You might be able to speed it up considerably by adding 2a. Continue with next iteration unless the turning number of the sequence of curves is a whole number.

You might be able to speed it up considerably by adding 2a. Continue with next iteration unless the turning number of the sequence of curves is a whole number. You add 1/8 to the turning number for each clockwise curve and subtract 1/8 for each CCW (for numerical stability you would rather add of subtract 1 and check for multiples of 8).