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December 2nd, 2015, 05:29 AM   #1
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mesh conectivity using directed acyclic graph & mesh approx surface using conectivity

Hi there! I'm new here and I'm not from the field of math/computer science. However I always get involved in topics related to it. Please guys, if what I ask is trivial be patient with me

I'm building up an algorithm to construct a mesh approximating a given surface. I guess there are many algorithms out there for this. However, in my case I need this mesh to have a special connectivity. This connectivity emerges when I define a sequence of nodes in which every node may be connected by edges to the next nodes of the sequence but never to the previous ones. I have done a bit of research and in order to construct this connectivity I thought of using a directed acyclic graph since this allows me to construct the sequence of nodes I need. I later wish to construct a mesh approximating a given surface using the defined connectivity. Questions:

1) Can a mesh be still called "mesh" if it has no faces, only edges and vertices?
2) Does it make sense to use the directed acyclic graph for definning the connectivity of a geometric mesh? Is it common to do this? Any reference?
3) Are there well-known methods to construct directed acyclic graphs?
4) Can I construct the mesh approximating a given surface using a defined connectivity? Any well-known method for this? How in simple terms this process works? mapping? Can I do it if the graph is directed or should I first turn the graph into an undirected one? I get confused in the jump from connectivity graph to geometric mesh...

I hope the questions 1 and 2 are trivial and the methods I need for 3 and 4 are pretty standard.

Cheers, and thanks guys for your time!

Last edited by boolean; December 2nd, 2015 at 05:53 AM.
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March 17th, 2016, 10:15 PM   #2
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It looks like you are trying to solve a very specific problem, so you may need an advice from specialists who have been involved in that area of research for many years. It might be easier to obtain an already fully working, rigorously tested product, and then to adapt to your needs. As a suggestion, you may want to have a look here (the examples provided may have similarity to your types of geometries):

QUAD-SURFACE: Quadrilateral mesh generation for surfaces
Quadrilateral mesh of jet engine nozzle
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March 30th, 2016, 10:14 AM   #3
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Hello boolean,

I am not an expert.

I looked up on the web "connectivity graph", it is saying that "In a connected graph, there are no unreachable vertices".

So right away it is called a connected graph. That is important to know.

That means that each of the faces are connected to each other.



Some additional web research yields this page:
here

That page recommends wikipedia's page on "reachability" which should answer all of your questions at once since it deals with "reachability in a directed graph setting".

https://en.wikipedia.org/wiki/Reachability

Thanks,
GreenBeast
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1mesh, 2mesh, acyclic, approximate, connectivity, directed, directed acyclic graph, graph, mes, mesh, surface



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