Coordinate layouts and dimensions
Meaning and scope
A coordinate layout identifies the components, or ordinates, attached to a location. XY, XYZ, XYM and XYZM distinguish spatial ordinates from an optional measure. Knowing the number of components alone is insufficient: a three-value coordinate can describe either XYZ or XYM.
This page gives an informative explanation of the Simple Features and SQL/MM models cited below. It describes concepts independently of library APIs, database storage and serialization support.
Informative explanation
Coordinate layouts
| Layout | Ordered ordinates | Coordinate dimension | Spatial ordinates | Measure ordinates |
|---|---|---|---|---|
| XY | x, y | 2 | 2 | 0 |
| XYZ | x, y, z | 3 | 3 | 0 |
| XYM | x, y, m | 3 | 2 | 1 |
| XYZM | x, y, z, m | 4 | 3 | 1 |
Coordinate dimension here counts all ordinates in the layout, including M. Spatial dimension, when used to describe the coordinate space, counts the spatial ordinates: X and Y, plus Z when present. The measure column counts M separately. Thus XYZM has four coordinate components, not four spatial axes. These counts explain the layouts; they are not a statement of support by every format, geometry type or implementation.
X and Y locate a point in its reference system. Z is an additional spatial ordinate, often elevation or altitude, but its meaning depends on that reference system. The letters alone do not establish axis direction, order or units; see the CRS section.
M associates a measurement with a location. For example, a road survey might attach distance along a route to each sampled point. The application defines what that measure means and its units; M is neither an elevation nor necessarily time. Its values need not increase along a path. The conceptual distinction between Z and M follows OGC 06-103r4, 6.1.2.1 and 6.1.2.5, and the SQL/MM draft, 4.2.1.
Coordinate dimension and topological dimension
Topological dimension describes the geometry's intrinsic shape rather than its coordinate layout: a Point is zero-dimensional, a Curve one-dimensional, and a Surface two-dimensional in the models considered here. Adding Z or M does not turn a point into a curve or a surface into a solid.
| Informative example | Layout | Coordinate dimension | Spatial ordinates | Topological dimension |
|---|---|---|---|---|
| Survey marker with elevation | XYZ | 3 | 3 | 0 |
| Road path with route distances | XYM | 3 | 2 | 1 |
| Terrain surface with measurements | XYZM | 4 | 3 | 2 |
The phrase “three-dimensional geometry” can therefore be ambiguous. Specify whether it means a Z-bearing coordinate layout, an intrinsic dimension, or an operation that actually uses Z. The geometry model explains intrinsic dimensions and collection behavior.
Reading and using a layout
The tuples below are informative examples, not format syntax or CRS declarations. Identical values in the third position have different meanings depending on the declared layout.
XY: (10, 20) x=10, y=20
XYZ: (10, 20, 30) x=10, y=20, z=30
XYM: (10, 20, 30) x=10, y=20, m=30
XYZM: (10, 20, 30, 5) x=10, y=20, z=30, m=5
Retain the layout when interpreting or exchanging coordinates. Counting three values cannot distinguish a spatial height from a measure. Format declarations and dimensional markers belong to the Formats section and the verified representation reference.
Storage and calculation are separate capabilities. In Simple Features 1.2.1,
map-geometry operations use the horizontal projection and ignore Z and M
(6.1.2.5). The SQL/MM draft separately identifies ordinary and ST_3D*
operations (4.2.1.1). Neither storing Z nor accepting four ordinates guarantees
that a particular operation calculates in three-dimensional space or uses M.
Check the operation's specification and implementation scope.
Normative foundations
- OGC 06-103r4, Simple Feature Access 1.2.1: 6.1.2.1 identifies the four coordinate layouts and the meanings of Z and M; 6.1.2.2 distinguishes intrinsic geometry dimension; 6.1.2.5 explains measures and map-geometry operations. See the dimensions requirement record and official specification.
- ISO/IEC CD 13249-3:201x(E), 2009-01-16 Committee Draft: 4.2.1 defines coordinate layouts and Z/M meanings; 4.2.1.1 distinguishes dimension, coordinate dimension, Z presence, measured state and ordinary/3D operations. See the SQL/MM dimensions reference. These citations identify the project-held draft, not a final ISO edition; the standard page records the source and evidence limits.
These foundations are attributed separately. This explanation does not claim that all operations or representation rules of the two sources are equivalent.
Related implementations
The release-scoped Simple Features support record and SQL/MM support record identify verified LongitudeOne capabilities and limitations. The Spatial Core 1.x primitives guide owns the corresponding library usage details. Layout metadata alone does not establish geometry, serializer or spatial-operation conformance.
Database restrictions and extensions require platform-specific evidence; they do not redefine the coordinate concepts above. No DBMS support is assessed here.
Return to the Spatial concepts overview.