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AFAIK, many physics engines like Physx and Havok don't incorporate cylinder as basic shape because it is expensive than sphere, box and capsule. But bullet engine does incorporate cylinder as a basic shape. Do they found any fast algorithm to simulate the cylinder and what is that?

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Havok.. hkpCylinderShapeClass. Why do you suspect a cylinder is more expensive than a capsule? I don't know about Physx, but Havok most certainly supports cylinders, capsules and very complex geometries. But the cylinder is not considered expensive. Of course, the sphere is the "most" trivial, with the box following. The cylinder/capsule should follow (it's actually based on segment vs something collision queries, and these are actually pretty cheap to compute). –  teodron Sep 17 '13 at 11:26

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I don´t know about the speed or exact nature of the cylinder shaped collider in bullet, but this paper gives a nice overview about cylinder collision.

If you are only after the implementation of their collision you may want to start here and try to recreate what they are doing with it.

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