computer science

Minimum bounding rectangle

Minimum bounding rectangle is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Minimum bounding rectangle rather than just read about it. In short: In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents of a two-dimensional object (e.g. point, line, polygon) or set of objects within its x-y coordinate system; in other words min(x), max(x), min(y), max(y). The MBR is a 2-dimensional case of the minimum bounding box.

Key takeaways

Minimum bounding rectangle belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Minimum bounding rectangle to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Minimum bounding rectangle from memory before moving on to harder problems.

Reference excerpt

In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents of a two-dimensional object (e.g. point, line, polygon) or set of objects within its x-y coordinate system; in other words min(x), max(x), min(y), max(y). The MBR is a 2-dimensional case of the minimum bounding box. MBRs are frequently used as an indication of the general position of a geographic feature or dataset, for either display, first-approximation spatial query, or spatial indexing purposes. The degree to which an "overlapping rectangles" query based on MBRs will be satisfactory (in other words, produce a low number of "false positive" hits) will depend on the extent to which individual spatial objects occupy (fill) their associated MBR. If the MBR is full or nearly so (for example, a mapsheet aligned with axes of latitude and longitude will normally entirely fill its associated MBR in the same coordinate space), then the "overlapping rectangles" test will be entirely reliable for that and similar spatial objects. On the other hand, if the MBR describes a dataset consisting of a diagonal line, or a small number of disjunct points (patchy data), then most of the MBR will be empty and an "overlapping rectangles" test will produce a high number of false positives. One system that attempts to deal with this problem, particularly for patchy data, is c-squares.

MBRs are also an essential prerequisite for the R-tree method of spatial indexing.

As spatial metadata Owing to their simplicity of expression and ease of use for searching, MBRs (frequently as "bounding box" or "bounding coordinates") are also commonly included in relevant standards for geospatial metadata, i.e. metadata that describes spatial (geographic) objects; examples include DCMI Box as an extension to the Dublin Core metadata scheme, "Bounding Coordinates" in the (U.S.) FGDC metadata standard, and "Geographic Bounding Box" in the (2003–current) ISO 19115 Metadata Standard for geographic information (ISO/TC 211). It is also (as "boundingBox") an element in Geography Markup Language (GML), that is utilised by a range of Web Service specifications from the Open Geospatial Consortium (OGC). In the ISO 19107 Spatial Schema (ISO/TC 211), MBR appears as the datatype GM_Envelope that is returned by the envelope() operation on the root class GM_Object.

See also Bounding parallelogram C-squares Darboux integral Elongatedness Geographic information system Geospatial metadata Largest empty rectangle, also known as maximal empty rectangle Minimum bounding box R-tree Shapefile Spatial index Convex hull

References

External links Geospatial Methods website

Illustrations

Worked examples

Example 1 — a first encounter with Minimum bounding rectangle

Start with the simplest possible case. Write down what Minimum bounding rectangle claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Minimum bounding rectangle before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Minimum bounding rectangle ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Minimum bounding rectangle

In research: Minimum bounding rectangle appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Minimum bounding rectangle in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Minimum bounding rectangle is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cartography, Geometric algorithms, so understanding it makes those chapters shorter.
In everyday life: Look for Minimum bounding rectangle outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Minimum bounding rectangle in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Minimum bounding rectangle means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Minimum bounding rectangle out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Minimum bounding rectangle in simple terms?

Why does Minimum bounding rectangle matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Minimum bounding rectangle?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Minimum bounding rectangle.