I had the same question and did not manage to find an API call for this.
Its hard to be 100% sure but I don't think it exists.
This [1] is perhaps of interest,
-jelle
[1] http://www.nathanieltroutman.net/content/calculating-minimum-volume-boun...
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how to get the oriented bounding box of TopoDS_Shape
how to get the oriented bounding box of TopoDS_Shape?not axis-aligned bounding boxes
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Please try GProp_PGProps and GProp_PrincipalProps to get the principal data.
Ding