  Determining the masses of new physics particles appearing in decay chains is
an important and longstanding problem in high energy phenomenology. Recently it
has been shown that these mass measurements can be improved by utilizing the
boundary of the allowed region in the fully differentiable phase space in its
full dimensionality. Here we show that the practical challenge of identifying
this boundary can be solved using techniques based on the geometric properties
of the cells resulting from Voronoi tessellations of the relevant data. The
robust detection of such phase space boundaries in the data could also be used
to corroborate a new physics discovery based on a cut-and-count analysis.
