EN ISO 19123:2007

SLOVENSKI STANDARD
01-junij-2007
Geografske informacije – Shema za geometrijo podatkovnega sloja in funkcije (ISO
19123:2005)
Geographic information - Schema for coverage geometry and functions (ISO
19123:2005)
Geoinformation - Coverage Geometrie- und Funktionsschema (ISO 19123:2005)
Information géographique - Schéma de la géométrie et des fonctions de couverture (ISO
19123:2005)
Ta slovenski standard je istoveten z: EN ISO 19123:2007
ICS:
35.240.70 Uporabniške rešitve IT v IT applications in science
znanosti
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 19123
NORME EUROPÉENNE
EUROPÄISCHE NORM
March 2007
ICS 35.240.70
English Version
Geographic information - Schema for coverage geometry and
functions (ISO 19123:2005)
Information géographique - Schéma de la géométrie et des Geoinformation - Coverage Geometrie- und
fonctions de couverture (ISO 19123:2005) Funktionsschema (ISO 19123:2005)
This European Standard was approved by CEN on 25 February 2007.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the
official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
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Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2007 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 19123:2007: E
worldwide for CEN national Members.

Foreword
The text of ISO 19123:2005 has been prepared by Technical Committee ISO/TC 211
"Geographic information/Geomatics” of the International Organization for Standardization (ISO)
and has been taken over as EN ISO 19123:2007 by Technical Committee CEN/TC 287
"Geographic Information", the secretariat of which is held by NEN.

This European Standard shall be given the status of a national standard, either by publication of
an identical text or by endorsement, at the latest by September 2007, and conflicting national
standards shall be withdrawn at the latest by September 2007.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to implement this European Standard: Austria, Belgium,
Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United
Kingdom.
Endorsement notice
The text of ISO 19123:2005 has been approved by CEN as EN ISO 19123:2007 without any
modifications.
INTERNATIONAL ISO
STANDARD 19123
First edition
2005-08-15
Geographic information — Schema for
coverage geometry and functions
Information géographique — Schéma de la géométrie et des fonctions
de couverture
Reference number
ISO 19123:2005(E)
©
ISO 2005
ISO 19123:2005(E)
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ii © ISO 2005 – All rights reserved

ISO 19123:2005(E)
Contents Page
Foreword. v
Introduction . vi
1 Scope . 1
2 Conformance. 1
3 Normative references . 2
4 Terms, definitions, abbreviated terms and notation . 2
4.1 Terms and definitions. 2
4.2 Abbreviated terms . 7
4.3 Notation . 7
5 Fundamental characteristics of coverages.8
5.1 The context for coverages . 8
5.2 The coverage schema . 9
5.3 CV_Coverage. 10
5.4 CV_DomainObject. 13
5.5 CV_AttributeValues . 13
5.6 CV_CommonPointRule. 14
5.7 CV_DiscreteCoverage . 14
5.8 CV_GeometryValuePair. 15
5.9 CV_ContinuousCoverage . 16
5.10 CV_ValueObject . 17
5.11 CV_InterpolationMethod . 18
5.12 Subclasses of CV_ContinuousCoverage . 18
6 Discrete coverages. 18
6.1 Discrete coverage types . 18
6.2 CV_DiscretePointCoverage . 19
6.3 CV_PointValuePair. 20
6.4 CV_DiscreteGridPointCoverage. 20
6.5 CV_GridPointValuePair . 21
6.6 CV_DiscreteCurveCoverage . 21
6.7 CV_CurveValuePair . 22
6.8 CV_DiscreteSurfaceCoverage . 22
6.9 CV_SurfaceValuePair . 24
6.10 CV_DiscreteSolidCoverage . 24
6.11 CV_SolidValuePair. 24
7 Thiessen polygon coverage . 25
7.1 Thiessen polygon networks . 25
7.2 CV_ThiessenPolygonCoverage. 25
7.3 CV_ThiessenValuePolygon . 27
8 Quadrilateral grid coverages . 27
8.1 General. 27
8.2 Quadrilateral grid geometry. 27
8.3 CV_Grid. 30
8.4 CV_GridEnvelope. 31
8.5 CV_GridPoint. 31
8.6 CV_GridCoordinate. 32
8.7 CV_GridCell . 32
8.8 CV_Footprint . 33
8.9 CV_RectifiedGrid . 33
ISO 19123:2005(E)
8.10 CV_ReferenceableGrid . 34
8.11 CV_ContinousQuadrilateralGridCoverage . 35
8.12 CV_GridValueCell. 36
8.13 CV_GridPointValuePair . 36
8.14 CV_GridValuesMatrix. 37
8.15 CV_SequenceRule . 38
8.16 CV_SequenceType. 38
9 Hexagonal Grid Coverages . 39
9.1 General . 39
9.2 CV_HexagonalGridCoverage . 39
9.3 CV_GridValuesMatrix. 41
9.4 CV_ValueHexagon . 41
10 Triangulated irregular network (TIN) coverages. 41
10.1 General . 41
10.2 CV_TINCoverage . 43
10.3 CV_ValueTriangle. 43
11 Segmented curve coverages . 44
11.1 General . 44
11.2 CV_SegmentedCurveCoverage . 45
11.3 CV_ValueCurve . 45
11.4 CV_ValueSegment . 46
11.5 Evaluation . 46
Annex A (normative) Abstract test suite. 47
Annex B (informative) UML Notation . 51
Annex C (informative) Interpolation methods. 56
Annex D (informative) Sequential enumeration. 60
Bibliography . 65

