//! A structured curvilinear 2-D patch: the mesh a body-fitted overset
//! patch lives on (`docs/overset_metal_campaign.md` §2.1, A-P0).
//!
//! Cells are indexed `(k, i)` with `i` along the body (`s`, possibly
//! periodic — an O-grid) and `k` across it (`n`, from the wall outward).
//! Nodes are stored as `(nn + 1) × (ns + 1)` coordinates even when the
//! patch is periodic: column `ns` is then a copy of column `0` (bitwise
//! when the periodic shift is zero), so every cell reads its four corners
//! from its own columns and the seam is never a special case.
//!
//! The `(s, n)` frame must be right-handed (every cell's corner loop
//! `(k,i) (k,i+1) (k+1,i+1) (k+1,i)` counter-clockwise, positive area): for
//! an O-grid with `n` pointing away from the body that means `s` runs
//! CLOCKWISE around it — walk the outline with the body on your right.
//!
//! Every face carries its geometry once: the area vector `S_f` (length ×
//! unit normal, oriented toward +s for s-faces and +n for n-faces), the
//! owner (−side) and neighbour (+side) cells, the centre-to-centre vector
//! `d_f` with the periodic shift already applied, and the owner's linear
//! interpolation weight. Boundary faces have one of owner/neighbour
//! missing and `d_f` spanning cell centre ↔ face centre, still oriented +.
//!
//! The metrics are what the collocated solver consumes; the solver never
//! touches node coordinates. Neighbour access goes through the face
//! lists, so the seam and the boundaries are handled here, once.

use crate::error::{CfdError, CfdResult};

/// One face of the patch with its geometry.
#[derive(Debug, Clone, Copy)]
pub struct Face {
    /// End nodes (flat node indices), ordered so that `S_f` is the
    /// +90° rotation of `n0 → n1` for s-faces and the −90° rotation for
    /// n-faces; the solver's tangential derivative runs `n0 → n1`.
    pub n0: usize,
    /// See `n0`.
    pub n1: usize,
    /// Face centre (midpoint of the two nodes).
    pub centre: [f64; 2],
    /// Area vector `S_f`: length × unit normal, oriented +s or +n.
    pub s: [f64; 2],
    /// Cell on the − side of the face (`None` on a − boundary).
    pub owner: Option<usize>,
    /// Cell on the + side of the face (`None` on a + boundary).
    pub neigh: Option<usize>,
    /// Owner centre → neighbour centre (periodic shift applied), or cell
    /// centre ↔ face centre on a boundary; always oriented +.
    pub d: [f64; 2],
    /// Owner weight for linear interpolation: `φ_f = w φ_P + (1 − w) φ_N`,
    /// distance-weighted. `1` on boundary faces (the interior cell).
    pub w: f64,
}

/// Which boundary of the patch a boundary face lies on.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum Side {
    /// `k = 0`: the body side (the wall of an O-grid).
    Inner,
    /// `k = nn`: the far side (the overlap ring of an O-grid).
    Outer,
    /// `i = 0` (non-periodic only).
    SStart,
    /// `i = ns` (non-periodic only).
    SEnd,
}

/// A structured curvilinear patch with precomputed metrics.
#[derive(Debug, Clone)]
pub struct PatchMesh {
    ns: usize,
    nn: usize,
    periodic: Option<[f64; 2]>,
    x: Vec<f64>,
    y: Vec<f64>,
    centre: Vec<[f64; 2]>,
    area: Vec<f64>,
    faces: Vec<Face>,
    n_sfaces: usize,
}

