Re: [rp-ml] STL files

Wesley Brooks wrote:

> Anyway, going back to the three rules;
>
> 1. All triangles much conform to the right hand rule
> 2. All exterior surfaces must be devoid of gaps
> 3. Each triangle must share two of its vertices with each adjacent triangle

> Should point three be changed to; 'Each triangle must share at most two
> of its vertices with each of the adjacent triangles'?

Either way, these rules don't prevent Klein bottles from happening.

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

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