Crate axiolid_minkowski

Minkowski sum and difference of planar-faced solids.

The convex case is the tractable one

The Minkowski sum of two convex polyhedra is the convex hull of their pairwise vertex sums. That is exact, needs no boolean solver, and is what minkowski_sum computes.

Non-convex operands have no such shortcut. The standard construction decomposes both into convex parts, sums every pair, and unions the results — which is why minkowski_sum_with takes a boolean provider. Cost is the product of the part counts, so it is budgeted rather than left to run away.

Difference is not the sum run backwards

A ⊖ B is the set of translations that keep B inside A: { x : x + B ⊆ A }. It is an erosion, not a hull of pairwise differences, and computing it as one is a common and silent error.

When A is convex the containment test reduces to the vertices of B, because a convex A containing every x + vᵢ contains their hull and therefore all of x + B. That gives

A ⊖ B = ⋂ᵢ (A − vᵢ)   over the vertices vᵢ of B

which is exact and computable with intersections alone. For non-convex A the reduction fails — A can contain each translated vertex while missing the material between them — so minkowski_difference_with refuses a non-convex subject by name rather than returning a result that is too large.

Curved operands

Both operations are defined here for planar-faced solids. A curved operand is refused, matching the rest of the offset work: the sum of two curved solids is not a polyhedron and approximating it silently would misreport what the result is.

Structs

MinkowskiEvidence

What was done to produce a Minkowski result.

MinkowskiOutcome

A Minkowski result and what it took to produce.

Enums

MinkowskiError

Why a Minkowski operation could not be performed.

Functions

minkowski_difference_with

Minkowski difference: the translations of tool that stay inside subject.

minkowski_sum

Minkowski sum of two CONVEX planar-faced solids.

minkowski_sum_with

Minkowski sum of two planar-faced solids, convex or not.