Polygon triangulation code

Discussion in 'Scripting' started by runevision, Jul 26, 2009.

  1. runevision

    runevision

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    I'm doing some mesh generation for a spare time project, and I've come to a point where I really need to be able to triangulate any specified 2D polygon - i.e. split a 2D polygon (convex or not) into triangles so that I can use those to generate a mesh.

    I've looked a bit on what's already available on the Net, and I found these two projects written in C#:

    - http://www.codeproject.com/KB/recipes/cspolygontriangulation.aspx

    - http://www.codeproject.com/KB/recipes/Art_Gallery_Problem.aspx

    However, I've tested both, and they're both buggy, meaning that they produce incorrect results for many polygons, where some triangles are outside the polygon.

    There are much more promising projects with source code floating around, but unfortunately not in C#. For example:

    - http://www.codeproject.com/KB/recipes/hgrd.aspx

    - http://www.cs.unc.edu/~dm/CODE/GEM/chapter.html

    If anyone have done polygon triangulation in Unity before (or just in C#) I'd be very interested in the code for that.

    Rune
  2. runevision

    runevision

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    Well, I finally have an algorithm that actually works. I'll clean it up and post it.

    Rune
  3. jcarpay

    jcarpay

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  4. runevision

    runevision

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  5. runevision

    runevision

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    Sorry, didn't see your post at first. :)

    Yeah, the script I posted uses the ear clipping method too. It's not the most efficient method. I believe it's O(n * n) and there are more advanced methods that can do it in O(n log n) - but it gets the job done.

    Rune
  6. jcarpay

    jcarpay

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  7. MH

    MH

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    Hi Rune,

    Do you happen to have a code for Java Script?

    Also, what if the polygon is 3D with vertices having (x,y,z) values?! Does it really matter if the object is or is not in 3d. From what I understand the trinagles' corners attach to the vertices in the order they are added. Is this right?!

    I desparately need a working JS code, please.
    Thanks for your reponse, in advance.
  8. runevision

    runevision

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    No, I'm afraid not.

    A polygon is planar by definition. If you have points in 3d space that are not co-planar then it's not a polygon and the algorithm won't apply.

    For example, the algorithm needs to be able to test whether a certain point is on one side or the other side of a line defined by two other points. Such a test makes sense in 2d but not in 3d.

    If you have points in 3d space that are co-planar, you can convert them into 2d points, then use the algorithm on those, and then use the returned vertex indices on the original 3d points.

    I'm not sure what you mean. How the triangels are formed depend on the shape of the polygon.

    If you're desperate, it should be no problem to learn the small differences between C# and JavaScript to be able to translate the script yourself. :)

    Rune
  9. nicoptere

    nicoptere

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    [I know this thread is getting old... ]

    it works very well!
    a nice feature would be to have a first pass to decompose complex ( self intersecting ) polygons.

    thank you very much for sharing :)
  10. karl_

    karl_

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    This code was very helpful in helping me get a grip on triangulation. Thanks a ton for sharing this.
  11. adven

    adven

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  12. Demonwhisperer

    Demonwhisperer

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    Hi Guys. I thought I'd post a version of this triangulation code I translated into javascript for anyone who needs it.

    You just need to create a Triangulator object like this:

    var tr:Triangulator = new Triangulator();
    tr.initTriangulator(verts2d);
    var triangles:int[] = tr.Triangulate();

    and then assign the triangles array to mesh.triangles of your desired mesh object.

    Hope somebody finds it useful.
    Enjoy

    Paul

    Attached Files:

  13. mcadesigns

    mcadesigns

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    I managed to convert to code to display the 2D shape in 3D world if that's what you mean.
  14. Sjiggle

    Sjiggle

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    I just wanted to share the following code. It allows both 2d and 3d points to be added to it. It's not the fastest method, I am sure there are improvements possible. Dear runevision, do you have any improvements ready?

    btw it's C#.

    Adding holes to the ear clipping is not as hard as it seems. If your edge finding tool is good enough, you will be able to make a difference between CCW and CW edges. Then sort these edges on their bounding box size (big to small) and cut a non visible line from the closest point of the inside to the outside edge (connecting the edges as a line). Then it's just a matter of triangulating.

    The version I am posting only tests if a point is inside a triangle, not on a triangle. If this is a problem, change

    Code (csharp):
    1.  
    2.         return ((aCROSSbp > 0.0)  (bCROSScp > 0.0)  (cCROSSap > 0.0));
    to

    Code (csharp):
    1.  
    2.         return ((aCROSSbp >= 0.0)  (bCROSScp >= 0.0)  (cCROSSap >= 0.0));
    Cheers and happy coding,

    View attachment $Triangulator.cs
  15. Eric5h5

    Eric5h5

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    Actually it is; I've done this and there are a lot of edge cases that aren't immediately obvious.

    --Eric
  16. Sjiggle

    Sjiggle

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    You are right, I am still not done.
  17. Mark Duffill

    Mark Duffill

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    Hi, I've fixed an issue where if you have degenerates (triangle with two or more points the same) it would fail to triangulate.

    To fix this inside Snip where it does:

    if (Mathf.Epsilon > (((B.x - A.x) * (C.y - A.y)) - ((B.y - A.y) * (C.x - A.x))))
    return false;

    I added:

    if (Mathf.Epsilon > (((B.x - A.x) * (C.y - A.y)) - ((B.y - A.y) * (C.x - A.x)))
    (A.SqDist(B) > SmallEpsilon A.SqDist(C) > SmallEpsilon B.SqDist(C) > SmallEpsilon)
    )
    return false;

    Where SmallEpsilon = 0.1 // you may want to tune this
    and SqDist = {var d = A-B; return d.X*d.X + d.Y*d.Y;}

    Thanks
  18. Lumen Digital

    Lumen Digital

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    Hi Mark

    That was a useful addition - here it is again in a directly applicable format...

    float smallEpsilon = 0.1f;
    if ( Mathf.Epsilon > (((B.x - A.x) * (C.y - A.y)) - ((B.y - A.y) * (C.x - A.x)))
    Vector2.SqrMagnitude(A-B) > smallEpsilon
    Vector2.SqrMagnitude(A-C) > smallEpsilon
    Vector2.SqrMagnitude(B-C) > smallEpsilon)
    return false;
  19. remigillig

    remigillig

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    For those visiting this thread later (like I just did), I made a C# port of the original SGI tesselator (which does 2D polygon decomposition/triangulation). It behaves quite nicely and is quite fast. You can find it at https://github.com/speps/LibTessDotNet
  20. MajorBulldozer

    MajorBulldozer

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    Thanks a lot for sharing it.
    it's very useful.
    Last edited: Aug 3, 2014
  21. RobAtWestpierstudio

    RobAtWestpierstudio

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    Hi. This project doesn't build out of the box: "Type or namespace 'Poly2Tri' does not exist in the current context". I don't see any external dependencies mentioned in your readme. Please advise!

    -Rob.