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$\sqrt{1 - (-1 + x\bmod 2)^2}\cdot\operatorname{sign}(-2 + x\bmod 4)$

Like half-circles connected to each other to look like waves:

plot http://vi-server.org/vi/_/func.png

Its plot looks smooth, but the function is actually not smooth.

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    @Jonas T, Why ugly? It's even continuous. And circle is not ugly, so that semi-circle is unlikely to be ugly, and this is the most logical way to make a "semicircle function".2011-04-28

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