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Copy pathclut.rs
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248 lines (232 loc) · 8.91 KB
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//! Multi-dimensional colour lookup tables (ICC CLUTs) with tetrahedral interpolation.
//!
//! Grid layout follows ICC.1: the first input channel varies slowest, output values of one
//! node are stored together. 3-input tables use tetrahedral interpola
10BC8
tion (Sakamoto 1980 /
//! Kasson et al. 1995); 4-input tables interpolate linearly along the first input between
//! two tetrahedral evaluations; other input counts use multilinear interpolation.
/// Maximum number of input or output channels of a CLUT.
pub const MAX_CHANNELS: usize = 15;
#[derive(Clone, Debug, PartialEq)]
pub struct Clut {
pub inputs: usize,
pub outputs: usize,
/// Grid points per input dimension (each ≥ 2, or 1 for a degenerate dimension).
pub grid: Vec<usize>,
/// Normalised node values, `outputs` per node.
pub data: Vec<f32>,
strides: Vec<usize>,
}
impl Clut {
/// Builds a table from node data. Panics if `data` has the wrong length.
pub fn new(grid: Vec<usize>, outputs: usize, data: Vec<f32>) -> Self {
let inputs = grid.len();
assert!((1..=MAX_CHANNELS).contains(&inputs) && (1..=MAX_CHANNELS).contains(&outputs), "bad CLUT dimensions");
let mut strides = vec![0usize; inputs];
let mut s = outputs;
for i in (0..inputs).rev() {
strides[i] = s;
s *= grid[i].max(1);
}
assert_eq!(data.len(), s, "CLUT data length");
Clut { inputs, outputs, grid, data, strides }
}
/// Number of nodes.
pub fn nodes(&self) -> usize {
self.data.len() / self.outputs
}
/// Builds a table by sampling `f` at every node (inputs normalised to `[0, 1]`).
pub fn sample(grid: Vec<usize>, outputs: usize, mut f: impl FnMut(&[f32], &mut [f32])) -> Self {
let inputs = grid.len();
let total: usize = grid.iter().product();
let mut data = vec![0.0f32; total * outputs];
let mut idx = vec![0usize; inputs];
let mut inp = vec![0.0f32; inputs];
for node in 0..total {
let mut rem = node;
for d in (0..inputs).rev() {
idx[d] = rem % grid[d];
rem /= grid[d];
}
for d in 0..inputs {
inp[d] = if grid[d] > 1 { idx[d] as f32 / (grid[d] - 1) as f32 } else { 0.0 };
}
f(&inp, &mut data[node * outputs..(node + 1) * outputs]);
}
Clut::new(grid, outputs, data)
}
#[inline]
fn locate(&self, d: usize, v: f32) -> (usize, f32, usize) {
let n = self.grid[d];
if n < 2 {
return (0, 0.0, 0);
}
let p = v.clamp(0.0, 1.0) * (n - 1) as f32;
let i = (p as usize).min(n - 2);
(i * self.strides[d], p - i as f32, self.strides[d])
}
/// Interpolates at `input` (`inputs` values) into `out` (`outputs` values).
#[inline]
pub fn eval(&self, input: &[f32], out: &mut [f32]) {
match self.inputs {
1 => self.eval1(input[0], out),
3 => {
let (b0, r0, s0) = self.locate(0, input[0]);
let (b1, r1, s1) = self.locate(1, input[1]);
let (b2, r2, s2) = self.locate(2, input[2]);
self.tetra(b0 + b1 + b2, [s0, s1, s2], [r0, r1, r2], out);
}
4 => {
let (b0, r0, s0) = self.locate(0, input[0]);
let (b1, r1, s1) = self.locate(1, input[1]);
let (b2, r2, s2) = self.locate(2, input[2]);
let (b3, r3, s3) = self.locate(3, input[3]);
let base = b0 + b1 + b2 + b3;
let mut lo = [0.0f32; MAX_CHANNELS];
self.tetra(base, [s1, s2, s3], [r1, r2, r3], &mut lo[..self.outputs]);
if r0 > 0.0 && s0 > 0 {
let mut hi = [0.0f32; MAX_CHANNELS];
self.tetra(base + s0, [s1, s2, s3], [r1, r2, r3], &mut hi[..self.outputs]);
for (o, (l, h)) in out.iter_mut().zip(lo.iter().zip(&hi)) {
*o = l + (h - l) * r0;
}
} else {
out[..self.outputs].copy_from_slice(&lo[..self.outputs]);
}
}
_ => self.eval_multilinear(input, out),
}
}
fn eval1(&self, v: f32, out: &mut [f32]) {
let (b, r, s) = self.locate(0, v);
for (k, o) in out.iter_mut().enumerate().take(self.outputs) {
let a = self.data[b + k];
let c = if s > 0 { self.data[b + s + k] } else { a };
*o = a + (c - a) * r;
}
}
/// Tetrahedral interpolation inside one cube of three dimensions.
