  Context. Analytical and numerical analysis of the SimpleX radiative transfer
algorithm, which features transport on a Delaunay triangulation. Aims. Verify
whether the SimpleX radiative transfer algorithm conforms to mathematical
expectations, to develop error analysis and present improvements upon earlier
versions of the code. Methods. Voronoi-Delaunay tessellation, classical Markov
theory. Results. Quantitative description of the error properties of the
SimpleX method. Numerical validation of the method and verification of the
analytical results. Improvements in accuracy and speed of the method.
Conclusions. It is possible to transport particles such as photons in a
physically correct manner with the SimpleX algorithm. This requires the use of
weighting schemes or the modification of the point process underlying the
transport grid. We have explored and applied several possibilities.
