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Find mappings between two surface meshes (for morphing)

  1. Nov 19, 2011 #1
    I want to morph two surface meshes made from triangles and quadrilaterals.

    They are already "compatible" so that one can be converted to the other simply by changing the coordinates of the vertices. No vertices, gaps, edges, etc. are created or destroyed.
    Not sure of the terminology. I think that means they have some or all of these properties:
    - Homeomorphic
    - Topologically equivalent
    - Combinatorially equivalent
    - The same in every way except the (x,y,z) coordinates and the numbering/labeling of the vertices/elements.

    I want to find all the possible ways the vertices could be numbered so the numbers match on both meshes. For example the circular mesh in the picture would have 6 ways to number the vertices 1,2,3,.. so they match the triangular mesh.

    [PLAIN]http://dl.dropbox.com/u/21857463/meshes.png [Broken]
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Nov 19, 2011 #2

    chiro

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    Last edited by a moderator: May 5, 2017
  4. Nov 19, 2011 #3
    Thanks chiro

    However, interpolation isn't my problem. I intend to simply use linear interpolation despite its problems.

    It's the stage before interpolation that I'm stuck on. How can I find the pairs of vertices to interpolate between? In my example there are 6 possible sets of corresponding pairs. If I know all of them, then I can choose any one and produce some sort of result.
     
  5. Nov 19, 2011 #4

    chiro

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    You can use interpolation schemes that interpolate between all sets of points if that is what you are asking.

    Just use a standard scheme and use those as your control points for the scheme.

    Is this what you want to do? Do you want to find a way to morph between images in some way that looks good?
     
    Last edited: Nov 19, 2011
  6. Nov 19, 2011 #5
    No. I don't want to interpolate. Actually I already have linear interpolation working fine.

    I want to find out which points to interpolate between. Most sets of pairs of points will produce a random tangle. I want to find, for example only those 6 sets shown in the picture.

    Currently I manually number the vertices. And I carefully make sure that both meshes have identical vertex numberings. That's not very convenient. I'd prefer the computer to find the possible numberings itself and then the user just chooses a suitable one from a limited selection of correct ones.
     
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