Crate axiolid_collide

Convex collision queries via the separating axis theorem.

What this answers, and what it deliberately does not

Two convex shapes are disjoint if and only if some axis exists on which their projections do not overlap. This crate finds such an axis, or proves none exists.

When the shapes are apart it also reports how far apart, because that is the question a rule check asks: not “do these collide” but “is there enough clearance”. The axiolid-inspect crate’s mesh clearance answers the same question for triangle soups; this answers it for convex shapes without building an index.

It does not report penetration depth. That is a deliberate refusal, consistent with axiolid-measure: a contact area and an interpenetration depth are different measurements, and collapsing them behind one number is how a caller ends up using the wrong one. Callers needing penetration depth for physics want EPA, which belongs in a physics engine rather than a certified geometry kernel.

Why SAT rather than GJK

For the shapes a model-checking rule actually has – boxes, extruded profiles, hulls with tens of vertices – SAT is direct, has no iteration count to tune, and its failure mode is a clean answer rather than a tolerance-dependent one. GJK wins on high vertex counts and on a generic support function; neither is the common case here, and published commercial model-checking geometry APIs ship convex hull and SAT-style tests without GJK/EPA at all.

Robustness

Projections are compared with an explicit tolerance rather than exactly. An axis derived from a cross product of two nearly parallel edges is numerically meaningless, so such axes are skipped instead of being allowed to report a spurious separation of ~1e-17.

Structs

Contact

The axis along which two shapes are furthest apart.

ConvexShape

A convex shape as its vertices and face normals.

Enums

SeparationResult

Outcome of a separating-axis query.

Functions

boxes_intersect

Whether two oriented boxes overlap.

contains_point

Whether a point lies inside or on a convex shape.

distance

Shortest distance between two convex shapes, or zero if they overlap.

intersects

Whether two convex shapes share any point.

separation

Find a separating axis between two convex shapes, or prove none exists.