iv © ISO 2005 – All rights reserved

ISO 19123:2005(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 19123 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics.
ISO 19123:2005(E)
Introduction
Geographic phenomena fall into two broad categories — discrete and continuous. Discrete phenomena are
recognizable objects that have relatively well-defined boundaries or spatial extent. Examples include buildings,
streams and measurement stations. Continuous phenomena vary over space and have no specific extent.
Examples include temperature, soil composition and elevation. A value or description of a continuous
phenomenon is only meaningful at a particular position in space (and possibly time). Temperature, for
example, takes on specific values only at defined locations, whether measured or interpolated from other
locations.
These concepts are not mutually exclusive. In fact, many components of the landscape may be viewed
alternatively as discrete or continuous. For example, a stream is a discrete entity, but its flow rate and water
quality index vary from one position to another. Similarly, a highway can be thought of as a feature or as a
collection of observations measuring accidents or traffic flow, and an agricultural field is both a spatial object
and a set of measurements of crop yield through time.
Historically, geographic information has been treated in terms of two fundamental types called vector data and
raster data.
“Vector data” deals with discrete phenomena, each of which is conceived of as a feature. The spatial
characteristics of a discrete real-world phenomenon are represented by a set of one or more geometric
primitives (points, curves, surfaces or solids). Other characteristics of the phenomenon are recorded as
feature attributes. Usually, a single feature is associated with a single set of attribute values. ISO 19107:2003
provides a schema for describing features in terms of geometric and topological primitives.
“Raster data”, on the other hand, deals with real-world phenomena that vary continuously over space. It
contains a set of values, each associated with one of the elements in a regular array of points or cells. It is
usually associated with a method for interpolating values at spatial positions between the points or within the
cells. Since this data structure is not the only one that can be used to represent phenomena that vary
continuously over space, this International Standard uses the term “coverage,” adopted from the Abstract
[1]
Specification of the Open GIS Consortium , to refer to any data representation that assigns values directly to
spatial position. A coverage is a function from a spatial, temporal or spatiotemporal domain to an attribute
range. A coverage associates a position within its domain to a record of values of defined data types.
In this International Standard, coverage is a subtype of feature. A coverage is a feature that has multiple
values for each attribute type, where each direct position within the geometric representation of the feature
has a single value for each attribute type.
Just as the concepts of discrete and continuous phenomena are not mutually exclusive, their representations
as discrete features or coverages are not mutually exclusive. The same phenomenon may be represented as
either a discrete feature or a coverage. A city may be viewed as a discrete feature that returns a single value
for each attribute, such as its name, area and total population. The city feature may also be represented as a
coverage that returns values such as population density, land value or air quality index for each position in the
city.
A coverage, moreover, can be derived from a collection of discrete features with common attributes, the
values of the coverage at each position being the values of the attributes of the feature located at that position.
Conversely, a collection of discrete features can be derived from a coverage, each discrete feature being
composed of a set of positions associated with specified attribute values.

vi © ISO 2005 – All rights reserved

INTERNATIONAL STANDARD ISO 19123:2005(E)

