  This is the first of a series of papers dedicated to unveil the mass
composition and dynamical structure of a sample of flattened early type
galaxies in the Coma cluster. We describe our modifications to the
Schwarzschild code of Richstone et al. (in preparation). Applying a Voronoi
tessellation in the surface of section we are able to assign accurate
phase-space volumes to individual orbits and to reconstruct the full
three-integral phase-space distribution function (DF) of any axisymmetric orbit
library. Two types of tests have been performed to check the accuracy with
which DFs can be represented by appropriate orbit libraries. First, by mapping
DFs of spherical gamma-models and flattened Plummer models on to the library we
show that the resulting line-of-sight velocity distributions and internal
velocity moments of the library match those directly derived from the DF to a
precision better than that of present day observational errors. Second, by
fitting libraries to the projected kinematics of the same DFs we show that the
distribution function reconstructed from the fitted library matches the input
DF to a rms of about 15 per cent over a region in phase-space covering 90 per
cent of the mass of the library. The achieved accuracy allows us to implement
effective entropy-based regularisation to fit real, noisy and spatially
incomplete data.
