8.9.3.19 IfcClothoid
8.9.3.19.1 Semantic definition
A clothoid is a planar curve in the form of a spiral. This curve has the property that the curvature varies linearly with the arc length.
Interpretation of the data shall be as follows:
C = SELF\IfcSpiral.Position.Location
x = SELF\IfcSpiral.Position.P[1]
y = SELF\IfcSpiral.Position.P[2]
A = ClothoidConstant
The clothoid is parameterized as:
$$\lambda(u)=C+A\sqrt{\pi}(\int_{0}^{u}\cos(\pi\frac{At^2}{2A})dt\ x+\int_{0}^{u}\sin(\pi\frac{At^2}{2A})dt\ y)$$
The parametric range is: ∞ < u < ∞
The arc length s of the curve, from the point C, is given by the formula:
$$s=Au\sqrt{\pi}$$
The curvature κ and radius of the curvature ρ, at any point of the curve, are related to the arc length s by the formulae:
$$\kappa=\frac{As}{A^3}, \rho=\frac{1}{\kappa}$$
The constant A, known as flatness or homothetic parameter of the clothoid, is specified as:
$$ A=\sqrt{LR}$$
where, L is the length measured from the inflection point; and R is the radius of the clothoid.
8.9.3.19.2 Entity inheritance

 IfcCurve
 IfcAnnotationFillArea
 IfcBooleanResult
 IfcBoundingBox
 IfcCartesianPointList
 IfcCartesianTransformationOperator
 IfcCsgPrimitive3D
 IfcDirection
 IfcFaceBasedSurfaceModel
 IfcFillAreaStyleHatching
 IfcFillAreaStyleTiles
 IfcGeometricSet
 IfcHalfSpaceSolid
 IfcLightSource
 IfcPlacement
 IfcPlanarExtent
 IfcPoint
 IfcSectionedSpine
 IfcSegment
 IfcShellBasedSurfaceModel
 IfcSolidModel
 IfcSurface
 IfcTessellatedItem
 IfcTextLiteral
 IfcVector
8.9.3.19.3 Attributes
#  Attribute  Type  Description 

IfcRepresentationItem (2)  
LayerAssignment  SET [0:1] OF IfcPresentationLayerAssignment FOR AssignedItems 
Assignment of the representation item to a single or multiple layer(s). The LayerAssignments can override a LayerAssignments of the IfcRepresentation it is used within the list of Items. 

StyledByItem  SET [0:1] OF IfcStyledItem FOR Item 
Reference to the IfcStyledItem that provides presentation information to the representation, e.g. a curve style, including colour and thickness to a geometric curve. 

IfcCurve (1)  
*  Dim  IfcDimensionCount 
This attribute is formally derived.
The space dimensionality of this abstract class, defined differently for all subtypes, i.e. for IfcLine, IfcConic and IfcBoundedCurve. 
IfcSpiral (1)  
1  Position  IfcAxis2Placement 
No description available. 
Click to show 4 hidden inherited attributes Click to hide 4 inherited attributes  
IfcClothoid (1)  
2  ClothoidConstant  IfcLengthMeasure 
The constant which defines the relationship between curvature and arc length for the curve. 
8.9.3.19.4 Examples
8.9.3.19.5 Formal representation
ENTITY IfcClothoid
SUBTYPE OF (IfcSpiral);
ClothoidConstant : IfcLengthMeasure;
END_ENTITY;