

1 Answers

1
votes

Your circle center point and your vector define a plane; intersect your plane with your box (specifically 6 planes that make up your box); that will give you a set of line segments. Using the point-line nearest point algorithm, determine the nearest point on each line segments to your center point; if the square of the distance (use the square distance for distance comparison, it's faster and just as accurate) between that point and your circle center point is less than the square of your radius, your box intersects with your circle.

Note: this process is generic; use of axis-aligned bounding boxes makes everything even easier.