On Thu, 11 Oct 2001 16:40:24 +0200, Nicolas Calimet wrote:
>> I think you're thinking of something besides Delaunay triangulation.  That's
>> a purely 2d technique and has nothing to do with meshes.
>
>	Mhhh, guess you're wrong, sorry.
>	Delaunay triangulation is commonly used in 3D (and maybe more dim.)
>to create meshes from different kind of data, e.g. a cloud of points. I had
>got a lot of internet references when looking at a related problem (mesh
>simplification) but unfortunately lost all while moving. Probably worth to
>search again since there might have new stuffs appearing  :o)

But it's not triangulation in that case; it's a more generalized sort of
related thing involving solids.  The whole idea of triangulation doesn't 
make sense unless all of the points are in a plane, because the notion of
"none of the other points fall in the circumscribed circle" doesn't make
sense.  You can construct a Voronoi diagram of sorts in 3-space and then 
take something that resembles a dual of that, but it wouldn't be quite the 
same sort of dual (because it swaps volumes with vertices and faces with 
edges, rather than the 2d version that swaps faces with vertices and has a 
1:1 correspondence between the two sets of edges) and it shouldn't be 
called a Delaunay triangulation (if for no other reason than that the 
mathematically interesting part of the result isn't the triangles, but the 
solids that they bound.)

-- 
#local R=<7084844682857967,0787982,826975826580>;#macro L(P)concat(#while(P)chr(
mod(P,100)),#local P=P/100;#end"")#end background{rgb 1}text{ttf L(R.x)L(R.y)0,0
translate<-.8,0,-1>}text{ttf L(R.x)L(R.z)0,0translate<-1.6,-.75,-1>}sphere{z/9e3
4/26/2001finish{reflection 1}}//ron.parker@povray.org My opinions, nobody else's

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