Minimum bounding box
the box or hyperrectangle of minimal dimensions that contains the set of interest
In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set S in N dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie. When other kinds of measure are used, the minimum box is usually called accordingly, e.g., "minimum-perimeter bounding box".
The minimum bounding box of a point set is the same as the minimum bounding box of its convex hull, a fact which may be used heuristically to speed up computation.
In the two-dimensional case it is called the minimum bounding rectangle.
Axis-aligned minimum bounding box
The axis-aligned minimum bounding box (or AABB) for a given point set is its minimum bounding box subject to the constraint that the edges of the box are parallel to the (Cartesian) coordinate axes. It is the Cartesian product of N intervals each of which is defined by the minimal and maximal value of the corresponding coordinate for the points in S.
Axis-aligned minimal bounding boxes are used as an approximate location of an object in question and as a very simple descriptor of its shape. For example, in computational geometry and its applications when it is required to find intersections in the set of objects, the initial check is the intersections between their MBBs. Since it is usually a much less expensive operation than the check of the actual intersection (because it only requires comparisons of coordinates), it allows quickly excluding checks of the pairs that are far apart.
Arbitrarily oriented minimum bounding box
The arbitrarily oriented minimum bounding box is the minimum bounding box, calculated subject to no constraints as to the orientation of the result. Minimum bounding box algorithms based on the rotating calipers method can be used to find the minimum-area or minimum-perimeter bounding box of a two-dimensional convex polygon in linear time, and of a three-dimensional point set in the time it takes to construct its convex hull followed by a linear-time computation.
The public source identifies “Minimum bounding box” as the box or hyperrectangle of minimal dimensions that contains the set of interest. This brief keeps that definition visible, then builds a research path around Minimum, bounding and hyperrectangle.
Why this record matters
A short description can identify a subject without explaining its stakes. For “Minimum bounding box”, the useful work is to connect “the box or hyperrectangle of minimal dimensions that contains the set of interest” to the records capable of establishing context and consequence.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Oct 7, 2024. The linked authority identifier is Q6865426. None of the 0 selected statements returned an explicit reference.
A concise general-reference account can conceal disagreements about scope, terminology or the weight assigned to individual sources. The source lead contains qualifying language; that uncertainty should survive quotation, summary and reuse. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Minimum bounding box”, its source revision and the description used here.
- Expand the search: follow Minimum bounding box primary sources, Minimum bounding box archive and Minimum research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Minimum bounding box”?
- Which institution is responsible for the underlying evidence?
- What terminology or title could unlock a more precise catalogue search?
Search terms from this dossier
This entry incorporates text from “Minimum bounding box” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.