Geographic information — Schema for coverage geometry and
functions
1 Scope
This International Standard defines a conceptual schema for the spatial characteristics of coverages.
Coverages support mapping from a spatial, temporal or spatiotemporal domain to feature attribute values
where feature attribute types are common to all geographic positions within the domain. A coverage domain
consists of a collection of direct positions in a coordinate space that may be defined in terms of up to three
spatial dimensions as well as a temporal dimension. Examples of coverages include rasters, triangulated
irregular networks, point coverages and polygon coverages. Coverages are the prevailing data structures in a
number of application areas, such as remote sensing, meteorology and mapping of bathymetry, elevation, soil
and vegetation. This International Standard defines the relationship between the domain of a coverage and an
associated attribute range. The characteristics of the spatial domain are defined whereas the characteristics of
the attribute range are not part of this standard.
2 Conformance
This International Standard specifies interfaces for several types of coverage objects. In addition, it supports
the interchange of coverage data independently of those interfaces. Thus, it specifies two sets of conformance
classes: one for implementation of the interfaces, the other for the exchange of coverage data. Each set
includes one conformance class for each type of coverage specified in this International Standard (Table 1).
Table 1 — Conformance classes
Conformance class Subclause
Simple coverage interface A.1.1
Discrete coverage interface A.1.2
Thiessen polygon coverage interface A.1.3
Quadrilateral grid coverage interface A.1.4
Hexagonal grid coverage interface A.1.5
TIN coverage interface A.1.6
Segmented curve coverage interface A.1.7
Discrete coverage interchange A.2.1
Thiessen polygon coverage interchange A.2.2
Quadrilateral grid coverage interchange A.2.3
Hexagonal grid coverage interchange A.2.4
TIN coverage interchange A.2.5
Segmented curve coverage interchange A.2.6
ISO 19123:2005(E)
In general, the interface conformance classes require implementation of all attributes, associations and
operations of relevant classes. This set includes a single conformance class (A.2.1) that supports a simple
interface for evaluation of any coverage type, but exposes none of the internal structure of the coverage. The
remainder of the set are conformance classes that support interfaces to specific coverage types that expose
additional information about the internal structure of the coverage.
The interchange conformance classes require only implementation of the attributes and associations of the
relevant classes.
The Abstract Test Suite in Annex A shows the implementation requirements necessary to conform to this
International Standard. Table 1 lists the subclauses of the Abstract Test Suite that apply for each conformance
class.
3 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO/TS 19103:2005, Geographic information — Conceptual schema language
ISO 19107:2003, Geographic information — Spatial schema
ISO 19108:2002, Geographic information — Temporal schema
ISO 19109:2005, Geographic information — Rules for application schema
ISO 19111:2003, Geographic information — Spatial referencing by coordinates
ISO 19115:2003, Geographic information — Metadata
4 Terms, definitions, abbreviated terms and notation
4.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
4.1.1
continuous coverage
coverage that returns different values for the same feature attribute at different direct positions within a
single spatial object, temporal object or spatiotemporal object in its domain
NOTE Although the domain of a continuous coverage is ordinarily bounded in terms of its spatial and/or temporal
extent, it can be subdivided into an infinite number of direct positions.
4.1.2
convex hull
smallest convex set containing a given geometric object
[2]
[adapted from Dictionary of Computing:1996 ]
4.1.3
convex set
geometric set in which any direct position on the straight-line segment joining any two direct positions in
the geometric set is also contained in the geometric set
[2]
[Dictionary of Computing:1996 ]
2 © ISO 2005 – All rights reserved

