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Innhold
1 General
1.1 Abbreviations
1.2 External references
1.3 EDMmodelServer referances
2 Using the Area Calculator
2.1 Preconditions
2.2 How AC works
2.3 Storing AC results
2.4 Running Area Calculator
2.5 Handling of error situations while calculating areas
2.5.1 Overlapping IfcSpaces
2.5.2 Areas not covered by space or building element
2.6 Virtual Spaces
3 Rules for calculation
3.1 Walls
3.2 BTA for building storey
3.3 Openings
3.4 Inclined (pitched) ceilings
3.5 Columns and other "inner" elements in a space
3.6 Staircases and similar
3.6.1 Finding stair footprints
3.6.2 Area of stair itself
3.7 Stairs with irregular cut lines
3.7.1 Footprints of spiral / curved stair
3.7.2 Free form stair
3.8 Staircases and openings
3.8.1 Staircase spanning multiple storeys in an opening
3.8.2 Staircase spanning multiple storeys with floor under stair
3.8.3 Spiral staircase spanning multiple storeys
3.9 Some additional considerations

General

Abbreviations

(English alternatives in italics)

External references

EDMmodelServer referances

1. EDMmodelServerManager™ Generell Brukermanual, versjon 3.2.13 (norsk)
2. EDMmodelServerManager™ BIM Upgrade Manual, version 0.2 (english)
3. EDMmodelServerManager™ Plugin Arealadministrasjon, versjon 0.65 (norsk)

Using the Area Calculator

Preconditions

How AC works

Base for calculation are IfcSpace geometry and not IfcWall or similar objects playing role as physical walls.
For outer walls the "Storey BTA polygon" for BTA of storey is used as limitation of "outer walls" instead of actual IfcWall instances. The BTA polygon is based on a "virtual BTA Space" that is supplied in the ArK data (CAD system). If the CAD system does not supply this space, it must be approximated by an AC component, this will impact accuracy significantly.
The produced result is not area values, but a set of polygons that defines different types of areas. The area values are calculated out of the polygons when needed. For each space and storey, the total area is composed of a set of polygons, each polygon composed of "outer" polygons representing positive contributions to the area, and a set of "inner" polygons intended for adjusting the area This is very common model and is usually called Simple Concave polygon with Holes (simplicity here means no self-intersection of edges).
.

Figure 1 Area polygons for a space
In this example UA is composed of two parts: PO1 og PO2, both of which has an "inner" polygon – a hole. The rest of the room is covered by an opening, represented by polygon O3.
The generated partial polygons are combined into composite polygons representing areas like UA, NTA etc. The rules for composing these polygons can relatively easy be adapted to national regulations and customer demands.
Generated composite polygons for UA can be edited using Polygon Editor as described in <TODO>.
The generated partial polygon types are listed in the following table:

Storing AC results

Calculation results are attached to the IfcSpace objects.
If space properties are used in lease contracts or similar, they cannot be changed. Hence, we must to a certain extent store both USED and CALCULATED values.
If a space is missing the BTAspace/NTAspace properties, the calculated properties can be copied directly . This is the usual case with a "new" BIM. For other situations, the transfer of calculated properties into used properties must be a managed process.
All properties are stored in the FM_Areas property set:

The partial polygons themselves uses an ifcRelSpaceBoundary (SBR) relation for each polygon connected to an ifcSpace. The SBR has attached an IfcPolyline containing "world" coordinates defining the polygon. The reason for using "world" coordinates is that the viewer uses the same, so it greatly eases the implementation of "Polygon Edit". Each SBR uses a naming convention to identify it as a space area polygon:

• Name "FM_Areas_zzz_outer_xxx" identifies an outer polygon, where xxx is a number starting from 1 (without any particular ordering) and zzz is a polygon class (text label as in 3.1).
• Name "FM_Areas_zzz_inner_xxx_yyy" identifies an outer polygon, where yyy is a number starting from 1 (without any particular ordering) and zzz is a polygon class (text label as in 3.1) and xxx is a number of outer polygon to which this inner polygon is bound.

Running Area Calculator

The area calculator is run for one storey at a time. Select a building storey in Model Explorer right-click and activate calculation by selecting 'Areal Fotavtrykk ► Arealkalkulator'.
IMPORTANT:
To get meaningful results out of an AC run, it has to be run on complete building storeys. If the AC is invoked on a lesser scope the accuracy of the polygons is unknown.
At the same time we should avoid overwriting polygons for spaces that have been manually corrected with polygon editor. Hence, the following are proposed:

• If indicated area calculator scope is an arbitrary set of spaces, the (re)calculation is run on entire storey, but only the space(s) indicated in the input scope have their polygons / areas updated.

