EN ISO 19148:2012

SLOVENSKI STANDARD
01-maj-2012
Geografske informacije - Linearno georeferenciranje (ISO 19148:2012)
Geographic information - Linear referencing (ISO 19148:2012)
Geoinformation - Standortbezogene Dienste - Lineares Bezugssystem (ISO 19148:2012)
Information géographique - Références linéaires (ISO 19148:2012)
Ta slovenski standard je istoveten z: EN ISO 19148:2012
ICS:
07.040 Astronomija. Geodezija. Astronomy. Geodesy.
Geografija Geography
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 19148
NORME EUROPÉENNE
EUROPÄISCHE NORM
February 2012
ICS 35.240.70
English Version
Geographic information - Linear referencing (ISO 19148:2012)
Information géographique - Référencement linéaire (ISO Geoinformation - Lineares Bezugssystem (ISO
19148:2012) 19148:2012)
This European Standard was approved by CEN on 21 January 2012.

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-CENELEC 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-CENELEC Management Centre has the same
status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, 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, Turkey and United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2012 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 19148:2012: E
worldwide for CEN national Members.

Contents Page
Foreword .3

Foreword
This document (EN ISO 19148:2012) has been prepared by Technical Committee ISO/TC 211 "Geographic
information/Geomatics" in collaboration with Technical Committee CEN/TC 287 “Geographic Information” the
secretariat of which is held by BSI.
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 August 2012, and conflicting national standards shall be withdrawn at
the latest by August 2012.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
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, Croatia, 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, Turkey and the United Kingdom.
Endorsement notice
The text of ISO 19148:2012 has been approved by CEN as a EN ISO 19148:2012 without any modification.

INTERNATIONAL ISO
STANDARD 19148
First edition
2012-02-15
Geographic information — Linear
referencing
Information géographique — Référencement linéaire

Reference number
ISO 19148:2012(E)
©
ISO 2012
ISO 19148:2012(E)
©  ISO 2012
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
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Published in Switzerland
ii © ISO 2012 – All rights reserved

ISO 19148:2012(E)
Contents Page
Foreword . iv
Introduction . v
1  Scope . 1
2  Conformance . 1
2.1  Conformance overview . 1
2.2  Conformance classes . 2
3  Normative references . 3
4  Terms and definitions . 3
5  Abbreviated terms . 6
6  Linear referencing . 6
6.1  Introduction . 6
6.2  Package: Linear Referencing System . 17
6.3  Package: Linear Referencing Towards Referent . 31
6.4  Package: Linear Referencing Offset . 33
6.5  Package: Linear Referencing Offset Vector . 39
6.6  Package: Linearly Located Event . 41
6.7  Package: Linear Segmentation . 47
Annex A (normative) Abstract test suite . 52
Annex B (informative) Generalized model for linear referencing . 56
Annex C (informative) Commonly used linear referencing methods and models . 59
Annex D (informative) Event and segmentation examples . 79
Bibliography . 86

ISO 19148:2012(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 19148 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics.

