There are quite a few more points included on contuatia 004.jpg. The curve does not impart torsion. It can be represented on a plane.
The principle axises for the spiral are z=4 and y=(7/10)(root 2)(r) - this can be seen in the contuatia 004.jpg)
I admit, I am not ready to unravel the "mysteries" of Cornu's Spiral. Luckily, this curve is not a Cornu Spiral. It is Logarithimic. The center is displaced from the principle axises, by z=4 and y=(7/10)(root 2)r.