use crate::geom::Point;

#[derive(Debug, Clone, Copy, PartialEq)]
pub struct Arc {
    pub start: Point,
    pub mid: Point,
    pub end: Point,
}

impl Arc {
    pub const fn new(start: Point, mid: Point, end: Point) -> Self {
        Self { start, mid, end }
    }

    pub fn centre_and_radius(&self) -> Option<(Point, f64)> {
        let (ax, ay) = (self.start.x, self.start.y);
        let (bx, by) = (self.mid.x, self.mid.y);
        let (cx, cy) = (self.end.x, self.end.y);
        let d = 2.0 * (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by));
        if d.abs() < f64::EPSILON {
            return None;
        }
        let ax2_ay2 = ax * ax + ay * ay;
        let bx2_by2 = bx * bx + by * by;
        let cx2_cy2 = cx * cx + cy * cy;
        let ux = (ax2_ay2 * (by - cy) + bx2_by2 * (cy - ay) + cx2_cy2 * (ay - by)) / d;
        let uy = (ax2_ay2 * (cx - bx) + bx2_by2 * (ax - cx) + cx2_cy2 * (bx - ax)) / d;
        let centre = Point::new(ux, uy);
        let r = centre.distance_to(self.start);
        Some((centre, r))
    }

    /// Sweep direction from start → end through mid, as +1 (CCW) or -1 (CW).
    pub fn sweep_sign(&self) -> f64 {
        let (ax, ay) = (self.start.x, self.start.y);
        let (bx, by) = (self.mid.x, self.mid.y);
        let (cx, cy) = (self.end.x, self.end.y);
        let cross = (bx - ax) * (cy - ay) - (by - ay) * (cx - ax);
        if cross >= 0.0 { 1.0 } else { -1.0 }
    }
}