iv © ISO 2012 – All rights reserved

ISO 19148:2012(E)
Introduction
This International Standard is a description of the data and operations required to support linear referencing.
This includes Linear Referencing Systems, linearly located events and linear segments.
Linear Referencing Systems enable the specification of positions along linear objects. The approach is based
[3]
upon the Generalized Model for Linear Referencing first standardized within ISO 19133:2005, 6.6. This
International Standard extends that which was included in ISO 19133, both in functionality and explanation.
ISO 19109 supports features representing discrete objects with attributes having values which apply to the
entire feature. ISO 19123 allows the attribute value to vary, depending upon the location within a feature, but
does not support the assignment of attribute values to a single point or length along a linear feature. Linearly
located events provide the mechanism for specifying attribution of linear objects when the attribute value
varies along the length of a linear feature. A Linear Referencing System is used to specify where along the
linear object each attribute value applies. The same mechanism can be used to specify where along a linear
object another object is located, such as guardrail or a traffic accident.
It is common practice to segment a linear object having linearly located events, based upon one or more of its
attributes. The resultant linear segments are attributed with just the attributes used in the segmentation
process, insuring that the linear segments are homogeneous in value for these segmenting attributes.
This International Standard differs from ISO 19133:2005, 6.6 in the following areas.
a) All occurrences of Linear Reference Method and Linear Reference System have been changed to Linear
Referencing Method and Linear Referencing System, respectively.
b) LR_Element has been renamed LR_LinearElement and further defined as being a feature or geometry or
topology. These shall support the newly introduced interface ILinearElement, meaning that it is possible
to measure (linearly) along them.
c) The newly introduced ILinearElement interface includes operations for returning the default Linear
Referencing Method of the linear element and any of its length or weight attribute values. It also includes
operations for translating between Linear Referencing Methods and/or linear elements.
d) The types of Linear Referencing Methods have been formalized as a CodeList. Names of common Linear
Referencing Methods have been added as an informative annex.
e) An additional attribute, constraint[0.*], has been added to Linear Referencing Method to specify the
constraints imposed by the method, such as “only allows reference marker referents”. This is an
alternative to subtyping the methods that would force a too-structured approach, inconsistent with the
Generalized Model, and would be indeterminate due to the wide variety of Linear Referencing Methods
currently in use.
f) The Linear Referencing Method “project” operation has been renamed “lrPosition” and moved to the
ISpatial interface and a second, opposite, operation “point” has been added. Only LR_Curves realize this
interface since their spatial representation is requisite for the two operations, along with the
ILinearElement interface.
g) The LR_PositionExpression measure attribute has been extracted out into a Distance Expression along with
the optional referent and offset roles consistent with the original theoretical model. This allows for specifying
only an LR_DistanceExpression when the LR_LinearElement and LR_LinearReferencingMethod are
already known.
h) Reference Marker has been generalized to LR_Referent to enable support for other referent types such
as intersections, boundaries and landmarks. This type has been formalized as a CodeList.
ISO 19148:2012(E)
i) A second, optional (towards) Referent has been added in a new (optional) package, Linear Referencing
Towards Referent (LRTR), for those Linear Referencing Methods which allow this to disambiguate
measurement direction.
j) Lateral Offsets have been moved to a new (optional) package, Linear Referencing Offset (LRO).
Horizontal, vertical, and combined horizontal and vertical offsets are now supported. Offset referent has
been generalized to allow for feature instances as well as character strings.
k) Vector Offsets have been adopted from ISO 19141. They exist in a new (optional) package, Linear
Referencing Offset Vector (LROV). An optional offset vector Coordinate Reference System (CRS) can be
provided if it is different from the CRS of the linear element.
l) The theoretical model on which the original standard was built is explained in Annex B.
m) More descriptive text is added throughout this International Standard to explain the concepts being
presented.
n) Minor changes to some class, attribute and role names have been made.
o) A new (optional) package, Linearly Located Event (LE) has been added which uses linearly referenced
positions to specify where along a linear feature a particular attribute value or other feature instance
applies.
p) A new (optional) package, Linear Segmentation (LS) has been added to support the generation of
homogeneous attributed linear segments from linear features with length-varying attribution.
q) Absolute Linear Referencing Method with non-zero linear element start is now accommodated.
r) lateralOffsetReferentType and verticalOffsetReferentType have been changed from CodeLists to
Character Strings.
vi © ISO 2012 – All rights reserved

INTERNATIONAL STANDARD ISO 19148:2012(E)

