//! The cut wall's closures beyond the first form (S2-4, S2-5): the
//! open-part centroid shifts of the cut faces and the spacing they give
//! the cross-direction diffusion (the default since S2-5), the exchange
//! distance toward solid neighbours, and the quadratic wall gradient.
use super::cutwall::CvGeometry;
use super::wall::Mask;

impl Mask {
    /// The shift of a face's open-part centroid from the face centre:
    /// `½h(1 − α)` along the wall normal's in-plane part, away from the
    /// body (zero for a full face or without the centroid diffusion). Read
    /// from the tables of [`Self::compute_face_shifts`].
    pub(super) fn face_shift(&self, c: usize, p: [i64; 3]) -> [f64; 3] {
        let (Some(t), Some(f)) = (self.face_shifts.as_ref(), self.lattice().face(c, p)) else {
            return [0.0; 3];
        };
        [t[c][3 * f], t[c][3 * f + 1], t[c][3 * f + 2]]
    }

    /// The per-face shift tables (three components interleaved).
    #[must_use]
    pub fn face_shift_tables(&self) -> Option<&[Vec<f64>; 3]> {
        self.face_shifts.as_ref()
    }

    /// Build the open-part centroid shifts of every cut face (S2-5).
    pub fn compute_face_shifts(&mut self) {
        let g = self.grid;
        let h = [g.dx, g.dy, g.dz];
        let lat = self.lattice();
        let sizes = [g.n_ufaces(), g.n_vfaces(), g.n_wfaces()];
        let mut tables = [
            vec![0.0; 3 * sizes[0]],
            vec![0.0; 3 * sizes[1]],
            vec![0.0; 3 * sizes[2]],
        ];
        for c in 0..3 {
            let (ni, nj, nk) = (
                g.nx + usize::from(c == 0),
                g.ny + usize::from(c == 1),
                g.nz + usize::from(c == 2),
            );
            for k in 0..nk {
                for j in 0..nj {
                    for i in 0..ni {
                        let p = [i as i64, j as i64, k as i64];
                        let Some(f) = lat.face(c, p) else { continue };
                        let Some(alpha) = self.aperture(c, p) else {
                            continue;
                        };
                        if alpha <= 0.0 || alpha >= 1.0 {
                            continue;
                        }
                        // Interior faces only (a control volume needs both cells).
                        let on_side = p[c] == 0 || p[c] as usize == [g.nx, g.ny, g.nz][c];
                        if on_side && !(c == 2 && self.periodic_z) {
                            continue;
                        }
                        let cv = self.cv_geometry(c, p);
                        let mut n = cv.wall;
                        n[c] = 0.0;
                        let a = (n[0] * n[0] + n[1] * n[1] + n[2] * n[2]).sqrt();
                        if a == 0.0 {
                            continue;
                        }
                        for d in 0..3 {
                            // `wall` points into the body: the open part lies the other way.
                            tables[c][3 * f + d] = -0.5 * h[d] * (1.0 - alpha) * n[d] / a;
                        }
                    }
                }
            }
        }
        self.face_shifts = Some(tables);
    }

    /// The distance over which a fluid face exchanges momentum with a solid
    /// neighbour face along `d`: the full spacing, or (S2-5) the axis
    /// distance from the open part's centroid to the wall, `min(h, d_f/|n_d|)`.
    pub(super) fn exchange_delta(&self, cv: &CvGeometry, d: usize) -> f64 {
        let h = [self.grid.dx, self.grid.dy, self.grid.dz][d];
        if !self.wall_exchange_axis {
            return h;
        }
        let a_w =
            (cv.wall[0] * cv.wall[0] + cv.wall[1] * cv.wall[1] + cv.wall[2] * cv.wall[2]).sqrt();
        if a_w == 0.0 {
            return h;
        }
        let n_d = cv.wall[d].abs() / a_w;
        if n_d < 1e-12 {
            return h;
        }
        (cv.distance / n_d).min(h)
    }

    /// The wall-gradient coefficients of the unknown face of component
    /// `c` at `p` with control volume `cv`: `u'(0) = c_1 (u_f − U_b) + c_2
    /// (u_n − U_b)` with `u_n` the face returned (one lattice step away
    /// from the body along the wall normal's dominant axis). Order 1, or
    /// no open neighbour: `(1/d_f, 0, None)`.
    pub(super) fn wall_gradient(
        &self,
        c: usize,
        p: [i64; 3],
        cv: &CvGeometry,
    ) -> (f64, f64, Option<usize>) {
        let linear = (1.0 / cv.distance, 0.0, None);
        if self.wall_order < 2 {
            return linear;
        }
        let a_w =
            (cv.wall[0] * cv.wall[0] + cv.wall[1] * cv.wall[1] + cv.wall[2] * cv.wall[2]).sqrt();
        if a_w == 0.0 {
            return linear;
        }
        let n = [cv.wall[0] / a_w, cv.wall[1] / a_w, cv.wall[2] / a_w];
        let mut d = 0;
        for k in 1..3 {
            if n[k].abs() > n[d].abs() {
                d = k;
            }
        }
        // `n` points into the body: step the other way.
        let mut q = p;
        q[d] -= if n[d] > 0.0 { 1 } else { -1 };
        let open = self.aperture(c, q).is_some_and(|a| a > 0.0);
        if !open {
            return linear;
        }
        let f = self.lattice().face(c, q).expect("open face");
        let h = [self.grid.dx, self.grid.dy, self.grid.dz];
        let d1 = cv.distance;
        let d2 = d1 + h[d] * n[d].abs();
        (d2 / (d1 * (d2 - d1)), -d1 / (d2 * (d2 - d1)), Some(f))
    }
}