ISO 19123:2005(E)
4.1.4
coordinate
one of a sequence of n numbers designating the position of a point in n-dimensional space
[ISO 19111:2003]
4.1.5
coordinate dimension
number of measurements or axes needed to describe a position in a coordinate system
[ISO 19107:2003]
4.1.6
coordinate reference system
coordinate system that is related to the real world by a datum
[ISO 19111:2003]
41.7
coverage
feature that acts as a function to return values from its range for any direct position within its spatial,
temporal or spatiotemporal domain
EXAMPLE Examples include a raster image, polygon overlay or digital elevation matrix.
NOTE In other words, a coverage is a feature that has multiple values for each attribute type, where each direct
position within the geometric representation of the feature has a single value for each attribute type.
4.1.8
coverage geometry
configuration of the domain of a coverage described in terms of coordinates
4.1.9
curve
1-dimensional geometric primitive, representing the continuous image of a line
[ISO 19107:2003]
NOTE The boundary of a curve is the set of points at either end of the curve.
4.1.10
Delaunay triangulation
network of triangles such that the circle passing through the vertices of any triangle does not contain, in its
interior, the vertex of any other triangle
4.1.11
direct position
position described by a single set of coordinates within a coordinate reference system
[ISO 19107:2003]
4.1.12
discrete coverage
coverage that returns the same feature attribute values for every direct position within any single spatial
object, temporal object or spatiotemporal object in its domain
NOTE The domain of a discrete coverage consists of a finite set of spatial, temporal, or spatiotemporal objects.
ISO 19123:2005(E)
4.1.13
domain
well-defined set
[ISO/TS 19103]
NOTE Domains are used to define the domain and range of operators and functions.
4.1.14
evaluation
〈coverage〉 determination of the values of a coverage at a direct position within the domain of the coverage
4.1.15
feature
0 abstraction of real world phenomena
[ISO 19101]
4.1.16
feature attribute
characteristic of a feature
[ISO 19101]
4.1.17
function
rule that associates each element from a domain (source or domain of the function) to a unique element in
another domain (target, co-domain or range)
[ISO 19107:2003]
4.1.18
geometric object
spatial object representing a geometric set
[ISO 19107:2003]
4.1.19
geometric primitive
geometric object representing a single, connected, homogeneous element of space
[ISO 19107:2003]
4.1.20
geometric set
set of direct positions
[ISO 19107:2003]
4.1.21
geometry value object
object composed of a set of geometry value pairs
4.1.22
geometry value pair
ordered pair composed of a spatial object, a temporal object or a spatiotemporal object and a record of
feature attribute values
4 © ISO 2005 – All rights reserved

ISO 19123:2005(E)
4.1.23
grid
network composed of two or more sets of curves in which the members of each set intersect the members of
the other sets in an algorithmic way
NOTE The curves partition a space into grid cells.
4.1.24
grid point
point located at the intersection of two or more curves in a grid
4.1.25
inverse evaluation
〈coverage〉 selection of a set of objects from the domain of a coverage based on the feature attribute values
associated with the objects
4.1.26
point
0-dimensional geometric primitive, representing a position
[ISO 19107:2003]
NOTE The boundary of a point is the empty set.
4.1.27
point coverage
coverage that has a domain composed of points
4.1.28
polygon coverage
coverage that has a domain composed of polygons
4.1.29
range
〈coverage〉 set of feature attribute values associated by a function with the elements of the domain of a
coverage
4.1.30
raster
usually rectangular pattern of parallel scanning lines forming or corresponding to the display on a cathode ray
tube
NOTE A raster is a type of grid.
4.1.31
record
finite, named collection of related items (objects or values)
[ISO 19107:2003]
NOTE Logically, a record is a set of pairs .
4.1.32
rectified grid
grid for which there is an affine transformation between the grid coordinates and the coordinates of an
external coordinate reference system
NOTE If the coordinate reference system is related to the earth by a datum, the grid is a georectified grid.
ISO 19123:2005(E)
4.1.33
referenceable grid
grid associated with a transformation that can be used to convert grid coordinate values to values of
coordinates referenced to an external coordinate reference system
NOTE If the coordinate reference system is related to the earth by a datum, the grid is a georeferenceable grid.
4.1.34
solid
3-dimensional geometric primitive, representing the continuous image of a region of Euclidean 3-space
[ISO 19107:2003]
NOTE A solid is realizable locally as a three-parameter set of direct positions. The boundary of a solid is the set of
oriented, closed surfaces that comprise the limits of the solid.
4.1.35
spatial object
object used for representing a spatial characteristic of a feature
[ISO 19107:2003]
4.1.36
spatiotemporal domain
〈coverage〉 domain composed of spatiotemporal objects
NOTE The spatiotemporal domain of a continuous coverage consists of a set of direct positions defined in relation to
a collection of spatiotemporal objects.
4.1.37
spatiotemporal object
object representing a set of direct positions in space and time
4.1.38
surface
2-dimensional geometric primitive, locally representing a continuous image of a region of a plane
[ISO 19107:2003]
NOTE The boundary of a surface is the set of oriented, closed curves that delineate the limits of the surface.
4.1.39
tessellation
partitioning of a space into a set of conterminous subspaces having the same dimension as the space being
partitioned
NOTE A tessellation composed of congruent regular polygons or polyhedra is a regular tessellation. One composed
of regular, but non-congruent polygons or polyhedra is a semi-regular tessellation. Otherwise, the tessellation is irregular.
EXAMPLES Graphic examples of tessellations may be found in Figures 11, 13, 20 and 22 of this International
Standard.
4.1.40
Thiessen polygon
polygon that encloses one of a set of points on a plane so as to include all direct positions that are closer to
that point than to any other point in the set
6 © ISO 2005 – All rights reserved