Geographic information — Linear referencing
1 Scope
This International Standard specifies a conceptual schema for locations relative to a one-dimensional object
as measurement along (and optionally offset from) that object. It defines a description of the data and
operations required to use and support linear referencing.
This International Standard is applicable to transportation, utilities, location-based services and other
applications which define locations relative to linear objects.
2 Conformance
2.1 Conformance overview
Clause 6 of this International Standard uses the Unified Modelling Language (UML) to present conceptual
schemas for describing the constructs required for Linear Referencing. These schemas define conceptual
classes that shall be used in application schemas, profiles and implementation specifications. This
International Standard concerns only externally visible interfaces and places no restriction on the underlying
implementations other than what is required to satisfy the interface specifications in the actual situation, such
as
 interfaces to software services using techniques such as SOAP;
 interfaces to databases using techniques such as SQL;
 data interchange using encoding as defined in ISO 19118.
Few applications require the full range of capabilities described by this conceptual schema. Clause 6,
therefore, defines a set of conformance classes that support applications whose requirements range from the
minimum necessary to define data structures to full object implementation. This flexibility is controlled by a set
of UML types that can be implemented in a variety of manners. Implementations that define full object
functionality shall implement all operations defined by the types of the chosen conformance class, as is
common for UML designed object implementations. It is not necessary for implementations that choose to
depend on external “free functions” for some or all operations, or forgo them altogether, to support all
operations, but they shall always support a data type sufficient to record the state of each of the chosen UML
types as defined by its member variables. It is acceptable to use common names for concepts that are the
same but have technically different implementations. The UML model in this International Standard defines
abstract types, application schemas define conceptual classes, various software systems define
implementation classes or data structures, and the XML from the encoding standard (ISO 19118) defines
entity tags. All of these reference the same information content. There is no difficulty in allowing the use of the
same name to represent the same information content even though at a deeper level there are significant
technical differences in the digital entities being implemented. This “allows” types defined in the UML model to
be used directly in application schemas.
ISO 19148:2012(E)
2.2 Conformance classes
2.2.1 General
Conformance to this International Standard shall consist of either data type conformance or both data type
and operation conformance.
2.2.2 Data type conformance
Data type conformance includes the usage of data types in application schemas or profiles that instantiate
types in this International Standard. In this context, “instantiate” means that there is a correspondence
between the types in the appropriate part of this International Standard, and the data types of the application
schema or profile in such a way that each standard type can be considered as a supertype of the application
schema data type. This means that an application schema or profile data type corresponding to a standard
type contains sufficient data to recreate that standard type's information content.
Table 1 assigns conformance tests to each of the packages in Clause 6. Each row in the table represents one
conformance class. A specification claiming data type conformance to a package in the first column of the
table shall satisfy the requirements specified by the tests given in the remaining columns to the right.
Table 1 — Data type conformance tests
Conformance test
Package
A.1.1 A.1.2 A.1.3 A.1.4 A.1.5 A.1.6
Linear Referencing System X — — — — —
Linear Referencing Towards Referent X X — — — —
Linear Referencing Offset X — X — — —
Linear Referencing Offset Vector X X X
— — —
Linearly Located Event X — — — X —
Linear Segmentation X — — — X X

2.2.3 Operation conformance
Operation conformance includes both the consistent use of operation interfaces and data type conformance
for the parameters, and return values used by those operations. Operation conformance also includes get and
set operations for attributes.
Table 2 assigns conformance tests to each of the packages in Clause 6. Each row in the table represents one
conformance class. A specification claiming operation conformance to a package in the first column of the
table shall satisfy the requirements specified by the tests given in the remaining columns to the right.
Table 2 — Operation conformance tests
Conformance test
Package
A.1.1 A.1.2 A.1.3 A.1.4 A.1.5 A.1.6
A.2.1 A.2.2 A.2.3 A.2.4 A.2.5 A.2.6
Linear Referencing System X — — — — —
Linear Referencing Towards Referent X X — — — —
Linear Referencing Offset X — X — — —
Linear Referencing Offset Vector X X X
— — —
Linearly Located Event X — — — X —
Linear Segmentation X — — — X X
2 © ISO 2012 – All rights reserved

