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//! Rust port of the ESDT ("Euclidean Subpixel Distance Transform") algorithm.
//!
//!
//! This algorithm was originally published as the [`@use-gpu/glyph`](https://www.npmjs.com/package/@use-gpu/glyph)
//! `npm` package, and was described in <https://acko.net/blog/subpixel-distance-transform/>.
use crate::img::{Bitmap, Image2d, NDCursor, NDCursorExt as _, Unorm8};
// HACK(eddyb) only exists to allow toggling precision for testing purposes.
#[cfg(sdfer_use_f64_instead_of_f32)]
type f32 = f64;
#[derive(Copy, Clone, Debug)]
pub struct Params {
pub pad: usize,
pub radius: f32,
pub cutoff: f32,
pub solidify: bool,
pub preprocess: bool,
// FIXME(eddyb) implement.
// pub postprocess: bool,
}
impl Default for Params {
fn default() -> Self {
Self {
pad: 4,
radius: 3.0,
cutoff: 0.25,
solidify: true,
preprocess: false,
// FIXME(eddyb) implement.
// postprocess: false,
}
}
}
/// Opaque `struct` allowing buffer reuse between SDF computations, instead of
/// reallocating all the buffers every time.
#[derive(Default)]
pub struct ReusableBuffers(ReusableBuffers2d, ReusableBuffers1d);
// Convert grayscale glyph to SDF
pub fn glyph_to_sdf(
glyph: &mut Image2d<Unorm8, impl AsMut<[Unorm8]> + AsRef<[Unorm8]>>,
params: Params,
reuse_bufs: Option<ReusableBuffers>,
) -> (Image2d<Unorm8>, ReusableBuffers) {
if params.solidify {
solidify_alpha(glyph.reborrow_mut());
}
glyph_to_esdt(glyph.reborrow_mut(), params, reuse_bufs)
}
// Solidify semi-transparent areas
fn solidify_alpha(mut glyph: Image2d<Unorm8, &mut [Unorm8]>) {
let (w, h) = (glyph.width(), glyph.height());
let mut mask: Vec<u8> = vec![0; w * h];
let get_data = |x: isize, y: isize| {
if x >= 0 && (x as usize) < w && y >= 0 && (y as usize) < h {
glyph[(x as usize, y as usize)]
} else {
Unorm8::MIN
}
};
let mut masked = 0;
// Mask pixels whose alpha matches their 4 adjacent neighbors (within 16 steps)
// and who don't have black or white neighbors.
for y in 0..(h as isize) {
for x in 0..(w as isize) {
let o = (x as usize) + (y as usize) * w;
let a = get_data(x, y);
// FIXME(eddyb) audit all comparisons with `254` and try removing them.
if a == Unorm8::MIN || a >= Unorm8::from_bits(254) {
continue;
}
let l = get_data(x - 1, y);
let r = get_data(x + 1, y);
let t = get_data(x, y - 1);
let b = get_data(x, y + 1);
let (min, max) = [a, l, r, t, b]
.into_iter()
.map(|x| (x, x))
.reduce(|(a_min, a_max), (b_min, b_max)| (a_min.min(b_min), a_max.max(b_max)))
.unwrap();
let [a, min, max] = [a, min, max].map(Unorm8::to_bits);
// FIXME(eddyb) audit all comparisons with `254` and try removing them.
if (max - min) < 16 && min > 0 && max < 254 {
// Spread to 4 neighbors with max
mask[o - 1] = mask[o - 1].max(a);
mask[o - w] = mask[o - w].max(a);
mask[o] = a;
mask[o + 1] = mask[o + 1].max(a);
mask[o + w] = mask[o + w].max(a);
masked += 1;
}
}
}
if masked == 0 {
return;
}
let get_mask = |x, y| mask[y * w + x];
// Sample 3x3 area for alpha normalization factor
for y in 0..h {
for x in 0..w {
let a = &mut glyph[(x, y)];
// FIXME(eddyb) audit all comparisons with `254` and try removing them.
