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I'm looking for an algorithm that will determine if a sphere is in any way touching an AABB or contained within it. Profile results indicate that this specific use is taking up a large percentage of my time, so it would be nice if it was as efficient as possible.

Edit: ATM, I've got this:

        bool IntersectsAABBWithSphere(Math::AABB rhs, Physics::Sphere sphere) const {
            auto aabbcenter = (rhs.BottomLeftClosest + rhs.TopRightFurthest) / 2.0f;
            auto SepAxis = sphere.origin - aabbcenter;
            auto Dist = Math::Length(SepAxis);
            SepAxis = Math::Normalize(SepAxis);
            if( SepAxis.x >= SepAxis.y && SepAxis.x >= SepAxis.z )
                SepAxis /= SepAxis.x;
            else if( SepAxis.y >= SepAxis.x && SepAxis.y >= SepAxis.z )
                SepAxis /= SepAxis.y;
                SepAxis /= SepAxis.z;

            auto extents = (rhs.TopRightFurthest - rhs.BottomLeftClosest);
            SepAxis.x *= extents.x / 2.0f;
            SepAxis.y *= extents.y / 2.0f;
            SepAxis.z *= extents.z / 2.0f;

            return Dist <= (sphere.radius + Math::Length(SepAxis));

My AABB's are currently represented as min/max, and my spheres as origin/magnitude.

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Perhaps you could share what you're currently doing? – Tetrad May 6 '12 at 0:41
@Tetrad: Dang, my mistake. – DeadMG May 6 '12 at 0:48

Found an SSE implementation in the paper and source code given here. Now that function has gone from 45% of my run-time, to so little I can't even find it in the list. win!

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How are you profiling. I'm curious because this hasn't come up in my thinking yet and I've never felt a need to do it for the simple programs I've written before but I think this would be useful for my game in the future for optimizing it. Is it simply a matter of tracking the amount of time in the given function areas or is there some other third party library or something you use? – Azaral May 6 '12 at 1:58
@Azaral: I use AMD Code Analyst. VS2010 Ultimate has a profiler built in, but for some reason mine doesn't work. It's a relatively simple CPU sampler- the program checks what function the CPU is in, say, 10000 times a second. You leave it running for a minute and you have a statistical sample of what functions the CPU is in most of the time. – DeadMG May 6 '12 at 4:20
Link is dead (500). This is why you copy the code in the answer - license permitting - or at least the name of said paper... sigh. – Thomas Nov 1 '13 at 7:05

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