ISO 19148:2012(E)
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, Geographic information — Conceptual schema language
ISO 19107, Geographic information — Spatial schema
ISO 19108, Geographic information — Temporal schema
ISO 19111, Geographic information — Spatial referencing by coordinates
4 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
4.1
attribute event
value of an attribute of a feature (4.4) that may apply to only part of the feature
NOTE 1 An attribute event includes the linearly referenced location (4.16) where the attribute value applies along the
attributed feature (4.2).
NOTE 2 An attribute event may be qualified by the instant (4.8) in which, or period (4.20) during which, the attribute
value applied.
4.2
attributed feature
feature (4.4) along which an attribute event (4.1) applies
4.3
direct position
position (4.21) described by a single set of coordinates within a coordinate reference system
[ISO 19107:2003, 4.26]
4.4
feature
abstraction of real world phenomena
[ISO 19101:2002, 4.11]
4.5
feature event
information about the occurrence of a located feature (4.17) along a locating feature (4.18)
NOTE 1 A feature event includes the linearly referenced location (4.16) of the located feature along the locating
feature.
NOTE 2 A feature event may be qualified by the instant (4.8) in which, or period (4.20) during which, the feature event
occurred.
4.6
geometric primitive
geometric object representing a single, connected, homogeneous element of space
[ISO 19107:2003, 4.48]
ISO 19148:2012(E)
4.7
height
h, H
distance of a point from a chosen reference surface measured upward along a line perpendicular to that
surface
[ISO 19111:2007, 4.29]
NOTE The surface is normally used to model the surface of the Earth.
4.8
instant
0-dimensional geometric primitive (4.6) representing position (4.21) in time
[ISO 19108:2002, 4.1.17]
NOTE The geometry of time is discussed in ISO 19108:2002, 5.2.
4.9
linear element
1-dimensional object that serves as the axis along which linear referencing (4.10) is performed
NOTE Also known as curvilinear element.
EXAMPLES Feature (4.4), such as “road”; curve geometry; directed edge topological primitive.
4.10
linear referencing
specification of a location (4.19) relative to a linear element (4.9) as a measurement along (and optionally
offset from) that element
NOTE An alternative to specifying a location as a two- or three- dimensional spatial position (4.22).
4.11
Linear Referencing Method
manner in which measurements are made along (and optionally offset from) a linear element (4.9)
4.12
Linear Referencing System
[1]
set of Linear Referencing Methods (4.11) and the policies, records and procedures for implementing them
4.13
linear segment
part of a linear feature (4.4) that is distinguished from the remainder of that feature by a subset of attributes,
each having a single value for the entire part
NOTE 1 A linear segment is a one-dimensional object without explicit geometry.
NOTE 2 The implicit geometry of the linear segment can be derived from the geometry of the parent feature.
4.14
linearly located
located using a Linear Referencing System (4.12)
4.15
linearly located event
occurrence along a feature (4.4) of an attribute value or another feature
NOTE 1 The event location (4.19) is specified using linearly referenced locations (4.16).
4 © ISO 2012 – All rights reserved

