       Re: reconstruction of 3D grid with connectivity

• To: mathgroup at smc.vnet.net
• Subject: [mg91411] Re: reconstruction of 3D grid with connectivity
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 20 Aug 2008 06:23:23 -0400 (EDT)
• Organization: Uni Leipzig
• References: <g8gj4j\$etq\$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de

```Hi,

a) your assumption "when u and v  are each incremented by given ustep
and vstep" because ParametricPlot3D[] make a irregular triangle mesh
you can see the mesh with

plt=ParametricPlot3D[{Cos[phi]*Sin[th], Sin[phi]*Sin[th], Cos[th]},
{th, 0, Pi}, {phi, 0, 2 Pi}, Mesh -> All]

b) the connectivity can be shown with

GraphPlot[
Union[Flatten[(Rule @@@ Partition[#, 2, 1, {-1}]) & /@
Cases[plt, _Polygon, Infinity][[1, 1]] /. (a_ -> b_) /;
a > b :> (b -> a)]
]]

Regards
Jens

Narasimham wrote:
> For surface ParametricPlot3D[{x = f(u,v), y = g(u,v), z = h(u,v)},
> {u,umin,umax,ustep},{v,vmin,vmax,vstep}]
>
> how to obtain the connectivity matrix (when u and v  are each
> incremented by given ustep and vstep), using Delaunay or Voronoi
> triangulations? In this case there would be curved or skewed
> quadrilaterals instead of triangles that discretizes the surface.When
> connectivity matrix and coordinate matrix are given with each  point
> ID reference number, the surface should be  reconstructed, i.e.,
> plotted, and/or Shown without again giving out the above command.
>
> Thanks in advance,
>
> Narasimham
>
>

```

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