  Partitionings (or segmentations) divide a given domain into disjoint
connected regions whose union forms again the entire domain. Multi-dimensional
partitionings occur, for example, when analyzing parameter spaces of simulation
models, where each segment of the partitioning represents a region of similar
model behavior. Having computed a partitioning, one is commonly interested in
understanding how large the segments are and which segments lie next to each
other. While visual representations of 2D domain partitionings that reveal
sizes and neighborhoods are straightforward, this is no longer the case when
considering multi-dimensional domains of three or more dimensions. We propose
an algorithm for computing 2D embeddings of multi-dimensional partitionings.
The embedding shall have the following properties: It shall maintain the
topology of the partitioning and optimize the area sizes and joint boundary
lengths of the embedded segments to match the respective sizes and lengths in
the multi-dimensional domain. We demonstrate the effectiveness of our approach
by applying it to different use cases, including the visual exploration of 3D
spatial domain segmentations and multi-dimensional parameter space
partitionings of simulation ensembles. We numerically evaluate our algorithm
with respect to how well sizes and lengths are preserved depending on the
dimensionality of the domain and the number of segments.
