# Tag Info

### How can one prove the duality of Voronoi and Delaunay?

The duality between Voronoi cells and vertices of the triangulation is pretty clear: each vertex of the Delaunay triangulation is a site in the Voronoi diagram which gets associated with its Voronoi ...
• 241
Accepted

### Relationship between number of nodes, elements and sides in a triangular 2D mesh

Yes there is a relationship, the Euler characteristic: For a 2-dimensional orientable manifold with boundaries embedded in $\mathbb{R}^3$, the Euler characteristic is $\chi = V - E + F = 2 - 2g - b$ ...
• 166
Accepted

### Is the marching triangles algorithm guaranteed to terminate?

According to the following paper, the algorithm creates cracks like you have (see figure 1 and surrounding discussion). Fournier, Marc. "Surface Reconstruction: An Improved Marching Triangle ...
• 3,143
Accepted

### How to remove triangles in a hollow hemisphere shape?

Rather than relying on a delaunay triangulation, you could consider making a structured mesh directly, as you know how you are constructing the points and the ...
• 1,008

### Delaunay triangulation for datasets with four or more co-circular points

You can use exact predicates to detect co-circular points, and use symbolic perturbation to consistently decide which triangles to generate. Regarding exact predicates: If your point coordinates ...
• 2,315

### How to remove triangles in a hollow hemisphere shape?

I agree with Mikael's suggestion to use a structured mesh if you can get away with it. But there is a more fundamental reason why the Delaunay function from matlab isn't doing what you want and I ...
• 10.3k
1 vote

### Can TETGEN generate triangulation of a 2D point set?

TetGen is specifically designed to perform 3-D meshes -> tetrahedralization. I do not see a reliable and direct way to use it explicitly as a 2-D mesher. It is well pointed out that Triangle has a "...
• 8,672
1 vote

### Iterating through a 3D triangle

To iterate over the triangle points you could follow this algorithm: find the longest edge and use it as direction for the inner loop, in the following it is assumed that the longest edge is (p1,p2) ...
• 111

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