Handling of error situations while calculating areas

Overlapping IfcSpaces

AC will check if a space overlaps/contains other spaces.
When space completely includes some other spaces, it is marked with OK=false and status is filled with GUIDs of spaces which are included in it; such space is excluded from calculation – no polygons are reported for it except base NTASpace.
When two spaces are partially overlapped, intersection area is written as NTAOverlap shape for ONE of the spaces (arbitrary one is chosen), then calculation is performed same way as for non-intersecting spaces.

Areas not covered by space or building element

In principle entire storey/building footprint should be "covered" by either space and/or building element footprints.
But when BTAStorey helper space is used, no building elements are considered, and there will be no 'white' areas except those explicitly drawn in BTAStorey helper space – for example if some room doesn't have space defined (or there's just an empty space between walls), its area will be shared by surrounding/neighbor spaces. To slightly reduce this effect, currently BTAWalls has a restriction on 'width' – it can not expand be more than 2m from space border.
When there's no BTAStorey helper space, only areas of building element footprints are 'added' to spaces – so it's keeping more 'white' areas potentially (but anyway same 2m restriction is also used in this case).

Virtual Spaces

There may exist spaces in the model that covers an entire wing, a zone or similar. Such aggregated spaces containing a lot of other spaces can be excluded from the AC process by marking them as "virtual". This can be done via report or with zoning tool. As mentioned in 3.3.1, such areas are excluded from calculations anyway, but 'virtual' mark will also remove them from result set.

Rules for calculation

This section describe the rules as they are, or should be, implemented in the area calculator. They are based on interpretation os standards and references, and on what is possible to automate. This section is not meant as a an explanation or definition on how area calculation should be performed in general.
The main references are [NS3940] with accompanying guide [NS3940-V].
[NS3940-V] recommends that rentable area UA is calculated as UA = (BTA – iMA). For commercial buildings there are two additional requirements for MA areas:

• The space should have access through a door, stair or similar
• The area should have a floor

Walls

[NS3940-V] Section 2.1 – "General" contains the following definition(s) for gross area:
Gross area (BTA) of a room is composed of all measurable "Measurable" here means "worthy of measurement" parts, limited by outside of outer walls at floor level, including finished external surface.
BTA is not given for open parts that partly are missing walls or roofs, except for special buildings like parking houses.
[NS3940-V] Section 2.2 – "Gross area for a room or an available area" contains the following definition for room gross area:
Gross area of a room, part of a storey or a separately occupied unit (e.g. a flat) is calculated from the outside of outer walls at floor level, including finished external surface. Towards adjacent rooms, separately occupied units or common areas, the area is calculated to centre of division walls.
As can be seen from the definition, it's not very specific in terms of defining what kind of building elements may constitute a wall.
There are several types of building elements that together may constitute a wall. By looking around in any building, it's clear that combinations of walls, columns, doors, windows and curtain walls, and probably also other elements, may constitute a wall according to the above quoted room gross area definition.
Nor does the standard, and its guidelines, describe how to measure in case of walls meeting at an angle.
To cope with this in BIM models, the following definition of "walls" is applied:

1. An inner wall between two spaces occupies the "area" between the space boundaries as shown in figures below.
2. An outer wall occupies the area between the storey BTA boundary and the space boundary as shown in figures below. The storey BTA boundary follows outside of building external walls.

Figure 1 - Storey BTA polygon

Figure 2 – Walls defined by Space and BTA polygons

BTA for building storey

BTA for building storey is composed of BTA for all included elements with some additions; Covered/roofed-over courtyards/atriums should be included in storey gross area for the storey in question, even if they conceptually usually have no BTA value by themselves.
Currently, this is achieved by using imposed BTA values for spaces as the ones specified above, either calculated or manually given as property input for these spaces. That means space "objects" has to be created even for these objects.
Verification of this has to be done manually with a viewer or similar.

Openings

General rule in section 1.1 in NS4940-V guidelines:

• To be measurable, an area should have a floor. The area should have floor. Exceptions are stair openings, elevator shafts and vertical shafts which are worthy of measurement even if they do not have a floor

Even if this is stated under "BTA for building storey", it is also applied to MA in connection to spaces, since there are no other identifiable rules for openings given.

