What's best shape for linear concentrated solar panel?

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I found 3 shapes which are suitable for concentrated solar panel.

1. Semicircle - first thing that comes to ones mind.
It's a simple shape, the position of the focal point is obvious.

2. Parabolic mirror
A bit more difficult shape.


3. Compound parabolic mirror

Compound parabolic mirror has an advantage over the parabolic mirror in acceptance angle. Collector doesn't necessarily need to track sun, because it's able to receive sunlight from a range of angles.

Is there any other shape, that might have interesting properties for the purpose of solar collector?
I found many DIY designs with semicircle mirrors. And many scientific papers with parabolic mirrors.
What is the advantage of parabolic mirrors are over semicircle mirrors?