## Some Basic, Computational and Invented Geospatial Terms

The terms and acronyms defined below pertain to geoprocessing in general. Mostly they derive from computational geometry, computer science, geography, cartography and spatial analysis. While many of these terms are relatively common, they may be used in idiosyncratic ways. Others are technical terms drawn from rather restricted vocabularies within science and mathematics. Still others are unpedigreed appellations of recent provenence, some of which the author pleads guilty of having perpetrated. Amendments, corrections and reactions to these definitions are welcomed; please send contributions to dutton@spatial-effects.com.

Accuracy (n) The fidelity with which measurements represent the reality they purport to describe.

AID (ack) Attractor Identifier; a QTM ID at a certain level of detail that names the attractor containing a given QTM quadrant.

Arc (n) A linear primitive, consisting of two or more points in a sequence; a polyline.

Attractor (n) A nodal region that dominates neighboring cells in a tessellation.

Attribute (n) An identifiable property of or fact about a location or an object.

Basis Number (n) A tesseral digit from 1 to K, where K is the number of child cells of a basis shape.

Basis Shape (n) A geometric shape, either a polygon or a polyhedron, in which a tessellation is rooted.

Cell (n) A topological primitive; an areal subdivision of a tessellation.

Characteristic Point (n) A point on a polyline or along a continuous curve that has perceptual significance in human recognition of a shape.

Coordinate (n) An ordered n-tuple of numbers that denotes the position of a point within some manifold and metric space.

Data (pl. n) Compiled or encoded facts abstracting aspects of a reality of interest; see trivia.

Data Model (n) A conceptual organization of phenomena for the purposes of data abstraction.

Data Quality (n) The accuracy, consistency, completeness, lineage and currency of a set of measurements; often described asmetadata.

Data Structure (n) A specific organization of sets of data elements in a computer's memory.

DLG (ack) Digital Line Graph: A standard encoding format for vector-topological map data developed by The U.S. Geological Survey (USGS).

Dodecahedron (n) A regular Platonic polyhedron consisting of 20 vertices, connected by 30 edges to form 12 pentagonal faces.

Edge (n) A boundary between faces connecting vertices of a graph; a one-cell. ; a line defining part of a polygon.

Entity (n) An an identifiable portion or element of physical reality possessing attributes and relationships of interest for the purposes of abstracting data models.

Face (n) A region in a graph bounded by edges; a two-cell.

Facet (n) A cell in a tessellation; e.g. a quadrant of a spherical triangular quadtree.

Feature (n) A set of one or more primitives having locations and attributes, identified as a unique geographic object; (v) to display, advertise or otherwise focus attention on specific entities.

Field (n) A tessellation of a spatial attribute describing variation of a single-valued surface.

Forest (n) A set of trees, specifically of related tree data structures (binary trees, quadtrees, etc). QTM has a forest of eight adjacent quadtrees covering the planet.

Fractal (n) An n-dimensional geometric object or set that exhibits the properties of self-similarity and fractal dimensionality.

Fractal Dimension (n) A measure of geometric complexity of forms; a real number equal to or greater than a form's Euclidean dimensionality.

Fullerene (n) Carbon molecule having 60 atoms arranged in the form of a soccerball, or truncated icosahedron. Named for inventor, architect and geometrician R. Buckminster Fuller.

Genus (n) The topological dimension of a spatial primitive.

Geocode (n) An alphanumeric identifier for a point, place or location which uniquely identifies what and/or where it is.

Geodata (n) Contraction of geographic data; one or more files of digital information describing geographic phenomena.

Geodesic (n) The shortest distance between two points on a curved surface; (adj) polyhedral representation of spheroids.

Geodesy (n) The science of measuring and modeling the size and shape of planets.

Geographic (adj) Pertaining to the spatial properties of phenomena on the surface of the Earth.

Geography (n) The science of modeling where things are and why.

GIS (ack) Geographic Information System: A digital facility for storing, retrieving, manipulating and displaying spatial and aspatial facts, usually representing remotely-sensed images, maps and attributes of real-world phenomena.

Graph (n) The network of faces, edges and vertices (0-, 1- and 2-cells) defined by a set of points, lines and polygons.

Graticule (n) A regular ruling across a model surface; a standard reference mesh based on a grid oriented in a manifold.

Grid (n) A regularly arrayed constellation of points.

Heap (n) A data structure consisting of a contiguous list of variable-length objects plus a contiguous list of pointers to addresses where those objects are stored.

Hierarchy (n) A cascading tree or pyramid of objects or locations, subdividing either regularly or irregularly.

Icosahedron (n) A regular Platonic polyhedron consisting of 12vertices, connected by 30 edges to form 20 triangular faces.

Identifier (n) A number or a character string that (uniquely) names an object or location for general reference; may serve as a search key or geocode.

Line (n) A 1-dimensional geometric object that can be embedded in a planar manifold and which occupies no area; two or more points connected sequentially.

Linear Quadtree (n) A quadtree data structure that records identifiers and attributes of the leaf nodes of a quaternary hierarchy, usually as a pre-ordered list.

Locality (n) A specific, relatively small region of geographic space.

Location (n) A well-defined region of space that may be thought of as occupying a point and explicitly identified by name or geocode.

Location Code (n) See geocode.

Manhattan Metric (n) A linear mapping in the Cartesian plane in which distance between points is the sum of x and y distance. Also denoted as IR1 space.

Manifold (n) A model surface characterized by its topological genus.