ISO 19123:2005(E)
4.1.41
topological dimension
minimum number of free variables needed to distinguish nearby direct positions within a geometric object
from one another
[ISO 19107:2003]
4.1.42
triangulated irregular network
tessellation composed of triangles
4.1.43
vector
quantity having direction as well as magnitude
NOTE A directed line segment represents a vector if the length and direction of the line segment are equal to the
magnitude and direction of the vector. The term vector data refers to data that represents the spatial configuration of
features as a set of directed line segments.
4.2 Abbreviated terms
GIS Geographic Information System
TIN Triangulated Irregular Network
UML Unified Modelling Language
4.3 Notation
The conceptual schema specified in this International Standard is described using the Unified Modelling
[4]
Language (UML) , following the guidance of ISO/TS 19103. Annex B describes UML notation as used in this
International Standard.
Several model elements used in this schema are defined in other International Standards developed by
ISO/TC 211. By convention within ISO/TC 211, names of UML classes, with the exception of basic data type
classes, include a two-letter prefix that identifies the standard and the UML package in which the class is
defined. UML classes defined in this International Standard have the two-letter prefix of CV. Table 2 lists the
other standards and packages in which UML classes used in this International Standard have been defined.
Table 2 — Sources of externally defined UML classes
Prefix International Package
Standard
EX ISO 19115 Extent
GF ISO 19109 General Feature Model
GM ISO 19107 Geometry
SC ISO 19111 Spatial Coordinates
TM ISO 19108 Temporal Schema
ISO 19123:2005(E)
5 Fundamental characteristics of coverages
5.1 The context for coverages
5.1.1 General
A coverage is a feature that associates positions within a bounded space (its domain) to feature attribute
values (its range). In other words, it is both a feature and a function. Examples include a raster image, a
polygon overlay or a digital elevation matrix.
A coverage may represent a single feature or a set of features.
5.1.2 Domain of a coverage
A coverage domain is a set of geometric objects described in terms of direct positions. It may be extended to
all of the direct positions within the convex hull of that set of geometric objects. The direct positions are
associated with a spatial or temporal coordinate reference system. Commonly used domains include point
sets, grids, collections of closed rectangles, and other collections of geometric objects. The geometric objects
may exhaustively partition the domain, and thereby form a tessellation such as a grid or a TIN. Point sets and
other sets of non-conterminous geometric objects do not form tessellations. Coverage subtypes may be
defined in terms of their domains.
Coverage domains differ in both the coordinate dimension of the space in which they exist and in the
topological dimension of the geometric objects they contain. Clearly, the geometric objects that make up a
domain cannot have a topological dimension greater than the coordinate dimension of the domain. A domain
of coordinate dimension 3 may be composed of points, curves, surfaces, or solids, while a domain of
coordinate dimension 2 may be composed only of points, curves or surfaces. ISO 19107:2003 defines a
number of geometric objects (subtypes of the UML class GM_Object) to be used for the description of
features. Many of these geometric objects can be used to define domains for coverages. In addition,
ISO 19108:2002 defines TM_GeometricPrimitives that may also be used to define domains of coverages.
Generally, the geometric objects that make up the domain of a coverage are disjoint, but this International
Standard does allow a coverage domain to contain overlapping geometric objects.
5.1.3 The range of a coverage
The range of a coverage is a set of feature attribute values. It may be either a finite or a transfinite set.
Coverages often model many associated functions sharing the same domain. Therefore, the value set is
represented as a collection of records with a common schema.
EXAMPLE A coverage might assign to each direct position in a county the temperature, pressure, humidity, and
wind velocity at noon, today, at that point. The coverage maps every direct position in the county to a record of four fields.
A feature attribute value may be of any data type. However, evaluation of a continuous coverage is usually
implemented by interpolation methods that can be applied only to numbers or vectors. Other data types are
almost always associated with discrete coverages.
Given a record from the range of a coverage, inverse evaluation is the calculation and exposure of a set of
geometric objects associated with specific values of the attributes. Inverse evaluation may return many
geometric objects associated with a single feature attribute value.
EXAMPLE Inverse evaluation is used for the extraction of contours from an elevation coverage and the extraction of
classified regions in an image.
8 © ISO 2005 – All rights reserved

