Re: [Algorithms] Verbal Definition of T-Junction
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From: Pai-Hung C. <pa...@ac...> - 2000-11-28 18:32:27
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Thanks Stephen! Your definitions are really inspiring. :-) BTW, does "split edge" means/refers to exactly the same thing as "T-junction"? Thank you, Paihung ----- Original Message ----- From: Stephen J Baker <sj...@li...> To: <gda...@li...> Sent: Tuesday, November 28, 2000 6:27 AM Subject: Re: [Algorithms] Verbal Definition of T-Junction > On Mon, 27 Nov 2000, Pai-Hung Chen wrote: > > > I am currently pondering about a good definition of T-junction in my thesis. > > Currently I can only come up with a poor description as follows: > > > > A T-junction refer to an undesirable case of mesh triangulation in which one > > or more vertices are not shared by all containing triangles, which forms a > > T-shaped edge intersection. > > That's not bad - and if we are *only* talking about meshes derived > from height fields, it's probably perfect. For something more general, > how about: > > A 'split edge' (my preferred term) refers to the undesirable case > where a vertex from polygon 'A' lies upon the edge of polygon 'B' at > a place where polygon 'B' has no vertex. > > Notice that there is also an issue with 'split-planes'. Imagine > a model of a building with four walls and a flat roof that overhangs > the walls on all four sides. The vertices of the wall polygons > can (and generally do) poke up through the roof for the same reason > that split-edges can crack apart and/or overlap. > > With that varient of the problem, it's not even necessary that > any of polygon 'A's vertices touch polygon 'B'... > > _____________ > / / > ______/_ _ _ _ _ _ /___ > | / B / | > | / / | > | /____________/ A | > |_______________________| > > If B is just resting on A, there will still be a nasty flickering > sliver of A showing through B where I have indicated with a dotted > line. This could just be due to poor Z precision - but even with > *perfect* hidden surface rendering, roundoff error can cause the > top two vertices of A to be slightly too high. > > So a more general definition of the problem might be: > > A 'split' refers to the undesirable case where all or > part of an edge of polygon 'A' lies in contact with > any part of polygon 'B' such that the vertices at the > ends of that edge do not correspond to the ends of any > edge of polygon 'B'. > > Ugh - too wordy. > > If you are going to be utterly rigorous then it's even > harder than that. I can imagine some acceptable cases > of splits - such as when the two polygons 'A' and 'B' > are placed such that only one of them is ever visible > (if they are back-to-back and backface-culling is enabled > for example). > > ---- > Steve Baker (817)619-2657 (Vox/Vox-Mail) > L3Com/Link Simulation & Training (817)619-2466 (Fax) > Work: sj...@li... http://www.link.com > Home: sjb...@ai... http://web2.airmail.net/sjbaker1 > > _______________________________________________ > GDAlgorithms-list mailing list > GDA...@li... > http://lists.sourceforge.net/mailman/listinfo/gdalgorithms-list > > |