Plotting data from a non regular concave grid

Hello,

I'd like to use Matlab to plot the data coming from a numerical simulation with an hydrodynamic code. I have the coordinates of the nodes of the mesh used for calculation, but the quantity I want to plot, the density of the fluid, is defined in the cell, not on the nodes. I want to have a plot which keeps the original mesh and draws a color for each cell corresponding to the density in the specified cell. Is it possible?

Unfortunately the original mesh is nonconvex, so that if I try to interpolate the data on a regular grid created by Matlab I get nontrivial values of the density even where the fluid is originally not present at all.

Thank you, Mattia