mathematics

Well-known text representation of geometry

Well-known text representation of geometry is a mathematics 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 Well-known text representation of geometry rather than just read about it. In short: Well-known text (WKT) is a text markup language for representing vector geometry objects. A binary equivalent, known as well-known binary (WKB), is used to transfer and store the same information in a more compact form convenient for computer processing but that is not human-readable.

Key takeaways

Well-known text representation of geometry belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Well-known text representation of geometry to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Well-known text representation of geometry from memory before moving on to harder problems.

Reference excerpt

Well-known text (WKT) is a text markup language for representing vector geometry objects. A binary equivalent, known as well-known binary (WKB), is used to transfer and store the same information in a more compact form convenient for computer processing but that is not human-readable. The formats were originally defined by the Open Geospatial Consortium (OGC) and described in their Simple Feature Access. The current standard definition is in the ISO/IEC 13249-3:2016 standard.

Geometric objects WKT can represent the following distinct geometric objects:

Point, MultiPoint LineString, MultiLineString Polygon, MultiPolygon, Triangle PolyhedralSurface TIN (Triangulated irregular network) GeometryCollection Coordinates for geometries may be 2D (x, y), 3D (x, y, z), 4D (x, y, z, m) with an m value that is part of a linear referencing system or 2D with an m value (x, y, m). Three-dimensional geometries are designated by a "Z" after the geometry type and geometries with a linear referencing system have an "M" after the geometry type. Empty geometries that contain no coordinates can be specified by using the symbol EMPTY after the type name. WKT geometries are used throughout OGC specifications and are present in applications that implement these specifications. For example, PostGIS contains functions that can convert geometries to and from a WKT representation, making them human readable. The OGC standard definition requires a polygon to be topologically closed. It also states that if the exterior linear ring of a polygon is defined in a counterclockwise direction, then it will be seen from the "top". Any interior linear rings should be defined in opposite fashion compared to the exterior ring, in this case, clockwise.

The following are some other examples of geometric WKT strings: (Note: Each item below is an individual geometry.)

Well-known binary Well-known binary (WKB) representations are typically shown in hexadecimal strings. The first byte indicates the byte order for the data:

0x00 : big endian 0x01 : little endian The next 4 bytes are a 32-bit unsigned integer for the geometry type, as described below:

Each data type has a unique data structure, such as the number of points or linear rings, followed by coordinates in 64-bit double numbers. For example, the geometry POINT(2.0 4.0) is represented as: 000000000140000000000000004010000000000000, where:

1-byte integer 00 or 0: big endian 4-byte integer 00000001 or 1: POINT (2D) 8-byte float 4000000000000000 or 2.0: x-coordinate 8-byte float 4010000000000000 or 4.0: y-coordinate

Format variations EWKT and EWKB – Extended Well-Known Text/Binary A PostGIS-specific format that includes the spatial reference system identifier (SRID) and up to 4 ordinate values (XYZM). For example: SRID=4326;POINT(-44.3 60.1) to locate a longitude/latitude coordinate using the WGS 84 reference coordinate system. It also supports circular curves, following elements named (but not fully defined) within the original WKT: CircularString, CompoundCurve, CurvePolygon and CompoundSurface. AGF Text – Autodesk Geometry Format An extension to OGC's Standard (at the time), to include curved elements; most notably used in MapGuide.

See also Simple Features Geography Markup Language Well-known text representation of coordinate reference systems

References

External links Simple Feature Access Specification ISO Spatial standard (there is a charge for this) BNF Notation of WKT Archived 2023-01-03 at the Wayback Machine EBNF Notation of WKT Online conversion between geometry objects representations Archived 2019-04-26 at the Wayback Machine

Illustrations

Worked examples

Example 1 — a first encounter with Well-known text representation of geometry

Start with the simplest possible case. Write down what Well-known text representation of geometry claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Well-known text representation of geometry 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 Well-known text representation of geometry 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 Well-known text representation of geometry

In research: Well-known text representation of geometry appears in mathematics 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 Well-known text representation of geometry 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: Well-known text representation of geometry is common in secondary-school and first-year university syllabi. It links to neighbouring topics GIS file formats, Markup languages, so understanding it makes those chapters shorter.
In everyday life: Look for Well-known text representation of geometry 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 Well-known text representation of geometry in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Well-known text representation of geometry 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 Well-known text representation of geometry out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Well-known text representation of geometry in simple terms?

Why does Well-known text representation of geometry matter?

Because it connects several mathematics 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 Well-known text representation of geometry?

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 Well-known text representation of geometry.