If you compare the results generated by the numeric integration and the approximation, they are very different. The approximation compares will with other software so there is likely a problem with the equation of the clothoid
This is a more general approach than the Taylor Series approximation and is applicable to all the other spiral types. I stubbed out a functor for IfcSecondOrderPolynomialSpiral, but haven't tested it. The purpose is to show the concept.