8_LinearPlacement.md

Chapter 8 — Linear Placement

8.0 Introduction

Most elements in the built environment for infrastructure works are located relative to an alignment rather than by absolute coordinates. A bridge pier, a drainage inlet, a light pole, a traffic sign — all are described in traditional engineering plans by where they fall along a road or railway centerline, how far they sit to the left or right of that centerline, and how high above (or below) a reference elevation they stand. This intuitive “station, offset, elevation” system has been the language of civil engineers for over a century.

IfcLinearPlacement is the IFC mechanism that formalizes this concept in accordance with ISO 19148 Geographic information - Linear referencing. It places and orients an object relative to a basis curve — typically an alignment curve — using an IfcPointByDistanceExpression to define the location and IfcAxis2PlacementLinear to define the axis directions.

This section covers:

• The concept of linear placement and how it maps from traditional engineering practice into IFC.
• The IFC class hierarchy: IfcLinearPlacement, IfcAxis2PlacementLinear, and IfcPointByDistanceExpression.
• How the local coordinate system is constructed at a placement point.
• Special cases: longitudinal offset for unreachable points, and placement along IfcOffsetCurveByDistances.
• ISO 19148 Linear Referencing and how its concepts relate to IFC linear placement.

8.1 Linear Placement in Practice

8.1.1 The Traditional Approach

Before examining IFC, it helps to recall how placement is expressed in conventional civil engineering plans. Two common cases illustrate the idea:

Case 1 — Bridge Pier (2D plan view). A bridge pier is located in plan by its station along the roadway alignment and its lateral offset from the centerline. A plan note might read “Pier 2 CL: Sta. 142+35.75, 12.50 ft Lt.” The elevation of the pier top is read separately from a profile view. No absolute coordinates are needed; the alignment provides the reference frame.

Case 2 — Drainage Inlet (3D). A storm drain inlet is placed at Sta. 198+12.42, offset 18.0 ft right of centerline, with its top grate set at elevation 312.75 ft (NAVD88). Here all three spatial dimensions are given: station gives position along the alignment, lateral offset gives the transverse position, and the elevation fixes the vertical position independently of the alignment profile.

Both cases share the same structure: a distance along a reference curve, plus offsets from it. IfcLinearPlacement captures exactly this structure.

8.1.2 The IFC Object Graph

The IFC classes that implement linear placement form a short chain, shown in Figure 8.1.2-1.

Figure 8.1.2-1 — IFC object graph for linear placement.

The PlacementRelTo attribute of IfcLinearPlacement establishes the reference context. When it is omitted, the placement is measured from the start of the basis curve defined in IfcPointByDistanceExpression. This is the standard case when the basis curve is an alignment defined in the project coordinate system.

Figure 8.1.2-2 schematically represents the linear placement of a bridge pier and a drain inlet.

Figure 8.1.2-2 — Conceptual diagram showing a plan view of an alignment with a bridge pier placed at a station/offset and a drain inlet placed at station/offset/elevation.

8.2 IfcLinearPlacement and IfcAxis2PlacementLinear

IfcAxis2PlacementLinear performs two independent jobs:

1. Location — fixing a point in space, via Location (typed IfcPoint, but constrained by a WHERE rule to be IfcPointByDistanceExpression). The point is found by walking DistanceAlong a BasisCurve and then applying up to three offsets (§8.2.1).
2. Orientation — fixing the direction of the placement's local axes, via the optional Axis and RefDirection attributes (§8.3).

These two jobs are independent. The offsets that determine Location are measured in a frame derived directly from the geometry of BasisCurve at DistanceAlong — not from whatever Axis/RefDirection values are chosen for orientation. An implementation evaluates Location the same way regardless of how, or whether, Axis and RefDirection are supplied.

