Polygon triangulation code

Scripting C# & .NET
1

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#:

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:

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

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

Rune

3

That’s great. I’m about to start a similar project. Here a link I found earlier: http://www.codesuppository.blogspot.com/

Uses the ear clipping method, which is nice.

4

Sorry for the triple post, but the script is now up here:

Rune

5

Sorry, didn’t see your post at first. :slight_smile:

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

Great stuff, thanks for sharing this!

7

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

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. :slight_smile:

Rune

9

[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 :slight_smile:

10

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

11

I knew I saw that code earlier :wink:
http://www.flipcode.com/archives/Efficient_Polygon_Triangulation.shtml

12

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

877985–32809–$Triangulator.js (3.62 KB)

13

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

14

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

        return ((aCROSSbp > 0.0)  (bCROSScp > 0.0)  (cCROSSap > 0.0));

to

        return ((aCROSSbp >= 0.0)  (bCROSScp >= 0.0)  (cCROSSap >= 0.0));

Cheers and happy coding,

1274726–56952–$Triangulator.cs (3.7 KB)

15

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

–Eric

1 Like
16

You are right, I am still not done.

1 Like
17

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.Xd.X + d.Yd.Y;}

Thanks

18

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

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 GitHub - speps/LibTessDotNet: C# port of the famous GLU Tessellator - prebuilt binaries now available in "releases" tab

2 Likes
20

Thanks a lot for sharing it.
it’s very useful.