01 / Begin one dimension lower
Can one object cast several prescribed shadows? Each requested 2D silhouette carves a constraint volume from 3D space. Inspect their intersection, then see how another view can remove material needed by an earlier shadow.
Why go to higher dimensions?
Three orthogonal views are not a universal guarantee of compatibility. Extra views can expose conflicts between requested silhouettes. A fourth spatial coordinate adds freedom: a 3D projection can then hide an entire direction. It still cannot satisfy contradictory requirements on the same projection.
4→3Higher-dimensional inversionDesign 2D / 3D targets, reconstruct a 4D hull, measure what matches
Try this first · compare the object and its evidence
- Keep fixed shadows selected. Orbit the solid and compare the different wall silhouettes.
- Change one light or target shape. Inspect which parts of the solid survive the new constraint.
- Enable the third light, then try fixed shape to reverse the question: given an object, what shadows does it cast?
Silhouette constraints bound a compatible solid; they do not uniquely recover its hidden interior. This familiar 3D → 2D example introduces the loss of information before moving to higher-dimensional slices.
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