  We present a fast algorithm for generating Laguerre diagrams with cells of
given volumes, which can be used for creating RVEs of polycrystalline materials
for computational homogenisation, or for fitting Laguerre diagrams to EBSD or
XRD measurements of metals. Given a list of desired cell volumes, we solve a
convex optimisation problem to find a Laguerre diagram with cells of these
volumes, up to any prescribed tolerance. The algorithm is built on tools from
computational geometry and optimal transport theory which, as far as we are
aware, have not been applied to microstructure modelling before. We illustrate
the speed and accuracy of the algorithm by generating RVEs with user-defined
volume distributions with up to 20,000 grains in 3D. We can achieve volume
percentage errors of less than 1% in the order of minutes on a standard desktop
PC. We also give examples of polydisperse microstructures with bands, clusters
and size gradients, and of fitting a Laguerre diagram to 3D EBSD measurements
of an IF steel.
