rotate method
override
Rotates the shape by the given angle (in radians) around the origin.
If origin is omitted, rotates around the shape's centroid.
Implementation
@override
Ellipse rotate(double angle, [Point<num>? origin]) {
// For an axis-aligned Ellipse, rotating perfectly requires transforming it into a general polygon
// or tracking an orientation angle. To maintain mathematical purity of our CRTP
// without expanding state unnecessarily, we rotate its geometric center around the origin.
final rotOrigin = origin ?? centroid;
final ox = rotOrigin.x.toDouble();
final oy = rotOrigin.y.toDouble();
final cx = _center.x.toDouble();
final cy = _center.y.toDouble();
final cosA = math.cos(angle);
final sinA = math.sin(angle);
final nx = cosA * (cx - ox) - sinA * (cy - oy) + ox;
final ny = sinA * (cx - ox) + cosA * (cy - oy) + oy;
return Ellipse(semiMajorAxis: semiMajorAxis, semiMinorAxis: semiMinorAxis, center: Point(x: nx, y: ny));
}