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

NOTE Typically, these are relatively smaller facilities such as buildings where constant factors are agreed on a project.

HISTORY New entity in IFC4X3_ADD1

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: $$ \theta=arctan\left(\frac{\text}{\text}\right) $$
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

$$ \begin x'\\ y'\\ z' \end = \begin cos\theta & -sin\theta & 0 \\ sin\theta & cos\theta & 0 \\ 0 & 0 & 1 \end \cdot \begin \text & 0 & 0 \\ 0 & \text & 0 \\ 0 & 0 & \text \end \cdot \begin \text & 0 & 0 \\ 0 & \text & 0 \\ 0 & 0 & \text \end \cdot \begin x \\ y \\ z \end + \begin \text \\ \text \\ \text \end $$

b) equation form

$$ \begin x' &= \text \cdot \text \cdot cos\theta \cdot x-\text \cdot \text \cdot sin\theta \cdot y+\text \\ y' &= \text \cdot \text \cdot sin\theta \cdot x+\text \cdot \text \cdot cos\theta \cdot y+\text \\ z' &= \text \cdot \text \cdot z+\text \end $$