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ISO 19148 defines linear referencing as the “specification of a location relative to a linear element as a measurement along (and optionally offset from) that element” [ISO-2]. The ISO standard is based on the Generalized Model for Linear Referencing. The Generalized Model has been well documented [e.g., PXS-2] and widely discussed because of its acceptance in a dozen software standards.

There are numerous disparate methods of specifying a linearly referenced location. The Generalized Model captures the essential concepts found in these various approaches. By viewing any of these approaches from this generalized context, it enables the translation of locations from one to another, rather than dictating that everyone use the same method.

The basic premise of the Generalized Model is that a linearly referenced location can be specified by:

– the linear element being measured (e.g., Alignment, Route)

– the Linear Referencing Method (LRM) used (e.g., stationing, chainage,

reference post, percentage)

– the measured value as a “distance along” the linear element

– optional offsets (lateral, vertical, vector) from the distance along location

Following this specification allows for the simple linear interpolation transformation between linearly referenced locations based on differing linear elements and/or LRMs. These transformations are closed, commutative, and transitive.

Linear elements (LE) can be features (e.g., a particular road), 1-dimensional geometries, or topological directed edges. LRMs can be absolute (measure from the start of the LE), relative (measure from some known location (a mile, kilometer, or reference post), or interpolative (e.g., percentage of the overall LE length). These two things provide the context for the measured value: you need to know if a measured value of .50 is one half mile from the start of Route 66 or half of the way to the end of the route.

Rather than constrain COBie to support a specific linear referencing approach (linear element type and LRM), the Generalized Model approach is proposed. It is helpful to look at some of the approaches used by the interviewed stakeholders to see how they can be viewed from the Generalized Model view.

Consider a hypothetical tube line called the Eastern Line. It passes through Waterloo Station (LCS Level 1 Code = E007) on its way to London Bridge Station (E009). Waterloo Station is 20 km from the start of the Eastern Line, London Bridge is 22.

One way to specify the linear referenced location of Waterloo Station would be (“Eastern Line”, “chainage”, 20000) where “Eastern Line” is the linear element along which measurement is made, “chainage” is the LRM which says that measurements are made in meters from the beginning of the linear element, and 20000 is the distance along the Eastern Line from its beginning to Waterloo Station, measured in meters. London Bridge would be (“Eastern Line”, “chainage”, 22000).

Looking closer, it becomes apparent that the stations themselves have length of track:

The ramp at Waterloo Station is 500 meters long, London Bridge is 400. It is now possible to treat these as linear elements. Waterloo Station would be the LCS coded section “E007-E- EBLO” linear element, where “E0007” is the LCS Level 1 Code for station, “E” is the LCS Level 2 Code for the Eastern line, and “EBLO” is the LCS Level 3 Code for the EastBound LOcal road/route. The eastbound local track between the stations would be linear element “E008-E- EBLO”.

It is now possible to specify linearly referenced locations along “E008-E-EBLO”. If a chainage LRM is again chosen, a linear referenced location specified as (“E008-E-EBLO”, “chainage”, 100) would be 100 meters along the track between these two stations measured from the start of this track section (i.e., the end of the Waterloo Station ramp).

The contractor who is constructing just this local section of the Eastern line might specify an asset (e.g., signal) location as (“E008-E-EBLO”, “chainage”, 100) or even as (“E008-E-EBLO”, “metric stationing”, 0+100). The eventual owner of the Eastern Line might prefer to see this same location as a linearly referenced location along the Eastern Line instead of the more local LCS coded section.

To accomplish this, the LCS coded sections first need to be located along the Eastern Line”:

LCS coded  section 

linear element  LRM  from distance  to distance 

E007‐E‐EBLO  EASTERN LINE  chainage  20000  20500 

E008‐E‐EBLO  EASTERN LINE  chainage 20500  22000 

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It is now easy to see that the signal that was located by the contractor as (“E008-E-EBLO”, “chainage”, 100) would be located by the owner as an equivalent (“EASTERN LINE”, “chainage”, 20600).

The possible methods of specifying this location is limitless because of the flexibility of linear element and LRM. As long as they are all specified using the Generalized Model, it is easy to translate between them. In the COBie proposal, EASTERN LINE would be a row in the

LOCATION (formerly SPACE) spread sheet. Each LCS coded section would be rows in the

COMPONENT spread sheet having a LOCATIONNAME of EASTERN LINE and having from and to

distance along measures specifying their limits along the Eastern Line. The LCS coded sections

would also be rows in the LOCATION spread sheet. The contractor could enter the signal as a

COMPONENT with a LOCATIONNAME equal to the LCS coded section and a from distance along as

the chainage measure from the start of the localized LCS coded section. When the owner reads the COBie file, he could transform this localized linear location to the absolute measure along the Eastern Line.

A totally different approach using a “relative” type of LRM is being investigated by Tube Lines. With a relative type of LRM, distance along measures are made from a known location (referent) along the linear element, instead of absolutely from the beginning of the linear element. Milepost, kilometer post, and reference post are examples. A linear referenced location of (“Track1”, “kilometer post”, 6+.500) signifies a location 500 meters beyond kilometer post 6 along Track1. If all kiloposts are exactly one kilometer apart, this is equivalent to the absolute linear referenced location (“Track1”, “chainage”, 6500).

Due to reconstructions, posts are typically not equidistant over time and are more properly called reference posts. They are handled in a similar fashion but it is necessary to know a priori the exact location of each of these posts. The location be specified as an absolute distance from the linear element start or as a relative distance from the previous post. The latter choice minimizes changes due to local construction-caused changes in the alignment length.

The Tube Lines proposal being considered is to make the start point of each LCS coded section above an Eastern Line referent from which relative measures can be made. The referent locations would be defined as in the Table below.

Linear Element Referent

Referent location Linear

Element LRM distanceAlong

EASTERN LINE  E007‐E‐EBLO  EASTERN LINE  chainage 20000

EASTERN LINE  E008‐E‐EBLO  EASTERN LINE 

relative

chainage E007‐E‐EBLO + 500

EASTERN LINE  E009‐E‐EBLO  EASTERN LINE 

relative

chainage E008‐E‐EBLO + 1500

Now the signal location can be specified as (“EASTERN LINE”, “relative chainage”, “E008‐E‐

EBLO + 100”), or 100 meters beyond the start of E008-E-EBLO. Since E008-E-EBLO is 500

meters beyond E007-E-EBLO, which is at absolute 20000, then the signal location once again is 20000+500+100=20600 from the start of the Eastern Line.