impl PatchMesh {
    /// Build a patch from node coordinates laid out `(nn + 1)` rows of
    /// `(ns + 1)` columns, flat index `k * (ns + 1) + i`.
    ///
    /// `periodic = Some(shift)` closes the s direction: column `ns` must
    /// equal column `0 + shift` (to 1e-12 relative; when `shift` is zero
    /// it is overwritten with a bitwise copy so the seam face metrics
    /// agree exactly). Every cell must have positive area.
    pub fn from_nodes(
        ns: usize,
        nn: usize,
        mut x: Vec<f64>,
        mut y: Vec<f64>,
        periodic: Option<[f64; 2]>,
    ) -> CfdResult<Self> {
        let cols = ns + 1;
        if ns < 4 || nn < 2 {
            return Err(CfdError::mesh(format!(
                "patch needs ns >= 4 and nn >= 2, got ns = {ns}, nn = {nn}"
            )));
        }
        if x.len() != (nn + 1) * cols || y.len() != x.len() {
            return Err(CfdError::mesh(format!(
                "patch nodes: expected {} coordinates, got {} / {}",
                (nn + 1) * cols,
                x.len(),
                y.len()
            )));
        }
        if let Some(shift) = periodic {
            let scale = 1e-12
                * x.iter()
                    .chain(y.iter())
                    .fold(0.0_f64, |m, v| m.max(v.abs()))
                    .max(1.0);
            for k in 0..=nn {
                let (a, b) = (k * cols, k * cols + ns);
                let (ex, ey) = (x[a] + shift[0], y[a] + shift[1]);
                if (x[b] - ex).abs() > scale || (y[b] - ey).abs() > scale {
                    return Err(CfdError::mesh(format!(
                        "periodic patch: node column {ns} != column 0 + shift at row {k}"
                    )));
                }
                if shift == [0.0, 0.0] {
                    x[b] = x[a];
                    y[b] = y[a];
                }
            }
        }

        let mut mesh = Self {
            ns,
            nn,
            periodic,
            x,
            y,
            centre: Vec::new(),
            area: Vec::new(),
            faces: Vec::new(),
            n_sfaces: 0,
        };
        mesh.build_cells()?;
        mesh.build_faces();
        Ok(mesh)
    }

    /// Cells along the body.
    pub fn ns(&self) -> usize {
        self.ns
    }
    /// Cells across the patch.
    pub fn nn(&self) -> usize {
        self.nn
    }
    /// Number of cells.
    pub fn cell_count(&self) -> usize {
        self.ns * self.nn
    }
    /// Whether the s direction is closed, and its translation.
    pub fn periodic(&self) -> Option<[f64; 2]> {
        self.periodic
    }
    /// Flat cell index of `(k, i)`.
    pub fn cell(&self, k: usize, i: usize) -> usize {
        k * self.ns + i
    }
    /// `(k, i)` of a flat cell index.
    pub fn cell_ki(&self, c: usize) -> (usize, usize) {
        (c / self.ns, c % self.ns)
    }
    /// Flat node index of row `k`, column `i`.
    pub fn node(&self, k: usize, i: usize) -> usize {
        k * (self.ns + 1) + i
    }
    /// Node coordinates.
    /// `[x_min, x_max, y_min, y_max]` over the nodes.
    pub fn bounding_box(&self) -> [f64; 4] {
        let (mut b, mut first) = ([0.0; 4], true);
        for (&x, &y) in self.x.iter().zip(&self.y) {
            if first {
                b = [x, x, y, y];
                first = false;
            } else {
                b[0] = b[0].min(x);
                b[1] = b[1].max(x);
                b[2] = b[2].min(y);
                b[3] = b[3].max(y);
            }
        }
        b
    }