#[inline]
fn tetra(&self, base: usize, s: [usize; 3], r: [f32; 3], out: &mut [f32]) {
let d = &self.data;
let [rx, ry, rz] = r;
let [sx, sy, sz] = s;
let c000 = base;
let c100 = base + sx;
let c010 = base + sy;
let c001 = base + sz;
let c110 = base + sx + sy;
let c101 = base + sx + sz;
let c011 = base + sy + sz;
let c111 = base + sx + sy + sz;
// Pick the tetrahedron containing (rx, ry, rz) and the path through the cube corners.
let (p1, p2, p3, w1, w2, w3) = if rx >= ry {
if ry >= rz {
(c100, c110, c111, rx, ry, rz)
} else if rx >= rz {
(c100, c101, c111, rx, rz, ry)
} else {
(c001, c101, c111, rz, rx, ry)
}
} else if rx >= rz {
(c010, c110, c111, ry, rx, rz)
} else if ry >= rz {
(c010, c011, c111, ry, rz, rx)
} else {
(c001, c011, c111, rz, ry, rx)
};
for (k, o) in out.iter_mut().enumerate().take(self.outputs) {
let v0 = d[c000 + k];
let v1 = d[p1 + k];
let v2 = d[p2 + k];
let v3 = d[p3 + k];
*o = v0 + (v1 - v0) * w1 + (v2 - v1) * w2 + (v3 - v2) * w3;
}
}
/// Trilinear interpolation (3 inputs), kept as a reference for accuracy comparisons.
pub fn eval_trilinear(&self, input: &[f32], out: &mut [f32]) {
assert_eq!(self.inputs, 3);
self.eval_multilinear(input, out);
}
/// Multilinear interpolation over all 2^n cube corners.
pub fn eval_multilinear(&self, input: &[f32], out: &mut [f32]) {
let n = self.inputs;
let mut base = 0usize;
let mut r = [0.0f32; MAX_CHANNELS];
let mut s = [0usize; MAX_CHANNELS];
for d in 0..n {
let (b, rr, ss) = self.locate(d, input[d]);
base += b;
r[d] = rr;
s[d] = ss;
}
let o = self.outputs;
out[..o].iter_mut().for_each(|v| *v = 0.0);
for corner in 0..(1usize << n) {
let mut w = 1.0f32;
let mut off = base;
for d in 0..n {
if corner & (1 << d) != 0 {
w *= r[d];
off += s[d];
} else {
w *= 1.0 - r[d];
}
}
if w == 0.0 {
continue;
}
for (k, v) in out[..o].iter_mut().enumerate() {
*v += w * self.data[off + k];
}
}
}
}
#[cfg(test)]
mod tests {
use super::*;
fn f3(p: &[f32], o: &mut [f32]) {
o[0] = p[0] * 0.5 + p[1] * 0.3 + p[2] * 0.2;
o[1] = p[0] * p[1];
o[2] = (p[2] * 3.0).sin() * 0.5 + 0.5;
}
#[test]
fn exact_on_nodes_and_linear_functions() {
let c = Clut::sample(vec![5, 5, 5], 3, f3);
let mut o = [0.0; 3];
c.eval(&[0.25, 0.5, 0.75], &mut o);
let mut w = [0.0; 3];
f3(&[0.25, 0.5, 0.75], &mut w);
for i in 0..3 {
assert!((o[i] - w[i]).abs() < 1e-6);
}
// Linear function is reproduced exactly anywhere.
c.eval(&[0.13, 0.77, 0.41], &mut o);
assert!((o[0] - (0.13 * 0.5 + 0.77 * 0.3 + 0.41 * 0.2)).abs() < 1e-6);
}
#[test]
fn four_d_and_multilinear_agree_on_linear() {
let f = |p: &[f32], o: &mut [f32]| o[0] = 0.1 * p[0] + 0.2 * p[1] + 0.3 * p[2] + 0.4 * p[3];
let c = Clut::sample(vec![3, 4, 5, 6], 1, f);
let mut a = [0.0];
let mut b = [0.0];
for p in [[0.1f32, 0.9, 0.3, 0.7], [1.0, 0.0, 0.5, 0.5], [0.33, 0.66, 0.99, 0.01]] {
c.eval(&p, &mut a);
c.eval_multilinear(&p, &mut b);
let want = 0.1 * p[0] + 0.2 * p[1] + 0.3 * p[2] + 0.4 * p[3];
assert!((a[0] - want).abs() < 1e-5 && (b[0] - want).abs() < 1e-5);
}
}
#[test]
fn one_and_two_d() {
let c = Clut::sample(vec![3], 2, |p, o| {
o[0] = p[0];
o[1] = 1.0 - p[0];
});
let mut o = [0.0; 2];
c.eval(&[0.25], &mut o);
assert!((o[0] - 0.25).abs() < 1e-6 && (o[1] - 0.75).abs() < 1e-6);
let c = Clut::sample(vec![2, 2], 1, |p, o| o[0] = p[0] + p[1]);
c.eval(&[0.5, 0.25], &mut o);
assert!((o[0] - 0.75).abs() < 1e-6);
}
}