OK so there are people around the internet who claim that they can implement this collision detection alogorithm(http://www.peroxide.dk/papers/collision/collision.pdf) without
additional intersection check...

In details this is a standard collision detection technique suitable for jump'n'run games like Rayman. The technique describes all the the moving entities with
elliposid, and all the static obsticles with tri-meshes. and then when moving those ellipsoids a "unit sphere - triangle" sweep test is performed.
The sweep test in theory should give us a maxumum allowed travel distance without any intersection with any triangle.

Soo.. I've implemented this and I't works amost eveytime,but sometimes when the sphere *accidentaly* gets too close to a triangle I get stuck, not able to move(sweep test always returns an intersection at moment t0=0.0f). This could
be an error in my Sweep test implementataion (i still cannot find it) or it could be in the "sliding" implementation but certanly the floating point percison helps...
In order to *cure" this isse I've implemented a function that intersects a sphere with a triangle and returns a vector that will "push" the sphere out of the triangle.

So my question is:

Have any of you implemented this technique without "fixing" the situation with intersection tests(or ?ny analogue)?