ISO 19123:2005(E)
5.1.4 Discrete and continuous coverages
Coverages are of two types. A discrete coverage has a domain that consists of a finite collection of geometric
objects and the direct positions contained in those geometric objects. A discrete coverage maps each
geometric object to a single record of feature attribute values. The geometric object and its associated record
form a geometry value pair. A discrete coverage is thus a discrete or step function as opposed to a continuous
coverage. Discrete functions can be explicitly enumerated as (input, output) pairs. A discrete coverage may be
represented as a collection of ordered pairs of independent and dependent variables. Each independent
variable is a geometric object and each dependent variable is a record of feature attribute values.
EXAMPLE A coverage that maps a set of polygons to the soil type found within each polygon is an example of a
discrete coverage.
A continuous coverage has a domain that consists of a set of direct positions in a coordinate space. A
continuous coverage maps direct positions to value records.
EXAMPLE Consider a coverage that maps direct positions in San Diego County to their temperature at noon today.
Both the domain and the range may take an infinite number of different values. This continuous coverage would be
associated with a discrete coverage that holds the temperature values observed at a set of weather stations.
A continuous coverage may consist of no more than a spatially bounded, but transfinite set of direct positions,
and a mathematical function that relates direct position to feature attribute value. This is called an analytical
coverage.
EXAMPLE A statistical trend surface that relates land value to position relative to a city centre is an example of a
continuous coverage.
More often, the domain of a continuous coverage consists of the direct positions in the union or in the convex
hull of a finite collection of geometric objects; it is specified by that collection. In most cases, a continuous
coverage is also associated with a discrete coverage that provides a set of control values to be used as a
basis for evaluating the continuous coverage. Evaluation of the continuous coverage at other direct positions
is done by interpolating between the geometry value pairs of the control set. This often depends upon
additional geometric objects constructed from those in the control set; these additional objects are typically of
higher topological dimension than the control objects. In this International Standard, such objects are called
geometry value objects. A geometry value object is a geometric object associated with a set of geometry
value pairs that provide the control for constructing the geometric object and for evaluating the coverage at
direct positions within the geometric object.
EXAMPLE Evaluation of a triangulated irregular network involves interpolation of values within a triangle composed
of three neighbouring point value pairs.
5.2 The coverage schema
The coverage schema is organized into seven packages with the inter-package dependencies shown in
Figure 1. The Coverage Core package is documented in this clause, and each of the other packages is
described in a separate clause as shown in Table 3.
ISO 19123:2005(E)
Figure 1 — Packages of the coverage schema
Table 3 — Documentation of coverage geometry packages
Package Clause
Coverage core 5
Discrete coverages 6
Thiessen polygon 7
Quadrilateral grid 8
Hexagonal grid 9
TIN 10
Segmented curve 11
5.3 CV_Coverage
5.3.1 General
The class CV_Coverage (Figure 2) is an instance of the <> GF_FeatureType (ISO 19109), which
therefore represents a feature type. CV_Coverage shall support three attributes, five operations, and three
associations.
5.3.2 domainExtent
The attribute domainExtent[1.*]EX_Extent shall contain the extent of the domain of the coverage. The data
type EX_Extent is defined in ISO 19115:2003. Extents may be specified in space, time or space-time.
5.3.3 rangeType
The attribute rangeType: RecordType shall describe the range of the coverage. The data type RecordType is
defined in ISO/TS 19103. It consists of a list of attribute name/data type pairs. A simple list is the most
common form of rangeType, but RecordType can be used recursively to describe more complex structures.
The rangeType for a specific coverage shall be specified in an application schema.
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ISO 19123:2005(E)
5.3.4 commonPointRule
The attribute commonPointRule: CV_CommonPointRule shall identify the procedure to be used for evaluating
the CV_Coverage at a position that falls either on a boundary between geometric objects or within the
boundaries of two or more overlapping geometric objects, where the geometric objects are either
CV_DomainObjects or CV_ValueObjects. The data type CV_CommonPointRule is defined in 5.6.
5.3.5 list
The operation list(): Set shall return the dictionary of CV_GeometryValuePairs
(5.8) that contain the CV_DomainObjects in the domain of the CV_C
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