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//! Forward and backward differencing for structured grid edges.
use crate::block::Block;
use crate::Float;
/// Backward and forward difference pair: `(backward, forward)`.
/// Each is a displacement vector `[dx, dy, dz]`.
pub type DiffPair = ([Float; 3], [Float; 3]);
/// Differencing data at a single node on a 2D face.
#[derive(Clone, Debug)]
pub struct FaceDiff {
pub p: usize,
pub q: usize,
/// Backward and forward differences along p.
pub dp: DiffPair,
/// Backward and forward differences along q.
pub dq: DiffPair,
}
/// Differencing data at a single node in a 3D block.
#[derive(Clone, Debug)]
pub struct BlockDiff {
pub i: usize,
pub j: usize,
pub k: usize,
/// Backward and forward differences along i.
pub di: DiffPair,
/// Backward and forward differences along j.
pub dj: DiffPair,
/// Backward and forward differences along k.
pub dk: DiffPair,
}
/// Compute forward and backward differences along each direction for a 2D face.
///
/// `x`, `y`, `z` are flat arrays of length `pmax * qmax`, stored row-major
/// (p varies fastest within each row of q).
pub fn find_face_edges(
x: &[Float],
y: &[Float],
z: &[Float],
pmax: usize,
qmax: usize,
) -> Vec<FaceDiff> {
let idx = |p: usize, q: usize| -> usize { q * pmax + p };
let mut result = Vec::with_capacity(pmax * qmax);
for p in 0..pmax {
for q in 0..qmax {
let id = idx(p, q);
// dp: backward and forward along p
let dp_b = if p > 0 {
let prev = idx(p - 1, q);
[x[prev] - x[id], y[prev] - y[id], z[prev] - z[id]]
} else {
[0.0, 0.0, 0.0]
};
let dp_f = if p < pmax - 1 {
let next = idx(p + 1, q);
[x[next] - x[id], y[next] - y[id], z[next] - z[id]]
} else {
[0.0, 0.0, 0.0]
};
// dq: backward and forward along q
let dq_b = if q > 0 {
let prev = idx(p, q - 1);
[x[prev] - x[id], y[prev] - y[id], z[prev] - z[id]]
} else {
[0.0, 0.0, 0.0]
};
let dq_f = if q < qmax - 1 {
let next = idx(p, q + 1);
[x[next] - x[id], y[next] - y[id], z[next] - z[id]]
} else {
[0.0, 0.0, 0.0]
};
result.push(FaceDiff {
p,
q,
dp: (dp_b, dp_f),
dq: (dq_b, dq_f),
});
}
}
result
}
/// Compute forward and backward differences along each direction for a 3D block.
pub fn find_edges(block: &Block) -> Vec<BlockDiff> {
let (ni, nj, nk) = (block.imax, block.jmax, block.kmax);
let mut result = Vec::with_capacity(ni * nj * nk);
for i in 0..ni {
for j in 0..nj {
for k in 0..nk {
let (cx, cy, cz) = block.xyz(i, j, k);
// di: backward and forward along i
let di_b = if i > 0 {
let (px, py, pz) = block.xyz(i - 1, j, k);
[px - cx, py - cy, pz - cz]
} else {
[0.0, 0.0, 0.0]
};
let di_f = if i < ni - 1 {
let (px, py, pz) = block.xyz(i + 1, j, k);
[px - cx, py - cy, pz - cz]
} else {
[0.0, 0.0, 0.0]
};
// dj: backward and forward along j
let dj_b = if j > 0 {
let (px, py, pz) = block.xyz(i, j - 1, k);
[px - cx, py - cy, pz - cz]
} else {
[0.0, 0.0, 0.0]
};
let dj_f = if j < nj - 1 {
let (px, py, pz) = block.xyz(i, j + 1, k);
[px - cx, py - cy, pz - cz]
} else {
[0.0, 0.0, 0.0]
};
// dk: backward and forward along k
let dk_b = if k > 0 {
let (px, py, pz) = block.xyz(i, j, k - 1);
[px - cx, py - cy, pz - cz]
} else {
[0.0, 0.0, 0.0]
};
let dk_f = if k < nk - 1 {
let (px, py, pz) = block.xyz(i, j, k + 1);
[px - cx, py - cy, pz - cz]
} else {
[0.0, 0.0, 0.0]
};
result.push(BlockDiff {
i,
j,
k,
di: (di_b, di_f),
dj: (dj_b, dj_f),
dk: (dk_b, dk_f),
});
}
}
}
result
}