stbenge <stb### [at] hotmailcom> wrote:

> If you find a way to match the edges of the triangles in POV, let me
> know. I've been busting my head all afternoon trying to figure it out!
> Edge matching would allow me to make some more interesting forms, like
> Escher-esque wicker baskets ;)

Not sure if it's what you're getting at, but perhaps take a look at my most
recent post in p.b.s-f.  The shape is a bit simpler than an icosahedron, but
the principle should be the same.  The general idea is as follows:

1) Set up two coordinate systems (x,y,z and a point).  Call them A and B.  These
can be calculated manually from vertices with vector operations.  We want to
link object A to some point in B.

2) Transform some point in B-coordinates, say <1,0,0> into the B frame of
reference to get its representation in absolute coordinates.

3) Inverse-transform it with the A coordinate system to get its corresponding
representation in A-coordinates.

4) Create an object in the A frame of reference at this point and transform it
into the A coordinates, except now it's at exactly the correct point in B
coordinates!

The result of this, if anyone can follow it, is that you can properly link
objects from two different coordinate systems with splines or whatever you
like.  If it's a regular geometric object, you can just labor over one part and
copy it symmetrically.  Nothing new, just a bit of vectors and matrices.  Works
for direction vectors too, just omit the translation when transforming.  Again,
the example file uses this, if you can decode what's going on.

 - Ricky

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