# 8.9.3.73 IfcThirdOrderPolynomialSpiral

## 8.9.3.73.1 Semantic definition

The IfcThirdOrderPolynomialSpiral 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 third order formulae:

Interpretation of the parameters:

C = SELF\IfcSpiral.Position.Location x = SELF\IfcSpiral.Position.P[1] y = SELF\IfcSpiral.Position.P[2] A3 = CubicTerm A2 = QuadraticTerm A1 = LinearTerm A0 = ContantTerm

and the third order polynomial spiral is parameterized as:

where:

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

## 8.9.3.73.4 Formal representation

ENTITY IfcThirdOrderPolynomialSpiral
SUBTYPE OF (IfcSpiral);
CubicTerm : IfcLengthMeasure;
LinearTerm : OPTIONAL IfcLengthMeasure;
ConstantTerm : OPTIONAL IfcLengthMeasure;
END_ENTITY;