8.18.3.7 IfcMapConversionScaled

8.18.3.7.1 Semantic definition

An IfcMapConversionScaled is a type of IfcMapConversion that supplies factors for coordinate conversion. The usage is restricted to when factors are explicitly exchanged.

For this transformation, IfcMapConversionScaled data are used for:

1. a scaling of the three axes (x,y,z), by the same IfcMapConversionScaled.Scale
2. a multiplication of the x-axis by IfcMapConversionScaled.FactorX
3. a multiplication of the y-axis by IfcMapConversionScaled.FactorY
4. a multiplication of the z-axis by IfcMapConversionScaled.FactorZ
5. followed by an anti-clockwise rotation about the z-axis of θ, where: $$ \theta=arctan\left(\frac{\text{XAxisOrdinate}}{\text{XAxisAbscissa}}\right) $$
6. and then a translation in (x,y,z) of IfcMapConversionScaled.Eastings, IfcMapConversionScaled.Northings, IfcMapConversionScaled.OrthogonalHeight.

Equations

Below are the relevant equations for IfcMapConversionScaled. The equations are given: a) in transformation matrix form, useful for programmers to understand the exact sequence of operations and b) in a simplified equation form, which is sufficient for calculating a single point.

a) matrix form

$$ \begin{bmatrix} x'\\ y'\\ z' \end{bmatrix} = \begin{bmatrix} cos\theta & -sin\theta & 0 \\ sin\theta & cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \cdot \begin{bmatrix} \text{FactorX} & 0 & 0 \\ 0 & \text{FactorY} & 0 \\ 0 & 0 & \text{FactorZ} \end{bmatrix} \cdot \begin{bmatrix} \text{Scale} & 0 & 0 \\ 0 & \text{Scale} & 0 \\ 0 & 0 & \text{Scale} \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix} + \begin{bmatrix} \text{Eastings} \\ \text{Northings} \\ \text{OrthogonalHeight} \end{bmatrix} $$

b) equation form

$$ \begin{align} x' &= \text{Scale} \cdot \text{FactorX} \cdot cos\theta \cdot x-\text{Scale} \cdot \text{FactorY} \cdot sin\theta \cdot y+\text{Eastings} \\ y' &= \text{Scale} \cdot \text{FactorX} \cdot sin\theta \cdot x+\text{Scale} \cdot \text{FactorY} \cdot cos\theta \cdot y+\text{Northings} \\ z' &= \text{Scale} \cdot \text{FactorZ} \cdot z+\text{OrthogonalHeight} \end{align} $$

8.18.3.7.2 Entity inheritance

1. • IfcCoordinateOperation
2. • IfcMapConversion
   • IfcRigidOperation
3. • IfcMapConversionScaled

8.18.3.7.3 Attributes

#	Attribute	Type	Description
IfcCoordinateOperation (2)
1	SourceCRS	IfcCoordinateReferenceSystemSelect	Source coordinate reference system for the operation.
2	TargetCRS	IfcCoordinateReferenceSystem	Target coordinate reference system for the operation.
IfcMapConversion (6)
3	Eastings	IfcLengthMeasure	Specifies the location along the easting of the coordinate system of the target map coordinate reference system.
4	Northings	IfcLengthMeasure	Specifies the location along the northing of the coordinate system of the target map coordinate reference system.
5	OrthogonalHeight	IfcLengthMeasure	Orthogonal height relative to the vertical datum specified.
6	XAxisAbscissa	OPTIONAL IfcReal	Specifies the value along the easting axis of the end point of a vector indicating the position of the local x axis of the engineering coordinate reference system.
7	XAxisOrdinate	OPTIONAL IfcReal	Specifies the value along the northing axis of the end point of a vector indicating the position of the local x axis of the engineering coordinate reference system. XAxisAbscissa it provides the direction of the local x axis within the horizontal plane of the map coordinate system.
8	Scale	OPTIONAL IfcReal	Scale to be used, when the units of the CRS are not identical to the units of the engineering coordinate system. If omitted, the value of 1.0 is assumed.
Click to show 8 hidden inherited attributes Click to hide 8 inherited attributes
IfcMapConversionScaled (3)
9	FactorX	IfcReal	No description available.
10	FactorY	IfcReal	No description available.
11	FactorZ	IfcReal	No description available.

8.18.3.7.4 Formal representation

ENTITY IfcMapConversionScaled
SUBTYPE OF (IfcMapConversion);
FactorX : IfcReal;
FactorY : IfcReal;
FactorZ : IfcReal;
END_ENTITY;

8.18.3.7.5 References

• IfcMapConversion