ISO 19148:2012(E)
NOTE 2 A linearly located event may be qualified by the instant (4.8) in which, or period (4.20) during which, the
linearly located event occurred.
NOTE 3 ISO 19108 limits events to a single instant in time and does not include the specification of a location.
4.16
linearly referenced location
location whose position (4.21) is specified using linear referencing (4.10)
4.17
located feature
feature (4.4) that is linearly located (4.14) along an associated (locating) feature
EXAMPLE A feature “bridge” may be a located feature along the feature “railway” [a locating feature (4.18)].
4.18
locating feature
feature (4.4) that is used to identify the location (4.19) of linearly located (4.14) features
EXAMPLE A feature “road” may be the locating feature for a feature “pedestrian crossing” [a located feature (4.17)].
4.19
location
identifiable geographic place
[ISO 19112 :2003, 4.4]
NOTE A location is represented by one of a set of data types that describe a position (4.21), along with metadata
about that data, including coordinates (from a coordinate reference system), a measure [from a Linear Referencing
System (4.12)], or an address (from an address system). [ISO 19133].
4.20
period
one-dimensional geometric primitive (4.6) representing extent in time
[ISO 19108:2002, 4.1.27]
NOTE A period is bounded by two different temporal positions (4.23).
4.21
position
data type that describes a point or geometry potentially occupied by an object or person
[ISO 19133:2005, 4.18]
NOTE A direct position (4.3) is a semantic subtype of position. Direct positions as described can define only a point
and, therefore, not all positions can be represented by a direct position. That is consistent with the “is type of” relation. An
ISO 19107 geometry is also a position, just not a direct position.
4.22
spatial position
direct position (4.3) that is referenced to a 2- or 3-dimensional coordinate reference system
NOTE An alternative to specifying a location (4.19) as a linearly referenced location (4.16).
4.23
temporal position
location (4.19) relative to a temporal reference system (4.24)
[ISO 19108:2002, 4.1.34]
ISO 19148:2012(E)
4.24
temporal reference system
reference system against which time is measured
[ISO 19108:2002, 4.1.35]
4.25
valid time
time when a fact is true in the abstracted reality
[ISO 19108:2002, 4.1.39]
5 Abbreviated terms
CRS Coordinate Reference System
LRM Linear Referencing Method
LRS Linear Referencing System
SOAP Single Object Access Protocol
SQL Structured Query Language
UML Unified Modelling Language
XSP Cross-Sectional Positioning
NOTE The UML notation described in ISO/TS 19103 is used in this International Standard.
6 Linear referencing
6.1 Introduction
6.1.1 Linear referencing concepts
6.1.1.1 General
Linear Referencing Systems are in wide use in transportation but are also appropriate in other areas such as
utilities. They allow for the specification of positions along linear elements by using measured distances along
(and optionally offset from) the element. This is in contrast to using spatial positions that use two- or three-
dimensional coordinates, consistent with a particular Coordinate Reference System (CRS).
Linearly referenced locations are significant for several reasons. First, a significant amount of information is
currently held in huge databases from legacy systems that pre-date Geographic Information Systems (GIS).
Many useful applications can and have been built on these data with no understanding of where on the earth's
surface the data are located. Knowing where they are located relative to a linear element such as a roadway
route or pipeline is sufficient to support these applications and can be used as a means of integrating data
from multiple, disparate sources.
In some situations, having a linearly referenced location along a known linear element is more advantageous
than knowing its spatial position. Consider a crash in need of emergency assistance. Knowing the linear
element (Northbound I-95) and the approximate linear location is superior to having a potentially more precise
spatial GPS location that is not of significant accuracy to determine whether it is northbound or southbound
I-95, especially if an impassable barrier separates the two carriageways.
The linearly referenced location as specified in this International Standard as a position expression, therefore,
has many uses. It can be used to tie information about a linear facility to a specific location along that facility. It
can also be used to find a position on the face of the earth by specifying how far along the position is (and
optionally offset from) on a particular linear element.
6 © ISO 2012 – All rights reserved