Map Generalization (n) The selection and simplified representation of cartographic detail appropriate to the scale and/or purpose of a map.

Map Scale (n) The ratio of the extent of features on a map to the entities on the ground that correspond to them, expressed as 1:N, where N is termed the scale denominator. Scale need not be constant everywhere in a map.

MBT (ack) Minimum Bounding Triangle, e.g., the smallest QTM facet that contains a given data object, such as a primitive.

mel (ack) Mesh ELement; a polygonal cell in a mesh used for spatial filtering, such as a square, triangle or hexagon.

Mesh (n) A graticule formed by edges of a tessellation. (a set of one-cells )

Metadata (n) Information compiled to summarize properties or provenance of a dataset; pertinent information omitted from a dataset.

Model (n) A conceptual image, analog, or physical representation of phenomena; (v) to define the elements of a system and organize them into a cognitive structure.

Nodal Region (n) An area dominated a node in a network or mesh.

Node (n) A vertex in a mesh; a point in a network or a graph where lines terminate and meet.

Nonnull-cell (n) A cell in a tessellation having a nonzero basis number.

Null-cell (n) A cell in a tessellation having a basis number of zero.

Object (n) An abstraction of a physical entity which has an identifier, and may have attributes as well as a location in space and time. Objects can have membership in (be instances of) a class.

Object-primary (adj) An approach to geometric computation that explicitely models discrete phenomena rather than the continuous space they occupy; usually refers to vector and topological data models

Octahedron (n) A regular Platonic polyhedron consisting of 6 vertices, connected by 12 edges to form 8 triangular faces all with equal areas, angles and edge lengths.

Octant (n) A single facet of an octahedron, a spherical right triangle (one eighth of a planet).

One-cell (n) The topological role played by an edge in a graph.

Place (n) A locality that can be distinquished from all other separate, adjoining and overlapping ones.

Platonic Solids (n) The set of regular polyhedra having identical faces and angles; there are five: tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron.

Point (n) A 0-dimensional location in space; if connected by lines to other points, also called a vertex.

Polyhedron (n) A solid bounded by planes and defined by the vertices and edges where they intersect.

Polygon (n) A 2-dimensional geometric object that can be embedded in a plane manifold and which defines a closed region or multiple disjoint ones.

Polyline (n) A 1-dimensional geometric element that can be embedded in a plane manifold and which defines a curve using a finite sequence of vertices.

Precision (n) The degree of detail available for a measurement.

Primitive (n) An simple geometric or topological object; a component of a feature, such as a point, a polyline or a simple polygon.

Quadtree (n) A hierarchical data structure that keeps track of a quaternary division of space or objects.

Quaternary (adj) Divided into or pertaining to four parts or things.

Quincunx (n) Arrangement of a square into five parts or things.

QTM (ack) Quaternary Triangular Mesh: A hierarchical triangular grid in which each cell may divide into four similar ones.

QTM ID (abbr) Quaternary Triangular Mesh Identifier: A numeric name for a leaf node in the QTM region quadtree. It is a sequence of up to 29 quaternary digits preceded by an octant ID (forest ID) from 1 through 8.

Range Query (n) A request to a computer program for the identities of spatial objects that occupy a region, usually a rectangle.

Raster (n) A grid of points, usually rectangular, within which tessellar data is collected, stored or displayed; (adj) the type of data that scanning devices collect and display.

RDP (abbr) Ramer-Douglas-Peucker; a global cartographic line simplification algorithm independently discovered ca. 1972 by Urs Ramer and David Douglas and used in map generalization.

Region (n) An identifiable two-dimensional area on a plane or a planet, often represented by polygons. A region can be convex or not, and either simply- or multiply-connected.

Segment (n) Line segment: a straight line connecting two vertices; an edge component of a polyline, polygon or polyhedron.

Self-similarity (n) A quality of a geometric object that causes it to look like itself regardless of the scale of representation; part of the definition of a fractal.

Space (n) A mesh of locations embedded in a manifold.

Space-primary (adj) An approach to geometric computation that explicitely models space rather than objects it contains; usually refers to raster data models

Spatial Index (n) A computed quantity that identifies the location of spatial data items in computer memory, particularly on a mass storage device; a gazetteer.

Surface (n) A connected region or two-cell, such as a polygon, which may undulate in three dimensions and serve as a container for objects and attributes.

Tessellar (adj) Pertaining to properties of and operations on tessellations; a form of spatial addressing that substitutes location codes for coordinates, sometimes organized as a hierarchy.

Tessellation (n) A set of similar or dissimilar shapes that fit together to exhaustively fill space, usually in some regular way.

Two-cell (n) The topological role played by a face in a graph.

Topological (adj) Properties of objects and space , such as adjacency and connectedness, that remain invariant under continuous transformations.

Trivia (pl. n) Compiled facts abstracting aspects of a reality not of interest; see data.

Vector (n) A connection between two points in space; an edge in a graph; a direction and distance in space; (adj) the type of data that point-addressable devices collect and display.

Vertex (n; vertices pl.) A mathematical point that serves to bound two or more edges in a graph, locates an inflection point in a polyline, or defines a node in a tessellation.

Voronoi Diagram (n) A graph constructed in N dimensions describing the neighborhoods if a set of points, such that all points within any polygonal partition are closer to its seed point than to any other seed point.

Zero-cell (n) The topological role played by a vertex in a graph.

ZOT (ack) Zenithial OrthoTriangular; name of a projection mapping an octahedron to a square domain in Manhattan Metric.   Home

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