High Quality Content by WIKIPEDIA articles! In mathematics, Euler operators are a small set of functions to create polygon meshes. They are closed and sufficient on the set of meshes, and they are invertible. A "polygon mesh" can be thought of as a graph, with vertices, and with edges that connect these vertices. In addition to a graph, a mesh has also faces: Let the graph be drawn ("embedded") in a two-dimensional plane, in such a way that the edges do not cross (which is possible only if the graph is a planar graph). Then the contiguous 2D regions on either side of each edge are the faces of the mesh. The Euler operators are functions to manipulate meshes. They are very straightforward: Create a new vertex (in some face), connect vertices, split a face by inserting a diagonal, subdivide an edge by inserting a vertex. It is immediately clear that these operations are invertible.

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