Function arc_ring_area

pub fn arc_ring_area(ring: &ArcRing) -> f64

Signed area enclosed by an arc ring.

Positive is counter-clockwise. The value is the polygon area over the vertices plus, for each arc edge, the signed area of its circular segment:

theta = 4 * atan(bulge)                 signed included angle
R     = chord * (1 + bulge^2) / (4 |bulge|)
extra = R^2 * (theta - sin theta) / 2   signed by theta

Keeping theta signed is what makes a reversed ring negate exactly: a clockwise circle must return -pi r^2, not +pi r^2. An unsigned segment term gets the disc right and the reversed disc wrong.