    pub fn node_xy(&self, n: usize) -> [f64; 2] {
        [self.x[n], self.y[n]]
    }
    /// Cell centroid.
    pub fn centre(&self, c: usize) -> [f64; 2] {
        self.centre[c]
    }
    /// Cell area.
    pub fn area(&self, c: usize) -> f64 {
        self.area[c]
    }
    /// All faces: s-faces first, then n-faces.
    pub fn faces(&self) -> &[Face] {
        &self.faces
    }
    /// Number of s-faces per row.
    pub fn sfaces_per_row(&self) -> usize {
        if self.periodic.is_some() {
            self.ns
        } else {
            self.ns + 1
        }
    }
    /// Face index of the s-face at node column `i` in cell row `k`
    /// (`i` in `0..sfaces_per_row()`; for a periodic patch column 0 is the
    /// seam, adjacent to cells `ns − 1` and `0`).
    pub fn sface(&self, k: usize, i: usize) -> usize {
        k * self.sfaces_per_row() + i
    }
    /// Face index of the n-face at node row `k` in cell column `i`
    /// (`k` in `0..=nn`).
    pub fn nface(&self, k: usize, i: usize) -> usize {
        self.n_sfaces + k * self.ns + i
    }
    /// Whether face `f` is an s-face.
    pub fn is_sface(&self, f: usize) -> bool {
        f < self.n_sfaces
    }
    /// The four faces of a cell with the sign that makes `sign · S_f` the
    /// outward area vector: `[west, east, south, north]`.
    pub fn cell_faces(&self, c: usize) -> [(usize, f64); 4] {
        let (k, i) = self.cell_ki(c);
        let east = if self.periodic.is_some() {
            (i + 1) % self.ns
        } else {
            i + 1
        };
        [
            (self.sface(k, i), -1.0),
            (self.sface(k, east), 1.0),
            (self.nface(k, i), -1.0),
            (self.nface(k + 1, i), 1.0),
        ]
    }
    /// Which boundary a face lies on, if any.
    pub fn side(&self, f: usize) -> Option<Side> {
        let face = &self.faces[f];
        match (face.owner, face.neigh) {
            (Some(_), Some(_)) => None,
            (None, Some(_)) => Some(if self.is_sface(f) {
                Side::SStart
            } else {
                Side::Inner
            }),
            (Some(_), None) => Some(if self.is_sface(f) {
                Side::SEnd
            } else {
                Side::Outer
            }),
            (None, None) => unreachable!("a face without cells"),
        }
    }
    /// The cells touching node `(k, i)` (2 to 4 of them; the seam node is
    /// resolved by wrapping when periodic).
    pub fn node_cells(&self, k: usize, i: usize) -> Vec<usize> {
        let mut out = Vec::with_capacity(4);
        let rows = [k.checked_sub(1), (k < self.nn).then_some(k)];
        let cols: [Option<usize>; 2] = if self.periodic.is_some() {
            let i = i % self.ns;
            [Some((i + self.ns - 1) % self.ns), Some(i)]
        } else {
            [i.checked_sub(1), (i < self.ns).then_some(i)]
        };
        for r in rows.into_iter().flatten() {
            for c in cols.into_iter().flatten() {
                out.push(self.cell(r, c));
            }
        }
        out
    }
    /// The interior cell of a boundary face.
    pub fn boundary_cell(&self, f: usize) -> usize {
        let face = &self.faces[f];
        face.owner.or(face.neigh).expect("a face without cells")
    }

    /// Mesh quality check: positive areas (built in), interior
    /// non-orthogonality angle below `max_angle_deg`, and no collapsed
    /// faces. The overset's later shapes (the cylinder–flag junction) must
    /// fail here loudly rather than produce a NaN in the solver.
    pub fn validate(&self, max_angle_deg: f64) -> Result<(), String> {
        let cos_min = max_angle_deg.to_radians().cos();
        for (f, face) in self.faces.iter().enumerate() {
            let len = (face.s[0] * face.s[0] + face.s[1] * face.s[1]).sqrt();
            let dl = (face.d[0] * face.d[0] + face.d[1] * face.d[1]).sqrt();
            if len == 0.0 || dl == 0.0 {
                return Err(format!(
                    "face {f} is collapsed (|S| = {len:.3e}, |d| = {dl:.3e})"
                ));
            }
            if face.owner.is_some() && face.neigh.is_some() {
                let cos = (face.s[0] * face.d[0] + face.s[1] * face.d[1]) / (len * dl);
                if cos < cos_min {
                    return Err(format!(
                        "face {f}: non-orthogonality {:.1}° exceeds {max_angle_deg}°",
                        cos.clamp(-1.0, 1.0).acos().to_degrees()
                    ));
                }
            }
        }
        Ok(())
    }

