NRR.BodySpace — convex-body hyperspace #
This aggregator re-exports the convex-body hyperspace API in dependency order.
Three body types are kept distinct:
NRR.Geometry.ConvexBody Planeis the solid planar body type: compact, convex, with nonempty interior. Solid bodies alone are not closed under Hausdorff degeneration.NRR.ConvexSubbody Kis the fixed-parent hyperspace of compact nonempty convex subsets of a solid bodyK. Its elements may be lower-dimensional, and the space is compact.NRR.BodySpace K Ais the closed lower-area subspace{C : ConvexSubbody K // A ≤ C.area}. WhenA > 0, every element is solid and admits the continuous bridgeBodySpace.toGeometryConvexBody.
The metric is Mathlib's Hausdorff distance on nonempty compact planar sets, transported through
ConvexSubbody.toNonemptyCompacts. The API includes continuity of area and Cauchy perimeter and
pointwise membership stability under Hausdorff convergence.