Re: [Algorithms] Verbal Definition of T-Junction

[Pai-Hung C. <pa...@ac...>]

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
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>
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