8.2.1 Distance Along the Basis Curve

IfcPointByDistanceExpression class has five key attributes:

Attribute	Type	Description
BasisCurve	IfcCurve	The curve relative to which the point's location is defined.
DistanceAlong	IfcCurveMeasureSelect	The parametric distance measured along the basis curve. Typically a plain IfcLengthMeasure.
OffsetLateral	OPTIONAL IfcLengthMeasure	Signed lateral offset. Positive to the left of the curve’s forward tangent; negative to the right (consistent with ISO 19148).
OffsetVertical	OPTIONAL IfcLengthMeasure	Signed vertical offset. Positive upward relative to BasisCurve.
OffsetLongitudinal	OPTIONAL IfcLengthMeasure	Signed offset in the tangent direction of the BasisCurve. See §8.2.1.1 for uses.

For a full 3D alignment (IfcGradientCurve or IfcSegmentedReferenceCurve), the DistanceAlong is measured along the horizontal projection of the 3D curve onto the global XY plane — that is, along the underlying IfcCompositeCurve that forms the basis of the 2.5D geometry and represents the plan view curve geometry. This is consistent with how stationing is defined in civil engineering: stationing is a horizontal measure.

The IfcPointByDistanceExpression.BasisCurve attribute is poorly named. This curve is the 3D alignment geometry curve composed from the 2D composite curves defining the 2.5D geometry. A better name for this attribute would be Directrix. This would be consistent with IfcSectionedSolidHorizontal.Directrix. The basis curve is the curve that forms the basis of the 2.5D geometry. This is the horizontal projection of IfcPointByDistanceExpression.BasisCurve onto a horizontal plane. Basis curve and IfcPointByDistanceExpression.BasisCurve are similarly named but have very different definitions. For this reason IfcPointByDistanceExpression.BasisCurve (or BasisCurve) is used when referring to the 3D curve and basis curve is used when referring to the 2D projection of the 3D curve onto a horizontal plane.

The three offsets are measured relative to a frame derived from BasisCurve itself at DistanceAlong — not relative to the Axis/RefDirection of the enclosing IfcAxis2PlacementLinear (§8.3). That curve-derived frame, shown in Figure 8.2.1-1, is defined as follows:

• Let T be the tangent to BasisCurve at DistanceAlong, pointing in the direction of increasing distance.
• OffsetLateral is measured perpendicular to T, in the horizontal plane (parallel to the global XY plane): positive to the left of T, negative to the right (ISO 19148 convention).
• OffsetVertical is measured perpendicular to T, within the vertical plane (the plane perpendicular to the global XY plane) containing T.
• OffsetLongitudinal is measured along T, applied last, from the point already displaced by OffsetLateral and OffsetVertical (see §8.2.1.1).

This is not the same as elevation. OffsetVertical is perpendicular to the tangent T, not to the global XY plane. When BasisCurve is horizontal at that point, the two happen to coincide, and OffsetVertical behaves exactly like a change in elevation. But on a graded alignment the tangent is inclined, so "perpendicular to the tangent" points partly sideways and partly up — OffsetVertical is not a pure elevation change. §8.3.3 works through a numeric example where confusing "perpendicular to the curve" with "vertical (elevation)" produces different placements.

Figure 8.2.1-1 — Offset directions used by IfcPointByDistanceExpression to locate a point P on an alignment, where T is the tangent to the alignment at P: OffsetLateral measured horizontal and perpendicular to T, OffsetVertical measured in the vertical plane containing T, and OffsetLongitudinal measured along T. The dashed path shows offset point Q constructed by applying OffsetLateral, then OffsetVertical, then OffsetLongitudinal, in that order.

8.2.1.1 Longitudinal Offset and Unreachable Points

What Is an Unreachable Point?

In plane geometry, every point off a smooth curve can be reached by some combination of distance along the curve plus a perpendicular offset. However, certain geometric configurations in horizontal alignment create locations that cannot be expressed as a station plus a purely transverse offset.

The classic example is an angle point — the intersection of two tangents in a horizontal alignment where no curve has been inserted. At an angle point, the curve has a sharp corner. A point located “outside” the angle — beyond the apex — lies in a zone where the perpendicular from the curve never reaches. This is depicted in Figure 8.2.1.1-1.

Figure 8.2.1.1-1 — Plan view showing two tangent lines meeting at an angle point (PI). The shaded region outside the angle cannot be reached by a station + lateral offset alone. An object in this region requires a longitudinal offset.