Inclined (pitched) ceilings

In order for an area to be MA ("worthy of measurement"), the free height above floor should be minimum 1.9 meter, or a minimum width of 0.6 meter. Parts of area under inclined ceilings should be included measured 0.6 m outside the height of 1.9 m.
This can be illustrated as below:

Figure 3 – Area under pitched ceiling
In this illustration, the hatched part of the floor is the MA area. Note that this rule applies to the MA and not the BTA. It also applies to multiple spaces at once as shown in figure.

Columns and other "inner" elements in a space

In general, columns inside a space are not influencing the area calculation.
However, as some CAD models can create "holes" in the space geometry around columns, they can be taken into account indirectly. It is advised to make sure that no such holes are present.

Staircases and similar

For calculating area in rooms under stairs or ramps, the same rules as for ceilings described in section 3.5 Inclined (pitched) ceilings above apply. Since stairs usually is related to openings, refer also to section 3.3 Openings
A staircase is "starting" at the bottom and "ending" at the top. If a staircase is going "through" a space/storey it is the part that goes UP to the next level that is considered part of the storey. See sections on stairs spanning multiple storeys for more.

Finding stair footprints

It is not as trivial as it sounds to identify "area below 1.90" under a stair. The basic rule used in AC is to "cut" the stair at 1.90 above floor level, and compare this footprint to the total footprint of the stair:

Figur 4 - Cutting the stair
Projecting the entire stair area and the intersections with cut plane to the XY plane yields us the following polygons:

• The area A1-A2-C2-C1-A1 is below 1.90 in height, or covered by the stair (first steps).
• The area C1-C2-D2-D1-C1 is under the stair and above 1.90 in free height.

Text step is to add the area according to the 60cnm-rule in [NS3940-V]. Since the «cut line» C1-C2 is a straight line this is fairly straight forward:

Figur 6 – Kompensering for 60cm -regel

Area of stair itself

Refer to the following figure from NS3940:

Figure 7 – Stair area
The rentable area ("Målbart Areal) is subtracted from the (projected) area of the stair/ramp. The remaining area is considered the area of the stair/ramp – marked "Resterende blir areal for trapp" in figure. Now the references do not tell us which room the "Areal for trap" belongs to, and who is "paying" for this area.
In the area calculator this is put together with the handling of openings:

• "Measurable area (BTA)" in the figure is included in the tha space at bottom of the stair – that is the space that «owns» the area under the stair.
• "Areal for trapp" in the figure is included in the «necessary opening for stair» I for the space at top of stair, that is, the space in the storey above.

It is a bit challenging to define and calculate «necessary opbning for stair» automatically, hance we apply the following:

• Necessary opening for stair is set to the (projected) area of stair itself
• Ideally, we should remove pieces remaining of the opening with a width less than 60 cm [NS3940]. However, since these remains can get a fairly complex shape, is it not easy to define what «width less than 60 cm « really is in these cases. A manual verification is therefore needed.

More details are supplied in following sections:

Stairs with irregular cut lines

Innhold
It is not as trivial as it sounds to identify "area below 1.90" under a stair. An important concept here is the "cut line" which is the common line between projected area (footprint) below 1.90 and projected area (footprint) above 1.90. For the simplest case this is a straight line. However, if the stair geometry is more complex the cut line will also be more complex. The reason for this could be as simple as a stir built as two beams bearing the foundation for the steps:
For the simplest case this is a straight line. However, if the stair geometry is more complex the cut line will also be more complex:

Figur 5 - Approximating the cut line
This approximation will probably only work if railings, fences etc is not taken into account. Until further notice, it is believed to be possible to filter these out by type.
If the stair includes railings and/or it is an open stair, the footprint becomes more complex:

Figur 6 - open stair with railings
The footprint of stair below 1.90 is lower left in figure. In this case it even contains "holes"; if these introduce problems it should be possibly to apply an algorithm to remove holes. Imposing the footprint for entire stair introduces several possibilities for points C1 and C2 and start/(en d of "cut line":

Figur 7 - footprints for symmetrical stair
As long as at least one of the C points can be found the previous algorithm should work. To ensure symmetry we can run algorithm twice, in CW and CCW directions, and pick first point found in both cases.
If it turns out to be problematic finding C points, we could apply an algorithm for making polygon convex on the stair-below-90 footprint:

Figure 8 – Apply convex footprint enclosing line
If the stair is "asymmetric" around its midpoint line, for example included railings but on only one side, the approach will not work the same way:

