# 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:

$$\lambda(u)=C+A\sqrt{\pi}(\int_{0}^{u}\cos(\pi\frac{At^2}{2|A|})dt\ x+\int_{0}^{u}\sin(\pi\frac{At^2}{2|A|})dt\ y)$$

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:

$$\kappa=\frac{As}{|A^3|}, \rho=\frac{1}{\kappa}$$

## 8.9.3.19.4 Formal representation

ENTITY IfcClothoid
SUBTYPE OF (IfcSpiral);
ClothoidConstant : IfcLengthMeasure;
END_ENTITY;