From: steve <sjbaker1_at_airmail.net>

Date: Wed Nov 08 2006 - 01:17:19 EET

Date: Wed Nov 08 2006 - 01:17:19 EET

Wesley Brooks wrote:

*> Anyway, going back to the three rules;
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*>
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*> 1. All triangles much conform to the right hand rule
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*> 2. All exterior surfaces must be devoid of gaps
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*> 3. Each triangle must share two of its vertices with each adjacent triangle
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*> Should point three be changed to; 'Each triangle must share at most two
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*> of its vertices with each of the adjacent triangles'?
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Either way, these rules don't prevent Klein bottles from happening.

*> Here's
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*> a set of rules which are an obvious development on the first three;
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*>
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*> 1. All triangles much conform to the right hand rule.
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*> 2. All exterior surfaces must be devoid of gaps.
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*> 3. Each triangle must share at most two of its points with each of the
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*> adjacent triangles.
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*> 4. Where a triangle shares two points with an adjacent triangle the
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*> order of the points must be a-b on one triangle ID list, and b-a, on the
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*> other.
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*> 5. Each point must be shared with at least three triangles.
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*> 6. Each edge must be, and only be common to two triangles.
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The addition of rule (4) solves the Klein bottle problem - but

adding rule (6) prevents you from making (say) two cubes that

touch along one edge - at that edge, four triangles legitimately

meet.

You'll need to add:

7) No triangle can intersect any other triangle.

But even with all of those rules - you could STILL have

pathalogical objects like a hollow sphere - where the

surface normals of the inner spherical surface SHOULD

face inwards towards the center of the sphere but

actually face outwards.

Inside-out objects in general are always good for a

laugh because inside-out surfaces are perfectly OK

so long as they are entirely embedded inside outside-in

objects.

Let's not even get started on precision issues.

Received on Thu Dec 07 23:56:53 2006

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