Using OffsetLongitudinal

IfcPointByDistanceExpression.OffsetLongitudinal provides the solution. A non-zero OffsetLongitudinal moves the placement point along T — the same tangent direction used to define the other offsets in §8.2.1 — after the lateral and vertical offsets are applied. The procedure is:

1. Locate the point on the basis curve at DistanceAlong, establish the corresponding point on the BasisCurve, and determine tangent T at that point.
2. Apply OffsetLateral perpendicular to T, in the horizontal plane.
3. Apply OffsetVertical perpendicular to T, within the vertical plane containing T.
4. Apply OffsetLongitudinal along T.

The resulting point is no longer “on” a perpendicular to the basis curve at DistanceAlong, but it is precisely located in 3D space.

Practical note: OffsetLongitudinal should be used only when necessary. For all ordinary station-offset placements, it should be omitted.

8.2.2 Stationing and DistanceAlong

Stationing is addressed comprehensively in Chapter 9. For the purposes of linear placement, the key point is that DistanceAlong is a geometric distance from the start of the basis curve, not a station label. These two quantities are related but not identical:

• Geometric distance begins at zero and increases continuously to the total length of the curve.
• Station value may begin at an arbitrary value (e.g., 10+00.00 = 1000 ft from some project reference), may include equation gaps or overlaps where stationing is reset, and may use different units (feet vs. meters).

When using IfcPointByDistanceExpression, supply the geometric distance, not the raw station label. If the alignment has an IfcReferent that defines the starting station, the geometric distance equals the station value minus the starting station value (adjusted for any station equations encountered along the way).

8.3 The Placement Coordinate System

§8.2 covered the first job of IfcAxis2PlacementLinear — fixing Location using offsets measured in a frame derived purely from BasisCurve's own geometry. This section covers the second, independent job: establishing the orientation of the placement's local axes via Axis and RefDirection. Nothing here changes how Location was computed in §8.2 — location and orientation are established independently, and an implementation must not let one influence the other.

8.3.1 Role of Axis and RefDirection

The orientation job of IfcAxis2PlacementLinear defines a local right-handed coordinate system at the placement point fixed in §8.2. Two optional attributes control that orientation:

Attribute	Role in local CS	Default
RefDirection	X-axis (forward direction)	Tangent to the 3D curve at Location
Axis	Z-axis (up direction)	See §8.3.2

The Y-axis is derived as the cross product of Axis × RefDirection (after normalization).

When Axis and RefDirection are both omitted, the implementation must supply defaults. This is the most common scenario and is described below.

8.3.2 Default Axis — An Open Issue

The ambiguity originates in how IfcAxis2PlacementLinear describes its optional attributes compared to its 3D counterpart. IfcAxis2Placement3D is explicit: its specification states that when Axis is omitted it defaults to (0, 0, 1) and when RefDirection is omitted it defaults to (1, 0, 0). No interpretation is required.

IfcAxis2PlacementLinear takes a different approach. Its specification states:

"Relative placement axes (Axis and RefDirection) are relative to the curve used for linear referencing provided in IfcPlacement.Location (IfcPointByDistanceExpression.BasisCurve), maintaining the relationship to the tangent of the curve."

This sentence says the axes are derived from the curve, not from global coordinates. The natural reading is that RefDirection defaults to the curve tangent — which implementations broadly agree on — and that Axis defaults to something perpendicular to that tangent in the general upward direction. On a flat alignment those two readings coincide: the upward perpendicular to a horizontal tangent is (0, 0, 1). On a graded alignment they diverge: "perpendicular to the 3D tangent in the upward direction" tilts with the grade and is no longer (0, 0, 1). The specification never resolves what "upward relative to the curve" concretely means, and that silence is the source of the ambiguity. A known open issue in the buildingSMART community tracks it (see IFC4.x-IF Issue #125 and IFC4.x-development Issue #732); a proposed resolution has been submitted as IFC4.x-development Pull Request #1118 but has not yet been accepted or merged.

