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In intercept detection, AABB is allways faster than OOB, the problem is that you canīt rotate the AABB, so you need to recompute the AABB and this could be expensive, OOB intercept detection is not cheaper but donīt need to recompute and it is a minimun volume container, in other hand, a sphere container instead is situable for this, donīt need to recompute (except the center) and it is cheap.
So:
AABB : Needs to recompute, cheaper intercept detection, medium volume and variable.
OOB : Dont needs to recompute, expensive intercept detection, fits volume and fixed too
Sphere : Dont needs to recompute, cheap intercept detection, big volume and fixed
Convex polyhedra: Needs to recompute, expensive intercept detection, minimal volume for convex objects.
Array of convexs polyhedras: Concaves polyhedras can transformate in an array of convexs polyhedras.
About distance Im not sure what for you need it. Penetration distance ... or?
Bye Pogacha
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