Comments on: Ratio of vertexes, edges and triangles in a Mesh The ratio in the article is actually exact for a toroidal mesh, and inexact for a spherical mesh (and for all meshes with Euler characteristic != 0). Above: 2V = T + 2 The 2 comes from the Euler characteristic of a sphere. In the limit, this is a V:T ratio of 2:1, but, for example, a tetrahedron has a V:T ratio of 1:1. The ratio in the article is actually exact for a toroidal mesh, and inexact for a spherical mesh (and for all meshes with Euler characteristic != 0).

Above:

2V = T + 2

The 2 comes from the Euler characteristic of a sphere. In the limit, this is a V:T ratio of 2:1, but, for example, a tetrahedron has a V:T ratio of 1:1.

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By: Luke Hutchinson/2011/06/15/ratio-of-vertexes-edges-and-triangles-in-a-mesh/#comment-5675 Luke Hutchinson Wed, 15 Jun 2011 14:46:23 +0000 This is a result that dates back to Euler's work on graph topology. As pointed out, the constant differs depending on the topology of the manifold. V - E + F = the Euler characteristic of the manifold. http://en.wikipedia.org/wiki/Euler_characteristic This is a result that dates back to Euler’s work on graph topology.

As pointed out, the constant differs depending on the topology of the manifold.

V – E + F = the Euler characteristic of the manifold. All this depends on the mesh topology. If the mesh has holes (like a torus), your calculations will no longer hold. All this depends on the mesh topology. If the mesh has holes (like a torus), your calculations will no longer hold.

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