Computing a rotation in interval arithmetic can lose tightness.
Instead of computing
a cos phi + b sin phi
which doesn't account for the difference in phase in the two sinusoids,
it is better to use
sqrt (a² + b²) * cos ( phi - atan2(a,b) )
which correctly estimates the maximum amplitude of the sum to be
sqrt(a²+b²) instead of abs(a) + abs(b).
This seems to worsen the performance of the interval Newton method
at the moment, possibly due to the complexity of the new formula,
which involves computing atan(b/a). Further investigation is needed.
Now we evaluate Bézier curves using an AABB computation. This results
in tighter intervals, which means that the cusp-finding algorithm
is better behaved.
also includes the start of a way to observe which equations
are being solved, which should help with improving the performance of
the interval Newton method