Two interpretations exist in practice:

1. Axis = global Z = (0, 0, 1). The Z-axis is always vertical regardless of alignment slope. The X-axis follows the horizontal tangent direction even when the curve has a vertical grade. This is natural for plan-oriented placement and matches traditional station-offset-elevation thinking.
2. Axis = perpendicular to the IfcPointByDistanceExpression.BasisCurve tangent, in the vertical plane containing that tangent (the plane containing the tangent that is normal to the global XY plane). The Z-axis tilts with the grade of the alignment. The local X-axis is truly tangent to the 3D curve. This reading follows directly from the curve-relative language in the specification, and produces the same orientation that IfcExtrudedAreaSolid would use when sweeping along the same path.

The connection between interpretation 2 and the broader IFC linear referencing model is not incidental. When evaluating a point along a 3D curve such as IfcGradientCurve or IfcSegmentedReferenceCurve, the resulting coordinate frame at that point is derived from the curve itself — the tangent at the evaluation distance determines the local forward direction, and the normal plane at that point governs the transverse and vertical axes. This is the frame that implementations compute when moving along a 3D alignment, as illustrated in the discussions of vertical and cant alignment geometry in Chapters 3 and 4. The perpendicular-to-3D-tangent interpretation of Axis is most consistent with that model: both derive orientation from the same 3D curve tangent, so a placement using interpretation 2 produces a frame congruent with what an implementation computes when evaluating the directrix at the same distance.

The practical consequence of this ambiguity is graphically illustrated in §10.5.5 — Figure 10.5.5-2 shows the same IfcSectionedSolidHorizontal model with Axis omitted rendered by two viewers that adopted opposite defaults, producing visibly different geometry on a 10% grade.

8.3.3 Linear Placement Example

This example evaluates an IfcLinearPlacement for an object located along an alignment. The object is to be located at a DistanceAlong of 201.0 m and a lateral offset of 2.0 m. The object is to be located 2.5 m above the alignment, measured vertically, and is to be oriented vertically. The desired placement of the object is at (201.0, 2.0, 52.75).

The horizontal alignment is straight towards the East. The vertical alignment is a constant gradient at a slope of 0.25 and starts at elevation 0.0.

The gradient parameters for a slope of $0.25$ are $d_x = 0.9701425,\ d_y = 0.2425356$.

One option is to define the object's position relative to the gradient curve using horizontal and vertical offsets. The relevant IFC is:

#5208 = IFCGRADIENTCURVE(/*details omitted*/)
#5297 = IFCLINEARPLACEMENT($, #5303, $);
#5303 = IFCAXIS2PLACEMENTLINEAR(#5304, #5305, $);

/* Placement defined relative to gradient curve */
#5304 = IFCPOINTBYDISTANCEEXPRESSION(IFCLENGTHMEASURE(201.), 2., 2.5, $, #5208);

/* Explicitly defined Axis direction */
#5305 = IFCDIRECTION((0., 0., 1.));

The object will be oriented vertically because the IfcAxis2PlacementLinear.Axis is explicitly defined as (0,0,1). If IfcAxis2PlacementLinear.Axis is omitted, the default orientation of the object may depend on the implementation as discussed in §8.3.2.

The point on the gradient curve is:

$$x = 201.0$$ $$z = (201.0)\frac{(0.2425356)}{(0.9701425)} = 50.25$$

The vertical offset is perpendicular to the vertical gradient. The offset from the gradient curve point is:

$$\Delta x = (2.5)(-0.2425356) = -0.606$$ $$\Delta y = (2.5)(0.9701425) = 2.425$$

The resulting placement is:

$$x + \Delta x = 201.0 - 0.606 = 200.394$$ $$y + \Delta y = 50.25 + 2.425 = 52.675$$

The object's placement is (200.394, 2.0, 52.675). This is not the desired placement. The object is not in the correct location because OffsetVertical is measured perpendicular to the curve's tangent (§8.2.1), not as a pure elevation change — on this 0.25 gradient the two are not the same.

The approach to achieve the desired placement is to use an IfcLinearPlacement.PlacementRelTo with $z = 2.5$.

