  Characterizing microstructure-material-property relations calls for software
tools which extract point-cloud- and continuum-scale-based representations of
microstructural objects. Application examples include atom probe, electron, and
computational microscopy experiments. Mapping between atomic- and
continuum-scale representations of microstructural objects results often in
representations which are sensitive to parameterization; however assessing this
sensitivity is a tedious task in practice.
  Here, we show how combining methods from computational geometry, collision
analyses, and graph analytics yield software tools for automated analyses of
point cloud data for reconstruction of three-dimensional objects,
characterization of composition profiles, and extraction of multi-parameter
correlations via evaluating graph-based relations between sets of meshed
objects. Implemented for point clouds with mark data, we discuss use cases in
atom probe microscopy that focus on interfaces, precipitates, and
coprecipitation phenomena observed in different alloys. The methods are
expandable for spatio-temporal analyses of grain fragmentation, crystal growth,
or precipitation.
