## Weighted triangulation

Recently we have found a way to allow non-circumcentric well-centered grid. The idea is based on a vertex weight that shift the circumcenter towards the barycenter. There is a prove of concept available in the `examples/`

directory.

What needs to be implemented is a way of assigning new coordinates to the cached circumcenters and to update the cached dual volumes. Also, there must be found a way to implement the shift of the circumcenter

`c* = c^old - 1/2 * grad(w)`

with `grad(w)`

constant on the element, and `grad`

the surface gradient in the tangent plane of the entity.

There is an explicit formula for an edge `e_ij = (x_i, x_j)`

:

`c*_ij = x_i + (|e_ij|^2 + w_i - w_j) / (2 |e_ij|^2) * e_ij`

Additionally we need a test for well-centeredness of a weighted triangulation and a local weight calculation (maybe based on a gauss-seidel relaxation of a laplace-beltrami equation, see "*Weighted Triangulations for Geometry Processing*" (de Geos, F. and Memari, P. and Mullen, P. and Desbrun, M.)