section 2.5.1 of Boyd and Vandenberghe's Convex Optimization. I do have an early draft of it.)įurthermore, obviously one could easily state (and prove) a "separating-axis theorem" if one wanted, but I find this silly as such a theorem trivially follows from the "separating hyperplane theorem" which is a KNOWN theorem that's _actually_ proved, used, and referred to in the theory of convex sets. I'm of the opinion that there is no such thing as a "separating-axis theorem."Ī lot of papers talk about the "separating-axis theorem " where X is a reference to (typically) the OBBTree paper by Gottschalk, Lin, and Manocha, but that paper doesn't ever talk about any separating-axis theorem! Indeed, I can't even locate a paper that attempts to formally state a separating-axis theorem! (There was a tech report by Gottschalk by that name but it was never published/completed.
Here's something I wrote elsewhere on this topic: I take it you consider this usage to be strictly incorrect?Yes.
#CHECK IF HYPERPLAN INTERSECTS ORTHANT PROFESSIONAL#
A quick Google search for the phrase 'use the separating axis theorem' seems to indicate that its use in this context is not uncommon (the search returns, among other things, some scholarly papers and some online posts by professional developers). the separating axis test (not theorem).Hm. However, you practically 'wrote the book' on collision detection (literally!), so if you say clipping would be faster then I believe it :) This is just 6 ray-vs-plane tests, which can be performed together using SIMD for additional speed.My thought was that the SAT might be faster for this purpose due to the lack of divisions and the efficiency of the plane tests (which, depending on the nature of the input data, could very well cull many if not most rays without any need for the six cross-product tests). I take it you consider this usage to be strictly incorrect? Quote:Instead the best approach is probably to treat the frustum as the intersection volume of 6 halfspaces and compute t_enter and t_exit for the six planes and see if t_enter < t_exit in which case there is an intersection (and otherwise not).
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