I am a colorist in post production and I am working on tools that generally speaking transform colors. For this purpose I am looking to design a function that accommodates the following points.
$$(-\pi, 0);\; (-\frac{2\pi}{3}, -1);\; (-\frac{\pi}{3}, -0.5);\; (0, 0);\; (\frac{\pi}{3}; 0.5);\; (\frac{2\pi}{3}, 1); (\pi, 0)$$
The function should be continuous, easy to compute and as precise as possible. From the given points one can see that I am looking for something halfway between a sinus and a sawtooth curve.
This is what I found so far:
It is relatively close but not quite as precise as I would want it to be and I don't like the little bumps in the straight part of the curve between $-\frac{2\pi}{3}$ and $\frac{2\pi}{3}$.
Any help is greatly appreciated.