ISO 19148:2012(E)
This International Standard proposes a consistent specification for describing linearly referenced locations that
also enables translation between different referencing methods and/or linear elements. It also specifies how
these position expressions can be used to specify how information that pertains to only a part of a linear
element can be specified as linearly located events.
A Linear Referencing System is a set of Linear Referencing Methods (LRM) and the policies, records and
procedures for implementing them. There are numerous, seemingly disparate, Linear Referencing Methods in
use today. There is no single, best method, as each has advantages in certain situations. It is, therefore,
unreasonable to propose a single standard Linear Referencing Method. The Generalized Model for Linear
[3]
Referencing has been developed which instead categorizes Linear Referencing Methods into a basic set of
common concepts. The additional advantage of this approach is that it also enables a singular method for
translating linearly referenced locations into locations specified by another method or along an alternative
linear element. This translation method is both closed and transitive, insuring round-tripping and translation
chaining.
The Generalized Model standardizes the content of a linearly referenced location as containing three
components: that which is being measured (linear element), the method of measurement (Linear Referencing
Method) and the measured value (distance expression).
6.1.1.2 Linear element
Linear element is the general term which encompasses anything that can be measured using linear
referencing. This includes ISO 191nn features, linear geometries and linear topologies.
Features do not have to be linear. A road feature, for example, may have multiple spatial representations to
support multiple applications. These can be high-precision linear curves to support civil engineering design,
low-resolution straight linestrings to support GIS applications, or areas to support pavement management
applications. The only requirement is that it be possible to measure along the feature in a linear, one-
dimensional, sense.
Features may represent fundamental entities, like a road element between two intersections, or more complex
entities, such as a highway route spanning an entire state or country. Depending on the application schema,
the feature can represent the entire road (width-wise) or only one of its carriageways. Therefore, this
International Standard uses the word “roadway” intentionally to mean either the full road or a single
carriageway.
Linear element features may have no geometry at all. Many existing systems store information about roads by
defining roadway characteristics along the roadway, without specifying where the road is physically located.
This does preclude the ability to translate spatial positions into linearly referenced locations along the feature.
However, it is possible to translate linearly referenced locations to other linear elements or to other Linear
Referencing Methods. Using linear referencing instead of its geometry to define roadway characteristics
directly against the feature enables the definition of multiple geometries for the feature without having to
repeat the roadway characteristics for each spatial representation. It also allows for the definition of roadway
characteristics when no geometry exists.
The linear geometry type of linear element includes instances of geometric curves, as these can be measured
along and their geometric location is known. It is, therefore, possible to project a spatial position onto the
linear geometry and represent its location as a linearly referenced location along the geometry. It is also
possible to translate a linearly referenced location along the geometry into two- or three-dimensional space.
Geometric curves are typically represented as attributes of features. Once a spatial position has been
projected onto the curve, it is then possible to translate this location into a linearly referenced location on the
feature itself.
The linear topology type of linear element includes instances of directed edges. Edges usually do not have a
length attribute but do have one or more weights associated with the cost of traversing the edge. Measuring
along an edge, therefore, entails pro rata distribution based upon the weight value(s). Only a limited number of
Linear Referencing Method types can be used for measuring edges.
ISO 19148:2012(E)
Linear elements can have attributes. If specified for the linear element, the value of these attributes applies to
the entire linear element. Attribute events enable attribute values to apply to part of the linear element
(see 6.1.1.5).
6.1.1.3 Linear Referencing Method
How a linear element is measured is specified by the Linear Referencing Method. Example Linear
Referencing Methods are included in Annex C. The Linear Referencing Method specifies whether the
measurement is absolute, relative, or interpolative. Absolute measurements, such as milepoint, hecto-metre
and kilometre-point, are made from the start of the linear element. Relative measurements, such as a milepost,
kilopost or reference post, are made from some known location along the linear element, called a referent.
Interpolative measurements, such as percentage or normalized, use linear interpolation along the entire length
of the linear element.
The Linear Referencing Method specifies if an additional, offset measurement can be made perpendicular to
the linear element to specify a location that does not lie directly on the linear element. The offset
measurement can be made from the linear element itself or relative from an offset referent, for example, 5 m
from the reference line of a road or 5 ft from the back of the curb, respectively.
The Linear Referencing Method specifies the units of measure for measuring along the linear element. This
results in the fundamental difference between a milepoint versus a kilometre-point Linear Referencing
Method; the first measures in miles, the second in kilometres. If a Linear Referencing Method allows offsets,
the Linear Referencing Method also specifies the units of measure for offset measurements.
Because of the wide variety of Linear Referencing Methods currently in use, it is possible to enumerate
particular constraints about the method, for example, to allow only reference marker type of referents for a
Reference Post Linear Referencing Method. Constraints for commonly used Linear Referencing Methods are
suggested in Annex C.
6.1.1.4 Distance Expression
6.1.1.4.1 Distance Along
The measured value which defines the location along the linear element in accordance with the Linear
Referencing Method is specified with a distance expression. In its simplest form, this is the “distance along”
the linear element for an absolute Linear Referencing Method. It specifies how far along the linear element to
measure from the start of the linear element in the direction towards the end of the linear element. The
resultant “along” location A is on the linear element, as shown in Figure 1. For example, a distance expression
with a “distance along” of 4,0 for a kilometre-point Linear Referencing Method along Route 1 specifies a
location on Route 1 that is measured 4,0 kilometres along the route from its start.
distance along
start end
linear element A
Figure 1 — Linearly referenced along location A with an absolute Linear Referencing Method
It is often the case that the measure at the start of the linear element is not equal to zero for a particular
absolute type of Linear Referencing Method. For example, in Figure 2, the linear element start has a
kilometre-point value of 0,5 km. An “absolute zero” point is, therefore, introduced to specify where an absolute
Linear Referencing Method shall begin measuring distance along values.
In Figure 2, absolute zero occurs 0,5 km prior to the start of the linear element for the specified absolute
Linear Referencing Method. A position expression having this Linear Referencing Method of kilometre-point
and a distance expression with a distance along value of 4,0 km specifies a location that is measured 4,0 km
8 © ISO 2012 – All rights reserved

