I want to simulate a 2d linear wave equation on a circle ($\displaystyle\frac{\partial^2 z(x,y,t)}{\partial t^2}=v^2\cdot\left(\displaystyle\frac{\partial^2 z(x,y,t)}{\partial x^2}+\displaystyle\frac{\partial^2 z(x,y,t)}{\partial y^2}\right)$).

To have a more significant result, I decided to use a hexagonal pattern (each point has 6 closest points at equidistant distance) as shown here: http://upload.wikimedia.org/wikipedia/en/8/81/Uniform_polyhedron-63-t0.png where the white dots are discrete checkpoints who have describe the actual value of the wave at a certain time.

To solve the problem, I want to use central differences to calculate a new situation out of the previous 2 (in time). How can I convert the central differences (that use $x,y$ values , however you rotate the situation there is maximum one dimension that fits) intro the checpoints based on the hexagonal structure?

I suppose I have to interpolate the point of a square structure out of the hexagonal points, or are there better/faster ways?