Figure 9 – Asymmetrical case
The line between identified points C1-1 and C2-1 are no longer a proper "cut line". TODO: Currently, a simple solution for this case is not identified. We must rely on stairs not including railings, or being symmetrical, and use C1C2 as cut line.
To enable polygon edit, and simplify the further calculation (60-cm rule), we should always perform this "cut line approximation" step.
When the "cut line" is approximated as a straight line the "60 cm rule" is rather easy to implement:

Figur 12 - Adding 60cm compensation
An acceptable and simple approximation is to create a rectangle with the cut line E1E2 as one of the sides, a parallel F1F1 as opposite side, the two other sides being 60cm in length.
There is one exception, for small curved/spiral staircases, where the compensation polygon will be a triangle version of the above: E1E2F1.

Footprints of spiral / curved stair

A spiral stair, as any other stair, is cut at each storey floor level and 1.90 above floor level as earlier described. The "cut line" forms the side of a rectangle or a triangle. The triangle approach is used if the "inner radius" if the stair is small enough, but at the time of writing it is still to decide how to find this radius and what limit value we should practice.

Figure 2 - rentable area under spiral stair alternative 2
C1-C2 is the cut line as for a straight stair, in principle it should not be any different to find, if the curves are projected and converted into polylines.

Free form stair

We might come across "free form stairs", a general approach is to "cut" the stair by bottom and top (next storey floor) and by again by 1.90 height and top, creating footprints, and analyze these in 2D. See figure below:

Figur 13 - Free form stair

Staircases and openings

Staircase spanning multiple storeys in an opening

If a staircase spans multiple storeys, it must be "cut" into separate sections, each section starting at floor level for the storey and ending at floor level for next storey, as shown with red lines in following figure:

Figure 3 - Multi storey stair with opening around stair
In this case the stair goes through an opening in each storey, the opening being smaller in top storey. There are three distinct polygons available, refer to figure below:

Figure 14 – up and down staircase with large hole
Note that the projected area (footprint) of stair can go outside the opening. Also we have assumed that the area under S1 going up is an opening. In rules below BTA0 stands for the BTA before compensating for staircase. Until decided otherwise, the following rules apply:

• In bottom storey U1 there is a floor under the stair, so rules for "staircase starting in this storey" apply.
• In the middle storeys 01 and 02 the footprint of the stair going DOWN from this storey is included in the BTA, while rest of the opening is NOT included.
  • BTA = BTA0 – Op + S0p
• In top storey 03 likewise, the footprint of the stair going DOWN from this storey is included in the BTA, while rest of the opening is NOT included.
  • BTA = BTA0 – Op + S0p

Staircase spanning multiple storeys with floor under stair

Another possibility is no opening under the staircase going up. As for previous case, the staircase spans multiple storeys, it must be "cut" into separate sections, each section starting at floor level for the storey and ending at floor level for next storey, as shown with red lines in following figure:

Figure 4 - staircase with floor under stair in each storey

Figure 15 – up and down staircase with small hole
Note that the opening area – the green line in figure – in this case only is for the stair leading UP to this storey. Hence following rules apply, BTA0 stands for the BTA before compensating for staircase:

• In bottom storey U1 there is a floor under the stair, so rules for "staircase starting in this storey" apply.
• In the middle storeys 01 and 02 there is a floor under stair, rules for "area under stair" is applied for the stair going UP from here. In addition the footprint of the stair going DOWN to level below is included in the BTA. Rest of opening is NOT included in total BTA.
  • BTA = BTA0 – Op - S1u + S0p
• In top storey 03 the footprint of the stair going DOWN from this storey is included in the BTA, while rest of the opening is NOT included.
  • BTA = BTA0 – Op + S0p

Spiral staircase spanning multiple storeys

The rules in previous section even hold for a spiral staircase:

Figure 16 – spiral staircase
Here there are no under-the-staircase areas in any but bottom storey. Rules become:

• In bottom storey U1 there is a floor under the stair, so rules for "staircase starting in this storey" apply.
• In the middle storeys 01 and 02 the footprint of the stair going DOWN from this storey is included in the BTA, while rest of the opening is NOT included.
  • BTA = BTA0 – Op + S0p
• In top storey 03 likewise, the footprint of the stair going DOWN from this storey is included in the BTA, while rest of the opening is NOT included.
  • BTA = BTA0 – Op + S0p

Again BTA0 stands for the BTA before compensating for staircase.

Some additional considerations

Special attention must be paid to cases like:

• Small staircases only leading from one floor level to another floor level within the same room.
• Such stairs should be ignored.