if *a == Unorm8::MIN || *a >= Unorm8::from_bits(254) {
continue;
}
let c = get_mask(x, y);
let l = get_mask(x - 1, y);
let r = get_mask(x + 1, y);
let t = get_mask(x, y - 1);
let b = get_mask(x, y + 1);
let tl = get_mask(x - 1, y - 1);
let tr = get_mask(x + 1, y - 1);
let bl = get_mask(x - 1, y + 1);
let br = get_mask(x + 1, y + 1);
let m = [c, l, r, t, b, tl, tr, bl, br]
.into_iter()
.find(|&x| x != 0)
.unwrap_or(0);
if m != 0 {
*a = Unorm8::from_bits((a.to_bits() as f32 / m as f32 * 255.0) as u8);
}
}
}
}
// Convert grayscale or color glyph to SDF using subpixel distance transform
fn glyph_to_esdt(
mut glyph: Image2d<Unorm8, &mut [Unorm8]>,
params: Params,
reuse_bufs: Option<ReusableBuffers>,
) -> (Image2d<Unorm8>, ReusableBuffers) {
// FIXME(eddyb) use `Params` itself directly in more places.
let Params {
pad,
radius,
cutoff,
solidify: _,
preprocess,
} = params;
let wp = glyph.width() + pad * 2;
let hp = glyph.height() + pad * 2;
let mut state = State::from_glyph(glyph.reborrow_mut(), params, reuse_bufs);
state.esdt_outer_and_inner(wp, hp);
// FIXME(eddyb) implement.
// if postprocess { state.relax_subpixel_offsets(glyph, pad); }
let mut sdf = Image2d::from_fn(wp, hp, |x, y| {
let i = y * wp + x;
let ReusableBuffers2d { xo, yo, xi, yi, .. } = &state.bufs_2d;
let outer = ((xo[i].powi(2) + yo[i].powi(2)).sqrt() - 0.5).max(0.0);
let inner = ((xi[i].powi(2) + yi[i].powi(2)).sqrt() - 0.5).max(0.0);
let d = if outer >= inner { outer } else { -inner };
Unorm8::encode(1.0 - (d / radius + cutoff))
});
if !preprocess {
paint_into_distance_field(&mut sdf, glyph.reborrow(), params);
}
(sdf, ReusableBuffers(state.bufs_2d, state.reuse_bufs_1d))
}
// Helpers
fn is_black(x: f32) -> bool {
x == 0.0
}
fn is_white(x: f32) -> bool {
x == 1.0
}
fn is_solid(x: f32) -> bool {
x == 0.0 || x == 1.0
}
// Paint original alpha channel into final SDF when gray
fn paint_into_distance_field(
sdf: &mut Image2d<Unorm8>,
glyph: Image2d<Unorm8, &[Unorm8]>,
params: Params,
) {
let Params {
pad,
radius,
cutoff,
..
} = params;
for y in 0..glyph.height() {
for x in 0..glyph.width() {
let a = glyph[(x, y)].decode();
if !is_solid(a) {
let d = 0.5 - a;
sdf[(x + pad, y + pad)] = Unorm8::encode(1.0 - (d / radius + cutoff));
}
}
}
}
/// 2D buffers, which get reused (see also `ReusableBuffers` itself).
#[derive(Default)]
struct ReusableBuffers2d {
// FIXME(eddyb) group `outer` with `{x,y}o`.
outer: Bitmap,
// FIXME(eddyb) group `inner` with `{x,y}i``.
inner: Bitmap,
xo: Vec<f32>,
yo: Vec<f32>,
xi: Vec<f32>,
yi: Vec<f32>,
}
struct State {
// FIXME(eddyb) do the grouping suggested in `ReusableBuffers2d`, to have
// `outer` and `inner` fields in here, to use instead of `ReusableBuffers2d`.
bufs_2d: ReusableBuffers2d,
reuse_bufs_1d: ReusableBuffers1d,
}
impl State {
fn from_glyph(
mut glyph: Image2d<Unorm8, &mut [Unorm8]>,
params: Params,
reuse_bufs: Option<ReusableBuffers>,
) -> Self {
let Params {
pad,
// FIXME(eddyb) should this still be taken as a separate `bool`?
preprocess: relax,
..
