If f(x) - a non-negative continuous function, so the number of lattice points in area $a\leq x \leq b$, $0 < y \leq f(x)$ is equal to $$\sum_{a\leq x \leq b}[f(x)]$$ where [f(x)] - integer part of f(x).
How could I apply this formula for a curve in polar coordinates? For example, $r = k \cdot cos(3\phi), k > 0$?
What books or articles could I read about this theme?