# 8.9.3.61 IfcSecondOrderPolynomialSpiral

## 8.9.3.61.1 Semantic definition

The IfcSecondOrderPolynomialSpiral is a specialization of IfcSpiral. The curvature κ and radius of the curvature ρ, at any point of the curve, are related to the arc length s by the second order formulae:

Interpretation of the parameters:

C = SELF\IfcSpiral.Position.Location x = SELF\IfcSpiral.Position.P[1] y = SELF\IfcSpiral.Position.P[2] A2 = QuadraticTerm A1 = LinearTerm A0 = ContantTerm

and the second order polynomial spiral is parameterized as:

where:

and the parametric range is: -∞ < u < ∞.

## 8.9.3.61.4 Formal representation

ENTITY IfcSecondOrderPolynomialSpiral
SUBTYPE OF (IfcSpiral);
END_ENTITY;