} = params;
let wp = glyph.width() + pad * 2;
let hp = glyph.height() + pad * 2;
let np = wp * hp;
let ReusableBuffers(bufs_2d, reuse_bufs_1d) = reuse_bufs.unwrap_or_default();
let mut state = Self {
bufs_2d,
reuse_bufs_1d,
};
let ReusableBuffers2d {
outer,
inner,
xo,
yo,
xi,
yi,
} = &mut state.bufs_2d;
outer.resize_and_fill_with(wp, hp, true);
inner.resize_and_fill_with(wp, hp, false);
for buf2d in [&mut *xo, yo, xi, yi] {
buf2d.clear();
buf2d.resize(np, 0.0);
}
for y in 0..glyph.height() {
for x in 0..glyph.width() {
let a = &mut glyph[(x, y)];
if *a == Unorm8::MIN {
continue;
}
// FIXME(eddyb) audit all comparisons with `254` and try removing them,
// especially this step that modifies the `glyph` itself.
if *a >= Unorm8::from_bits(254) {
// Fix for bad rasterizer rounding
*a = Unorm8::MAX;
outer.at(x + pad, y + pad).set(false);
inner.at(x + pad, y + pad).set(true);
} else {
outer.at(x + pad, y + pad).set(false);
inner.at(x + pad, y + pad).set(false);
}
}
}
//
// Generate subpixel offsets for all border pixels
//
let get_data = |x: isize, y: isize| {
if x >= 0 && (x as usize) < glyph.width() && y >= 0 && (y as usize) < glyph.height() {
glyph[(x as usize, y as usize)].decode()
} else {
0.0
}
};
// Make vector from pixel center to nearest boundary
for y in 0..(glyph.height() as isize) {
for x in 0..(glyph.width() as isize) {
let c = get_data(x, y);
// NOTE(eddyb) `j - 1` (X-) / `j - wp` (Y-) positive (`pad >= 1`).
let j = ((y as usize) + pad) * wp + (x as usize) + pad;
if !is_solid(c) {
let dc = c - 0.5;
// NOTE(eddyb) l(eft) r(ight) t(op) b(ottom)
let l = get_data(x - 1, y);
let r = get_data(x + 1, y);
let t = get_data(x, y - 1);
let b = get_data(x, y + 1);
let tl = get_data(x - 1, y - 1);
let tr = get_data(x + 1, y - 1);
let bl = get_data(x - 1, y + 1);
let br = get_data(x + 1, y + 1);
let ll = (tl + l * 2.0 + bl) / 4.0;
let rr = (tr + r * 2.0 + br) / 4.0;
let tt = (tl + t * 2.0 + tr) / 4.0;
let bb = (bl + b * 2.0 + br) / 4.0;
let (min, max) = [l, r, t, b, tl, tr, bl, br]
.into_iter()
.map(|x| (x, x))
.reduce(|(a_min, a_max), (b_min, b_max)| {
(a_min.min(b_min), a_max.max(b_max))
})
.unwrap();
if min > 0.0 {
// Interior creases
inner.at(x as usize + pad, y as usize + pad).set(true);
continue;
}
if max < 1.0 {
// Exterior creases
outer.at(x as usize + pad, y as usize + pad).set(true);
continue;
}
let mut dx = rr - ll;
let mut dy = bb - tt;
let dl = 1.0 / (dx.powi(2) + dy.powi(2)).sqrt();
dx *= dl;
dy *= dl;
xo[j] = -dc * dx;
yo[j] = -dc * dy;
} else if is_white(c) {
// NOTE(eddyb) l(eft) r(ight) t(op) b(ottom)
let l = get_data(x - 1, y);
let r = get_data(x + 1, y);
let t = get_data(x, y - 1);
let b = get_data(x, y + 1);
if is_black(l) {
xo[j - 1] = 0.4999;
outer.at(x as usize + pad - 1, y as usize + pad).set(false);
inner.at(x as usize + pad - 1, y as usize + pad).set(false);
}
if is_black(r) {
xo[j + 1] = -0.4999;
outer.at(x as usize + pad + 1, y as usize + pad).set(false);
inner.at(x as usize + pad + 1, y as usize + pad).set(false);
}
if is_black(t) {
yo[j - wp] = 0.4999;
outer.at(x as usize + pad, y as usize + pad - 1).set(false);
inner.at(x as usize + pad, y as usize + pad - 1).set(false);
}
if is_black(b) {
yo[j + wp] = -0.4999;
outer.at(x as usize + pad, y as usize + pad + 1).set(false);
inner.at(x as usize + pad, y as usize + pad + 1).set(false);
}
}
}
}
// Blend neighboring offsets but preserve normal direction
// Uses xo as input, xi as output
// Improves quality slightly, but slows things down.
