1. A non-transitory computer-readable storage medium comprising software that can be executed on a processor to symmetrize a modeled physical object by causing the processor to: identify a plurality of clusters, each comprising a plurality of symmetric point pairs that are each derived from a plurality of sampled surface points of the modeled physical object; calculate and apply each of a first plurality of displacement value pairs to corresponding sample positions of each of the plurality of symmetric point pairs within at least one cluster of the plurality of clusters, wherein the symmetry of the at least one cluster is increased; calculate a second plurality of displacement value pairs and contract the at least one cluster using the second plurality of displacement value pairs; merge two or more clusters of the plurality of clusters within the transformation space; and present a graphical representation of the symmetrized modeled physical object to a user.