Bounding box contains check

Axis-aligned bounding box containment is a fundamental spatial predicate used in mapping, computer graphics, collision broad-phases, GIS tile hierarchies, and viewport culling. Given two rectangles whose sides are parallel to the coordinate axes, the question is whether the outer box completely encloses the inner one—not merely whether they overlap or share a corner. This bounding box contains check accepts eight finite edge bounds (minimum and maximum X and Y for the outer container and the inner candidate), validates that each box has min less than or equal to max on both axes, and then evaluates four closed inequalities: the outer left edge must sit at or left of the inner left edge, the outer right at or right of the inner right, and the same nesting on the bottom and top. Equal boxes count as containment under closed edges.

What AABB containment means and how the four edges are tested

An axis-aligned bounding box, often abbreviated AABB, is defined by a minimum and maximum coordinate on each axis. Full containment of an inner box by an outer box means every point of the inner rectangle also belongs to the outer rectangle. Because both shapes are products of intervals, that set inclusion reduces to interval nesting on each axis independently: the inner X-interval must lie inside the outer X-interval, and the inner Y-interval must lie inside the outer Y-interval.

If any one of those four checks fails, the outer box does not fully contain the inner box—even when the boxes still intersect in a partial overlap or share a boundary only on one side. Degenerate zero-width or zero-height boxes are allowed when min equals max; a point-like box is contained when that point lies on or inside the outer edges. Two identical boxes also satisfy containment, because every edge is equal and the closed inequalities remain true.

This capability does not model rotated rectangles, geodesic spherical polygons, or antimeridian wrapping; it is the classic Cartesian AABB predicate used as a fast broad-phase filter before more expensive geometric tests.

What you enter, what you get and invalid boxes

An inverted box where min is strictly greater than max is rejected rather than silently swapped, because swapping would change the intended geometry without the caller's knowledge. The summary field contains is true only when all four edge flags are true. The equal flag is true when the two boxes share identical edges.

A short message describes full containment, identical boxes, or lists the failing edges when nesting does not hold. Example: outer box from (0,0) to (10,10) and inner box from (2,3) to (5,7) yields contains true with all four edge flags true. Partial overlap or a box that sticks out on one side yields contains false and names the failing side.

Validation failures are not billed.

Where a bounding box contains check earns its keep

Map and tile servers use AABB containment to decide whether a feature bbox is fully inside a viewport, a parent tile, or a geofence rectangle before loading higher-resolution geometry. Game engines and physics engines run the same four-edge test as a cheap broad-phase filter before triangle-level collision. GIS pipelines compare annotation boxes to region extents when clipping exports or validating that a drawn region sits entirely within a licensed map sheet.

Computer-vision and document-layout tools nest detection boxes inside page or crop rectangles to filter false positives that spill outside the frame. Failed validation does not consume balance.