Given a view frustum and a sphere, how do I exactly determine whether or not the sphere intersects the frustum? The typical way of checking a sphere against a frustum finds the signed distance of the sphere center from each frustum plane, but this isn't an exact test and will sometimes fail:

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One method is to split the frustum geometry into triangles and test each triangle against the sphere for an intersection but this is slow.

Can SAT be used with a sphere? Are there any other faster methods?


1 Answer 1


If the sphere center lies outside 1 of the planes, check for distance to plane. If it lies outside 2 of the planes, check for distance to the edge they form. If it lies outside three of the planes, check for distance to their shared intersection point.

If it's actually a sphere in pretransformed world space, you can intersect against the pretransformed rectangular prism and it's pretty easy. If you're really intersecting a sphere against a truncated pyramid frustum, then there's a little more math to work out, and some edge/corner cases (ha) to do with lying outside 3 faces that don't form a corner.


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