so, what is manifold geometry

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Old 10 October 2003   #1
so, what is manifold geometry

So far, I've been able to determine the following:

Non-manifold geometry is when polygons are arranged in weird ways. For example, take an hourglass and pinch it in the middle so that the geometry there goes down to one vertex at that spot. The whole hourglass is now non-manifold.

But... what's the definition of manifold? And how do you check if geometry is manifold or not?

henning
 
Old 10 October 2003   #2
It is geometry that can't be unfolded into a flat piece. Examples are two polygons next to each other, with normals facing in opposite directions, two planes that share a single vertex but no edge, and two polygons, with the edge extruded outward from the edge that both share (basically making a "T" shape out of 3 polygons).
 
Old 10 October 2003   #3
m
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Last edited by playmesumch00ns : 10 October 2003 at 09:08 AM.
 
Old 10 October 2003   #4
Manifold models are models where the volume is well defined.
They have the following properties:

Every edge belongs to two faces.
Every vertex is surrounded by one sequence of edges and faces.
Faces only intersect eachother in common edges en vertexes.
There is a material on only one side of a face

Another way of putting it, a manifold object is a shape that you can create in real life. non-manifold objects have qualities, where you have badly defined volumes in your shape, making it impossible to recreate the model exactly that way in real life.

Hope it helps..
 
Old 11 November 2003   #5
curiosity: a box without a face (5 square faces and a hole) is non-manifold?

i guess the answer would be the same as for a plane?


thanx
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Old 11 November 2003   #6
Yeah, thats non-manifold. The object contains no volume, because it isn't a closed space.
 
Old 11 November 2003   #7
I'm suspicious ...

I'm suspicious ...

That a lot of programs would not go through the rigor of trying to detect if a surface intersected itself in strange ways into order to qualify or disqualify something as a manifold.

In other words ... I bet with 9 or of 10 programs that want to operate only on manifolds, as least 9 would not care about how visually twisted the model is ... so long as the topology (which has nothing to do with the strictly visual) remains that of a manifold.

Just some thoughts. since we are talking about manifolds.
 
Old 11 November 2003   #8
Well, no they should check.

One of the constraints/properties of a manifold object is that faces should only intersect eachother in common edges or vertexes. So this is not only a topologic demand, but also a geometric demand. I don't know how most programs check for this, but there must be some fast check to satisfy this property.
 
Old 01 January 2006   #9
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