if relax {
let check_cross = |nx, ny, dc, dl, dr, dxl, dyl, dxr, dyr| {
((dxl * nx + dyl * ny) * (dc * dl) > 0.0)
&& ((dxr * nx + dyr * ny) * (dc * dr) > 0.0)
&& ((dxl * dxr + dyl * dyr) * (dl * dr) > 0.0)
};
for y in 0..(glyph.height() as isize) {
for x in 0..(glyph.width() as isize) {
// NOTE(eddyb) `j - 1` (X-) / `j - wp` (Y-) positive (`pad >= 1`).
let j = ((y as usize) + pad) * wp + (x as usize) + pad;
let nx = xo[j];
let ny = yo[j];
if nx == 0.0 && ny == 0.0 {
continue;
}
// NOTE(eddyb) c(enter) l(eft) r(ight) t(op) b(ottom)
let c = get_data(x, y);
let l = get_data(x - 1, y);
let r = get_data(x + 1, y);
let t = get_data(x, y - 1);
let b = get_data(x, y + 1);
let dxl = xo[j - 1];
let dxr = xo[j + 1];
let dxt = xo[j - wp];
let dxb = xo[j + wp];
let dyl = yo[j - 1];
let dyr = yo[j + 1];
let dyt = yo[j - wp];
let dyb = yo[j + wp];
let mut dx = nx;
let mut dy = ny;
let mut dw = 1.0;
let dc = c - 0.5;
let dl = l - 0.5;
let dr = r - 0.5;
let dt = t - 0.5;
let db = b - 0.5;
if !is_solid(l) && !is_solid(r) {
if check_cross(nx, ny, dc, dl, dr, dxl, dyl, dxr, dyr) {
dx += (dxl + dxr) / 2.0;
dy += (dyl + dyr) / 2.0;
dw += 1.0;
}
}
if !is_solid(t) && !is_solid(b) {
if check_cross(nx, ny, dc, dt, db, dxt, dyt, dxb, dyb) {
dx += (dxt + dxb) / 2.0;
dy += (dyt + dyb) / 2.0;
dw += 1.0;
}
}
if !is_solid(l) && !is_solid(t) {
if check_cross(nx, ny, dc, dl, dt, dxl, dyl, dxt, dyt) {
dx += (dxl + dxt - 1.0) / 2.0;
dy += (dyl + dyt - 1.0) / 2.0;
dw += 1.0;
}
}
if !is_solid(r) && !is_solid(t) {
if check_cross(nx, ny, dc, dr, dt, dxr, dyr, dxt, dyt) {
dx += (dxr + dxt + 1.0) / 2.0;
dy += (dyr + dyt - 1.0) / 2.0;
dw += 1.0;
}
}
if !is_solid(l) && !is_solid(b) {
if check_cross(nx, ny, dc, dl, db, dxl, dyl, dxb, dyb) {
dx += (dxl + dxb - 1.0) / 2.0;
dy += (dyl + dyb + 1.0) / 2.0;
dw += 1.0;
}
}
if !is_solid(r) && !is_solid(b) {
if check_cross(nx, ny, dc, dr, db, dxr, dyr, dxb, dyb) {
dx += (dxr + dxb + 1.0) / 2.0;
dy += (dyr + dyb + 1.0) / 2.0;
dw += 1.0;
}
}
let nn = (nx * nx + ny * ny).sqrt();
let ll = (dx * nx + dy * ny) / nn;
dx = nx * ll / dw / nn;
dy = ny * ll / dw / nn;
xi[j] = dx;
yi[j] = dy;
}
}
}
// Produce zero points for positive and negative DF, at +0.5 / -0.5.
