computes integers sin_num, cos_num and denom, such
that sin_num/denom approximates the sine of direction
$$(dirx,diry$$). The difference between the sine and
the approximating rational is bounded by eps_num/eps_den.

Precondition:

eps_num$$ 0.

Implementation

The approximation is based on Farey sequences as described in
the rational rotation method presented by Canny and Ressler at the
8th SoCG 1992. We use a slower version which needs no division operation
in the approximation.