A separating axis is an axis on which the projections of the objects A and B do not overlap. I am sorry, but I belief this article is just plain wrong and did a good job in confusing me.ġ.) The figure is wrong.
#Hyperplan dense how to
I still need to know how to fix the illustration, though - why are the Inkscape labels black?Ħ6.253.99.66 ( talk) 22:56, 10 January 2008 (UTC) Wrong I updated the text to hopefully serve both purposes. In fact, the reason I fixed the article was I sent someone here, and they didn't "get it." Also, presumably people using Wikipedia (instead of Mathworld or just a textbook) are not computational geometry mathematicians, and the duality between axis and hyperplane might not be immediately obvious. I come to this from practical computational geometry, where those two definitions are the most natural. Well, I disagree - a separating line is something that separates two objects, but a separating axis is the axis along which objects can be separated.
Oleg Alexandrov ( talk) 06:43, 10 January 2008 (UTC) In short, you do have a point, but I'd stick with the simpler formulation. And, "separating axis" does suggest more that the axis separates things, rather than the dual of the axis. The two formulations are trivially equivalent (if you are already familiar with it). How can I make it not generate those artifacts for the labeling text? When someone comes across the term "separating axis theorem," chances are pretty high that they did it because of some computational geometry need, the most common of which in practice is physical simulation such as found in games programming, and thus describing the actual separating axis and the property of the projection is necessary on the page. That axis is the dual of a separating plane. For example, in 3D, there is still a separating axis. It is also an important definition, because no matter what the dimensionality, the separating axis is always an axis. This is an important definition, because it suggests an algorithm for testing whether two convex solids intersect or not - and, in fact, it's heavily used in computational geometry, including computer games. In practice, the separating axis theorem says that if two convex objects are not penetrating, there exists an axis for which the projection of the objects will not overlap. I think you are confusing separating axis and separating line. Oleg Alexandrov ( talk) 06:50, 8 January 2008 (UTC) That would need fixing before it can be used. I'd also like to note that the modified image, with the projection, does not render well, I see black rectangles on the screen, as seen on the right.
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