Correct polynomial spiral equations

[RickBrice]

Problem
The $\lambda(u)$ equations for IfcSecond, IfcThird, and IfcSeventhOrderPolynomialSpiral are incorrect. The equations are of the form:

$$\lambda(u) = C + \int_{0}^{u}\cos \theta(t) dt x \int_{0}^{u}\sin \theta(t) dt y$$

The integrals yield scalar values while C is a location with length units.

Solution(s)
I think the equation should be
$$\lambda(u) = C + L ( \int_{0}^{u}\cos \theta(t) dt x \int_{0}^{u}\sin \theta(t) dt y )$$
where $L$ is the arc length when $u=1.0$.

The documentation might also benefit from stating $u=1.0$ when $\theta=\frac{\pi}{2}$

Require schema changes?

• yes
• ✓ no
• don't know

Require documentation changes?

• ✓ yes
• no
• don't know

[RickBrice]

The hand calculations in issue #146 suggest that the integral equations may be correct, but there are likely other inaccuracies in the documented equations for the Ifc___PolynomialSpiralCurve types.

[RickBrice]

After learning of the correct repository for ifc rail unit tests, I am able to exactly match horizontal and vertical for the polynomial spirals. Have not yet compared unit test results with cant. I’ll close this issue with no changes required.

@peterrdf @apinzenoehler @evandroAlfieri