/* Local placement with z = 2.5. Linear placement is relative to this coordinate frame. */
#5139 = IFCLOCALPLACEMENT($, #5143);
#5140 = IFCDIRECTION((0., 0., 1.));
#5141 = IFCDIRECTION((1., 0., 0.));
#5142 = IFCCARTESIANPOINT((0., 0., 2.5));
#5143 = IFCAXIS2PLACEMENT3D(#5142, #5140, #5141);

#5208 = IFCGRADIENTCURVE(/*details omitted*/)

/* Linear placement relative to the local placement defined above. */
#5297 = IFCLINEARPLACEMENT(#5139, #5303, $);

#5303 = IFCAXIS2PLACEMENTLINEAR(#5304, #5305, $);

/* Placement defined relative to gradient curve. Note that vertical offset is omitted */
#5304 = IFCPOINTBYDISTANCEEXPRESSION(IFCLENGTHMEASURE(201.), 2., $, $, #5208);

/* Explicitly defined Axis direction */
#5305 = IFCDIRECTION((0., 0., 1.));

From before, the point on the gradient curve is:

$$x = 201.0,\quad z = 50.25$$

There is no vertical offset relative to the gradient curve. However, this point is relative to a local placement with $z = 2.5$. The elevation of the object is $50.25 + 2.5 = 52.75$.

The object's placement is (201.0, 2.0, 52.75).

In this approach, the location of the object relative to the gradient curve is treated as an incremental offset from the origin of the IfcLinearPlacement.PlacementRelTo coordinate system.

8.4 Fallback Cartesian Position

IfcLinearPlacement.CartesianPosition is an optional IfcAxis2Placement3D attribute that provides a fallback geometry placement for receiving applications that do not support linear placement. An importing application that does not implement linear placement evaluation can read the stored Cartesian frame directly, without evaluating any curve geometry.

The attribute is populated by the exporting application, which evaluates RelativePlacement against the alignment geometry and stores the resulting absolute 3D frame in the project coordinate system before writing the file. The buildingSMART Validation Service treats CartesianPosition as a best-practice requirement: a file that omits it will be flagged as not conforming to best practices, and a file that includes it must pass consistency checking — the origin and axes of CartesianPosition must match the evaluated result of RelativePlacement to within model tolerance. A mismatched fallback is worse than no fallback, because it silently places the object at the wrong location for receivers that fall back to the Cartesian frame.

8.5 Linear Placement along IfcOffsetCurveByDistances

IfcOffsetCurveByDistances is an interpolated curve defined by a series of offset values measured from a basis curve. The offset values at intermediate positions are linearly interpolated between the defined sample points, forming a piecewise-linear offset profile. This is used, for example, to define a road edge line whose lateral distance from the centerline varies gradually. Offset curves are comprehensively discussed in Chapter 5.

8.5.1 The Approximate Length Problem

Because IfcOffsetCurveByDistances is a sampled, interpolated curve rather than an analytically defined curve, its arc length is only approximate. The arc length depends on the density of the sample points along the curve: more sample points produce a more accurate length estimate, but the length is never exact for a truly curved basis.

This approximation has a critical consequence for linear placement: when IfcPointByDistanceExpression.BasisCurve is an IfcOffsetCurveByDistances, the DistanceAlong value cannot be mapped to a unique, precisely determined point on the curve. Two implementations with different sampling densities may compute slightly different positions for the same DistanceAlong value.

8.5.2 Recommendations

For applications requiring precise linear placement:

1. Prefer using the parent alignment (e.g., the IfcCompositeCurve representing the horizontal alignment) as the BasisCurve, and use OffsetLateral to account for any transverse offset from the centerline. This avoids the approximation problem entirely.
2. If placement along an offset curve is unavoidable, document the sampling density of the IfcOffsetCurveByDistances so that receivers can evaluate the precision of derived positions.
3. Do not rely on DistanceAlong values along an IfcOffsetCurveByDistances being reproducible across different software implementations.

8.6 ISO 19148 Linear Referencing

8.6.1 Background

ISO 19148 Geographic information — Linear referencing is the international standard that formalizes the concept of locating features along a linear element. IFC4x3’s infrastructure extensions draw on ISO 19148 concepts, and Pset_LinearReferencingMethod (applicable to IfcAlignment and IfcReferent) is defined in terms of ISO 19148.