    fn build_cells(&mut self) -> CfdResult<()> {
        let (ns, nn) = (self.ns, self.nn);
        self.centre = vec![[0.0; 2]; ns * nn];
        self.area = vec![0.0; ns * nn];
        for k in 0..nn {
            for i in 0..ns {
                // Corners counter-clockwise: (k,i) (k,i+1) (k+1,i+1) (k+1,i).
                let n = [
                    self.node(k, i),
                    self.node(k, i + 1),
                    self.node(k + 1, i + 1),
                    self.node(k + 1, i),
                ];
                let (mut a2, mut cx, mut cy) = (0.0, 0.0, 0.0);
                for q in 0..4 {
                    let (p0, p1) = (n[q], n[(q + 1) % 4]);
                    let cross = self.x[p0] * self.y[p1] - self.x[p1] * self.y[p0];
                    a2 += cross;
                    cx += (self.x[p0] + self.x[p1]) * cross;
                    cy += (self.y[p0] + self.y[p1]) * cross;
                }
                if a2 <= 0.0 {
                    return Err(CfdError::mesh(format!(
                        "patch cell ({k}, {i}) has non-positive area {:.3e}",
                        0.5 * a2
                    )));
                }
                let c = self.cell(k, i);
                self.area[c] = 0.5 * a2;
                self.centre[c] = [cx / (3.0 * a2), cy / (3.0 * a2)];
            }
        }
        Ok(())
    }

    fn build_faces(&mut self) {
        let (ns, nn) = (self.ns, self.nn);
        let per_row = self.sfaces_per_row();
        let mut faces = Vec::with_capacity(nn * per_row + (nn + 1) * ns);

        // s-faces: at node column i, between cells (k, i-1) and (k, i).
        for k in 0..nn {
            for i in 0..per_row {
                let (owner, neigh, col) = if self.periodic.is_some() {
                    if i == 0 {
                        // The seam: geometry from column ns (owner's side),
                        // the neighbour (cell 0) sits one period ahead.
                        (Some(self.cell(k, ns - 1)), Some(self.cell(k, 0)), ns)
                    } else {
                        (Some(self.cell(k, i - 1)), Some(self.cell(k, i)), i)
                    }
                } else {
                    (
                        (i > 0).then(|| self.cell(k, i - 1)),
                        (i < ns).then(|| self.cell(k, i)),
                        i,
                    )
                };
                let (n0, n1) = (self.node(k, col), self.node(k + 1, col));
                let t = [self.x[n1] - self.x[n0], self.y[n1] - self.y[n0]];
                let s = [t[1], -t[0]];
                let seam_shift = if self.periodic.is_some() && i == 0 {
                    self.periodic.unwrap_or([0.0; 2])
                } else {
                    [0.0; 2]
                };
                faces.push(self.make_face(n0, n1, s, owner, neigh, seam_shift));
            }
        }
        self.n_sfaces = faces.len();

        // n-faces: at node row k, between cells (k-1, i) and (k, i).
        for k in 0..=nn {
            for i in 0..ns {
                let owner = (k > 0).then(|| self.cell(k - 1, i));
                let neigh = (k < nn).then(|| self.cell(k, i));
                let (n0, n1) = (self.node(k, i), self.node(k, i + 1));
                let t = [self.x[n1] - self.x[n0], self.y[n1] - self.y[n0]];
                let s = [-t[1], t[0]];
                faces.push(self.make_face(n0, n1, s, owner, neigh, [0.0; 2]));
            }
        }
        self.faces = faces;
    }

    fn make_face(
        &self,
        n0: usize,
        n1: usize,
        s: [f64; 2],
        owner: Option<usize>,
        neigh: Option<usize>,
        shift: [f64; 2],
    ) -> Face {
        let centre = [
            0.5 * (self.x[n0] + self.x[n1]),
            0.5 * (self.y[n0] + self.y[n1]),
        ];
        let (d, w) = match (owner, neigh) {
            (Some(p), Some(q)) => {
                let cp = self.centre[p];
                let cq = [self.centre[q][0] + shift[0], self.centre[q][1] + shift[1]];
                let dp = ((centre[0] - cp[0]).powi(2) + (centre[1] - cp[1]).powi(2)).sqrt();
                let dq = ((cq[0] - centre[0]).powi(2) + (cq[1] - centre[1]).powi(2)).sqrt();
                ([cq[0] - cp[0], cq[1] - cp[1]], dq / (dp + dq))
            }
            (Some(p), None) => {
                let cp = self.centre[p];
                ([centre[0] - cp[0], centre[1] - cp[1]], 1.0)
            }
            (None, Some(q)) => {
                let cq = self.centre[q];
                ([cq[0] - centre[0], cq[1] - centre[1]], 1.0)
            }
            (None, None) => unreachable!("a face without cells"),
        };
        Face {
            n0,
            n1,
            centre,
            s,
            owner,
            neigh,
            d,
            w,
        }
    }
}