Triangulate a quad mesh in C#

How to take a mesh of quad faces and return a mesh with triangle faces.

The principle of the algorithm is to look at each quad and split them into two triangles. It chooses the split by the shortest diagonal across the quad.

The code is written in C# for Rhino/Grasshopper, using the Rhino mesh structure. However, it can be easily adapted to any mesh application.

  public Mesh Triangulate(Mesh x)
    int facecount = x.Faces.Count;
    for (int i = 0; i < facecount; i++)
      var mf = x.Faces[i];
        double dist1 = x.Vertices[mf.A].DistanceTo(x.Vertices[mf.C]);
        double dist2 = x.Vertices[mf.B].DistanceTo(x.Vertices[mf.D]);
        if (dist1 > dist2)
          x.Faces.AddFace(mf.A, mf.B, mf.D);
          x.Faces.AddFace(mf.B, mf.C, mf.D);
          x.Faces.AddFace(mf.A, mf.B, mf.C);
          x.Faces.AddFace(mf.A, mf.C, mf.D);

    var newfaces = new List<MeshFace>();
    foreach (var mf in x.Faces)
      if(mf.IsTriangle) newfaces.Add(mf);

    return x;

Before and after:

triangulate mesh


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