In geometry, the barycentric subdivision is a standard way of dividing an arbitrary convex polygon into triangles, a convex polyhedron into tetrahedra, or, in general, a convex polytope into simplices with the same dimension, by connecting the barycenters of their faces in a specific way.
The name is also used in topology for a similar operation on cell complexes. The result is topologically equivalent to that of the geometric operation, but the parts have arbitrary shape and size. This is an example of a finite subdivision rule.
Both operations have a number of applications in mathematics and in geometric modeling, especially whenever some function or shape needs to be approximated piecewise, e.g. by a spline.
Read more about Barycentric Subdivision: Barycentric Subdivision of A Simplex, Barycentric Subdivision of A Convex Polytope, Barycentric Subdivision in Topology, Applications, Repeated Barycentric Subdivision, Relative Barycentric Subdivision
Famous quotes containing the word subdivision:
“I have no doubt but that the misery of the lower classes will be found to abate whenever the Government assumes a freer aspect and the laws favor a subdivision of Property.”
—James Madison (1751–1836)