Understanding the ISO 19148 model helps implementers correctly interpret DistanceAlong values, especially when data is exchanged between systems that use different linear referencing conventions.

8.6.2 Key ISO 19148 Concepts

Linear Referencing Method (LRM). An LRM defines the rules for measuring distance along a linear element. The most common types are:

LRM Type	Description	Highway Example
Absolute	Distance measured continuously from a fixed start point.	Route mileage from a state border.
Relative	Distance measured from a nominated referent (not the start).	“0.4 km past interchange 12.”
Interpolated Position	Location expressed as a fraction between two known referents.	Between mileposts 43 and 44.

Pset_LinearReferencingMethod records the LRM type (LRMType), its name (LRMName), and the units of measure (LRMUnit) for an alignment or referent element.

Referents and Milestones vs. Stationing. In European road practice, distance along a route is often expressed using kilometer posts (KP) or reference posts — physical markers at known locations. A KP system is a Relative or Reference Post LRM: distance is measured to the nearest upstream post, plus an offset. In North American highway practice, stationing is an Absolute LRM: every point on the alignment is assigned a cumulative distance from the project start, expressed as ccc+dd.dd (hundreds of feet) or in meters.

The key difference:

• Stationing (Absolute LRM): DistanceAlong in IFC closely matches the station value (after accounting for any starting station offset defined by an IfcReferent).
• KP / Reference Post (Relative LRM): DistanceAlong in IFC is always the absolute geometric distance from the curve start. A KP value must be converted to a geometric distance before use in IfcPointByDistanceExpression.

8.6.3 LRM Name Examples from ISO 19148 Annex C

ISO 19148 Annex C lists recognized LRM name aliases. Common examples include:

Name	Common Alias	Typical Region
milepoint	milepost, MP	USA, Canada
kilometer point	KP, PK	Europe, Latin America
chainage	ch	UK, Australia, India
reference post	RP	Rail, some roads

Pset_LinearReferencingMethod.LRMName should use one of these recognized names where possible for maximum interoperability.

8.6.4 Impact on DistanceAlong

Regardless of the LRM in use for labelling purposes, IfcPointByDistanceExpression.DistanceAlong is always the geometric distance from the start of BasisCurve. LRM labels (station values, KP values, etc.) are a display convention managed through IfcReferent and Pset_LinearReferencingMethod, not through DistanceAlong directly.

See Chapter 9 (Referents and Stationing) for a detailed treatment of how station labels are stored and how to convert between station labels and geometric distances.

8.7 Summary and Implementation Checklist

#	Item	Notes
1	Use IfcLinearPlacement for all infrastructure elements located relative to an alignment.	Prefer this over IfcLocalPlacement with absolute coordinates for alignment-relative objects.
2	Supply DistanceAlong as the geometric arc length from the start of BasisCurve.	Convert station labels to geometric distances first; use IfcReferent to record station label metadata.
3	Use signed OffsetLateral: positive = left, negative = right.	Consistent with ISO 19148 convention.
4	Do not assume OffsetVertical is a true elevation offset.	OffsetVertical is measured perpendicular to the curve's tangent (§8.2.1), which only equals elevation when the alignment is flat at that point. For a true vertical (elevation) offset on a graded alignment, place the object relative to a PlacementRelTo frame instead (see the worked example in §8.3.3).
5	Set Axis = (0,0,1) explicitly to remove ambiguity.	Do not rely on the default; the default is not unambiguously defined in the IFC schema.
6	Use OffsetLongitudinal only for geometrically unreachable points (e.g., outside an angle point).	For all ordinary placements, omit or set to zero.
7	Avoid using IfcOffsetCurveByDistances as BasisCurve for precise placement.	Use the parent alignment with OffsetLateral instead.
8	Record the LRM type and units in Pset_LinearReferencingMethod on the IfcAlignment.	Required for correct interpretation of IfcReferent stationing labels.
9	Provide CartesianPosition only when exchanging with applications that lack linear placement support; omit otherwise.	Regenerate it after any alignment geometry change; validate consistency with the buildingSMART Validation Service.