Module exact_distance

Certified distance between the boundaries of two exact B-reps (#125, C18).

What is certified

boundary_distance returns an interval [lower, upper] that contains the true minimum distance between the two boundaries, and two points, one on each boundary, exactly upper apart. Both ends are guarantees, not estimates:

• upper is the distance between two points that lie on the boundaries: points on edges, or surface points at parameters the face’s domain is certified to contain (the crate-private Domain classifier).
• lower comes from bounding spheres that enclose every point of a patch of a face’s parameter domain, from Lipschitz bounds on the exact surface, with a margin for rounding. Patches are dropped only when certified to lie outside the face.

A rule that compares a distance with a limit asks boundary_clearance, which refines only until the interval clears the limit and otherwise says Clearance::Indeterminate – a value within rounding of the limit is never reported as a pass or a fail.

Method

Branch and bound over pairs of elements, one from each B-rep: face patches (a rectangle of a face’s parameters) and edge spans. The pair with the smallest lower bound is refined by splitting its larger element. Refinement stops when the smallest remaining lower bound is within the requested accuracy of the best upper bound, or the step budget runs out; either way the interval returned is sound.

Bounds are second order where the family allows: the range of d . x over a patch is exact for planes, cylinders, elliptical cylinders, cones, spheres and tori and for line, circle and ellipse edges, and d is taken along the line between centres and along each patch’s normal. A face patch whose normals cannot point at the other element is dropped from that pair (critical_possible): the closest pair of two separated boundaries is critical on each face it lies inside or lies on an edge, and edges are elements of their own.

Convergence

An isolated nearest pair (pole to pole, apex to sphere, a wall to a block face) closes to 1e-9 in well under a second. Where the nearest points form a whole line – two parallel columns – every slice along that line is a near-minimal pair and refinement slows; ask such cases for a looser accuracy, or use boundary_clearance, which stops as soon as the limit is cleared. The step budget is fixed; when it runs out the interval returned is still sound, only wider.

Scope

This is the distance between BOUNDARIES. Two solids that overlap measure the distance between their surfaces where they cross (zero), but a solid wholly inside another measures the gap between the two boundaries, not zero. Containment is a separate classification.

Structs

DistanceBounds

An interval certain to contain the distance between two boundaries.

Enums

Clearance

How a certified distance compares with a limit.

Functions

boundary_clearance

Refine the distance only until it clears limit.

boundary_distance

Distance between the boundaries of a and b, to within accuracy.