//! S2-3 pre-flight (host): the flag + cylinder body at ny 62 — the mask
//! builds, its cut geometry closes, the counts and the build time (the
//! moving body's per-step host rebuild cost) are recorded.
use rtx_cfd::solvers::incompressible::embedded3::{Body, Boundaries, Grid, Mask, Side};

const H: f64 = 0.41;
const FLAG_X0: f64 = 0.6;
const FLAG_LEN: f64 = 0.35;
const FLAG_HALF: f64 = 0.01;
const FLAG_SPAN: f64 = 0.2;
const AMP: f64 = 0.084;
const BETA_L: f64 = 1.875_104_069;

fn mode(s: f64) -> f64 {
    let b = BETA_L;
    let sigma = (b.sinh() - b.sin()) / (b.cosh() + b.cos());
    let phi = |s: f64| (b * s).cosh() - (b * s).cos() - sigma * ((b * s).sinh() - (b * s).sin());
    phi(s) / phi(1.0)
}

fn flag_2d(x: f64, y: f64, phase: f64) -> f64 {
    let n = 40;
    let mut best = f64::INFINITY;
    let point = |m: usize| {
        let s = m as f64 / n as f64;
        (FLAG_X0 + s * FLAG_LEN, 0.2 + AMP * mode(s) * phase)
    };
    for m in 0..n {
        let (ax, ay) = point(m);
        let (bx, by) = point(m + 1);
        let (ex, ey) = (bx - ax, by - ay);
        let u = (((x - ax) * ex + (y - ay) * ey) / (ex * ex + ey * ey)).clamp(0.0, 1.0);
        let d = ((x - ax - u * ex).powi(2) + (y - ay - u * ey).powi(2)).sqrt();
        best = best.min(d);
    }
    best - FLAG_HALF
}

fn flag_3d(x: f64, y: f64, z: f64, phase: f64, r: f64) -> f64 {
    let d2 = flag_2d(x, y, phase);
    let q1 = d2 + r;
    let q2 = (z - 0.5 * H).abs() - 0.5 * FLAG_SPAN + r;
    (q1.max(0.0).powi(2) + q2.max(0.0).powi(2)).sqrt() + q1.max(q2).min(0.0) - r
}

#[test]
fn flag_body_builds_at_ny_62() {
    let ny = 62;
    let h = H / ny as f64;
    let nx = (2.5 / h).round() as usize;
    let g = Grid::cubic(nx, ny, ny, h);
    let cyl = |x: f64, y: f64| ((x - 0.2_f64).powi(2) + (y - 0.2_f64).powi(2)).sqrt() - 0.05;
    for phase in [0.0, 1.0] {
        let body = Body::from_sdf(move |x, y, z, _t| cyl(x, y).min(flag_3d(x, y, z, phase, h)));
        let b = Boundaries {
            x1: Side::PressureOutlet,
            ..Boundaries::default()
        };
        let start = std::time::Instant::now();
        let mask = Mask::build_cut(&body, g, 0.0, b).expect("mask");
        let build = start.elapsed().as_secs_f64();
        let cut = mask.cut().unwrap();
        let (area, closure) = cut.wall_area_and_closure();
        let solid = g.cells() - mask.fluid_cells();
        println!(
            "  phase {phase}: {} cells, {} fluid, {solid} solid, {} merged; wall area {area:.4} m² (cylinder 0.129 + flag ~0.156), closure {:.2e}; build {build:.2} s",
            g.cells(),
            mask.fluid_cells(),
            mask.merged_cells(),
            (closure[0].powi(2) + closure[1].powi(2) + closure[2].powi(2)).sqrt()
        );
        assert!(solid > 1000 && mask.fluid_cells() > g.cells() / 2);
        assert!((closure[0].powi(2) + closure[1].powi(2) + closure[2].powi(2)).sqrt() < 1e-9);
    }
}