Package-level declarations

The decision tier: predicates answering Boolean where the operator tier answers geometry — incidence (on), containment (contains, spelled in/!in), and region overlap (intersects). Every answer is rounded at the SCALE quantum.

Every predicate is closed — the boundary belongs to the shape:

so the three states partition exactly at the quantum and on implies inside (p on c implies p in c). intersects is closed on the same terms, giving on-implies-intersects — the derived families agree with on at the boundary by construction. The strict (open) interior is deliberately unnamed — negation spells it: p !in -c holds exactly when p is strictly inside c, because both orientations are closed and only the strict interior escapes the complement.

The on family

on tests whether a point lies on a shape's boundary.

Precision is not uniform across the pairings: the Line, Segment, and Polygon forms are all-linear and robust at the SCALE quantum; the Circle forms are quadratic, so the residual grows with the radius and a point near a large circle's boundary may fail the test. Callers wanting a "near" test need their own tolerance.

The contains family

contains decides containment, boundary included. It is a Kotlin operator fun, so the call-site spellings are the language's: point in circle reads inside-or-on, and point !in circle the strict outside — neither inside nor on, the boundary belonging to the shape. There are deliberately no inside/outside functions: one relation, one name, with in/!in as its syntax.

Every form is orientation-aware: an inside-out circle's interior is the unbounded region outside it, and an inside-out polygon — wound clockwise — contains the closed complement of its loop. The circle forms share on's quadratic precision caveat. Classic polygon containment follows the nonzero winding rule, so self-touching and self-crossing loops classify by winding; the inside-out reading is its complement, boundary included either way.

The intersects family

intersects tests region overlap — "not disjoint": two shapes intersect when they share at least one point, touching included. Polygon operands count as closed regions (interior plus boundary); segments and lines as their point sets. The predicate is symmetric, and cross-type pairings come in both operand orders.

A polygon operand is its oriented solid region: a classic polygon fills its loop, an inside-out one the closed complement. Two inside-out polygons always intersect — both solid regions are unbounded, and far enough out every direction belongs to both. The name is the DE-9IM sense of intersects — not DE-9IM overlaps, which would exclude containment and touching. The boolean answer is the whole product: the crossing geometry itself comes from meet.