ISO 19148:2012(E)
along the linear element from absolute zero. The result is an along location A that is 3,5 km from the start of
the linear element.
distance along = 4
start
absolute linear element end
A = 3,5
= 0,5
zero
Figure 2 — Absolute Linear Referencing Method with non-zero linear element start
For an interpolative Linear Referencing Method, the distance expression is comprised of a single measure
value. Here this value is used with linear interpolation to determine the location along the linear element based
on the length (or weight) of the linear element as shown in Figure 3. A distance expression with a measured
value of 60 for a percentage Linear Referencing Method along Route 1, which has a length of 50 km, specifies
an along location A on Route 1 which is 30 km along the route from its start.
distance along
start end
linear element
A
length
Figure 3 — Linearly referenced along location A with an interpolative Linear Referencing Method
6.1.1.4.2 Referents
For relative Linear Referencing Methods, the “distance along” is measured along the linear element from a
known location on the linear element, called a “from referent”, as shown in Figure 4. For example, a distance
expression with a “distance along” of 0,5 for a kilometre-post Linear Referencing Method along Route 1
specifies an along location A on Route 1 that is 0,5 km along the route from the specified kilometre-post
located at referent location R. If the kilometre-post is located 4,0 km from the start of Route 1, then the
resultant location is 4,5 km from the start of the route.
distance
along
R
start linear element A end
Figure 4 — Linearly referenced along location A with a relative Linear Referencing Method
Referent types vary between Linear Referencing Methods. These include, for example, intersections,
administrative and maintenance boundaries, landmarks and physical reference markers.
If the Linear Referencing Method is of type Linear Referencing Method With Towards Referent, a “towards
referent” can be added to a distance expression to disambiguate the direction in which the measurement is
from referent
ISO 19148:2012(E)
made, as shown in Figure 5. Measurements are made in the direction from the “from referent” towards the
“towards referent”, regardless of the directional sense of the linear element being measured.
distance
along
R
linear element A
Figure 5 — Linearly referenced along location A with from and towards referents
6.1.1.4.3 Offsets
If the Linear Referencing Method is of type Linear Referencing Method With Offset, the distance expression
may include an offset expression to specify locations not directly on the linear element. Each position
expression may have either
a) a lateral offset
1) measured left or right (perpendicular to) the linear element reference line from the distance along
point,
2) measured left or right (perpendicular to) a lateral offset referent,
3) measured in a “lateral” direction defined by the LRS from the distance along point,
4) specified by convention;
b) a vertical offset
1) measured opposite to or in the direction of gravity, above or below the linear element from the
distance along point,
2) measured opposite to or in the direction of gravity above or below a vertical offset referent,
3) measured in a “vertical” direction defined by the LRS from the distance along point;
c) a lateral offset and a vertical offset, measured as stated above;
d) a vector offset measured along a vector from the linear element; or
e) no offset at all.
For lateral offsets, the lateral offset distance specifies the distance measured perpendicular to the linear
element at the location specified by the “distance along” (point A) to the linearly referenced offset location O,
as shown in Figure 6.
10 © ISO 2012 – All rights reserved

from referent
towards referent
lateral
lateral
lateral
offset
offset
referent
distance
distance
offset
ISO 19148:2012(E)
distance along
A
start end
linear element
O
Figure 6 — Linearly referenced offset location O with a lateral offset distance
If a lateral offset referent is also included, then the resultant location is determined as shown in Figure 7. First,
an along location A is determined by the distance along the linear element. Then a referent offset location RO
is determined by intersecting the lateral offset referent with a normal to the linear element through location A.
If A is a vertex of the linear element, then that part of the linear element occurring just prior to A is used to
determine the direction of the normal. Finally, the offset location O can be determined by measuring the lateral
offset distance along a line that is normal to the lateral offset referent at location RO. If RO is a vertex of the
lateral offset referent, then that part of the lateral offset referent occurring just prior to RO is used to determine
the direction of the normal. Here, “just prior” assumes that the lateral offset referent is defined in the same
relative direction as the linear element.
The lateral offset referent can be the name of an entity in the real world, such as curb, to enable the
specification of the location as “5 ft back of curb”. Alternatively, the offset referent can be an instance of a
feature, such as a feature representing the curb. If the linear element and feature instance have associated
linear geometri
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