// Splits xs into xo/xi
for y in 0..(glyph.height() as isize) {
for x in 0..(glyph.width() as isize) {
// NOTE(eddyb) `j - 1` (X-) / `j - wp` (Y-) positive (`pad >= 1`).
let j = ((y as usize) + pad) * wp + (x as usize) + pad;
// NOTE(eddyb) `if relax` above changed `xs`/`ys` in the original.
let (nx, ny) = if relax {
(xi[j], yi[j])
} else {
(xo[j], yo[j])
};
if nx == 0.0 && ny == 0.0 {
continue;
}
let nn = (nx.powi(2) + ny.powi(2)).sqrt();
let sx = if ((nx / nn).abs() - 0.5) > 0.0 {
nx.signum() as isize
} else {
0
};
let sy = if ((ny / nn).abs() - 0.5) > 0.0 {
ny.signum() as isize
} else {
0
};
let c = get_data(x, y);
let d = get_data(x + sx, y + sy);
// FIXME(eddyb) is this inefficient? (was `Math.sign(d - c)`)
let s = (d - c).total_cmp(&0.0) as i8 as f32;
let dlo = (nn + 0.4999 * s) / nn;
let dli = (nn - 0.4999 * s) / nn;
xo[j] = nx * dlo;
yo[j] = ny * dlo;
xi[j] = nx * dli;
yi[j] = ny * dli;
}
}
state
}
fn esdt_outer_and_inner(&mut self, w: usize, h: usize) {
{
let Self {
bufs_2d:
ReusableBuffers2d {
outer,
inner,
xo,
yo,
xi,
yi,
},
reuse_bufs_1d,
} = self;
esdt(outer, xo, yo, w, h, reuse_bufs_1d);
esdt(inner, xi, yi, w, h, reuse_bufs_1d);
}
}
}
// 2D subpixel distance transform by unconed
// extended from Felzenszwalb & Huttenlocher https://cs.brown.edu/~pff/papers/dt-final.pdf
fn esdt(
mask: &mut Bitmap,
xs: &mut [f32],
ys: &mut [f32],
w: usize,
h: usize,
reuse_bufs_1d: &mut ReusableBuffers1d,
) {
reuse_bufs_1d.critical_minima.clear();
reuse_bufs_1d.critical_minima.reserve(w.max(h));
let mut xs = Image2d::from_storage(w, h, xs);
let mut ys = Image2d::from_storage(w, h, ys);
for x in 0..w {
let mut mask_xy_cursor = mask
.cursor_at(0, 0)
.zip(
// FIXME(eddyb) combine `xs` and `ys` into the same `Image2d`.
ys.cursor_at(0, 0).zip(xs.cursor_at(0, 0)),
)
.map_abs_and_rel(move |y| (x, y), |dy| (0, dy));
mask_xy_cursor.reset(0);
esdt1d(mask_xy_cursor, h, reuse_bufs_1d)
}
for y in 0..h {
let mut mask_xy_cursor = mask
.cursor_at(0, 0)
.zip(
// FIXME(eddyb) combine `xs` and `ys` into the same `Image2d`.
xs.cursor_at(0, 0).zip(ys.cursor_at(0, 0)),
)
.map_abs_and_rel(move |x| (x, y), |dx| (dx, 0));
mask_xy_cursor.reset(0);
esdt1d(mask_xy_cursor, w, reuse_bufs_1d)
}
}
/// 1D buffers (for `esdt1d`), which get reused between calls.
//
// FIXME(eddyb) the name is outdated now that there's only one buffer.
#[derive(Default)]
struct ReusableBuffers1d {
critical_minima: Vec<CriticalMinimum>,
}
// FIXME(eddyb) clean up the names after all the refactors.
struct CriticalMinimum {
// FIXME(eddyb) this is really just a position, since it's not used to
// index anything indirectly anymore, but rather indicates the original `q`,
// and is used to compare against it in the second iteration of `esdt1d`.
v: usize, // Array index
z: f32, // Voronoi threshold
f: f32, // Squared distance
b: f32, // Subpixel offset parallel
t: f32, // Subpixel offset perpendicular
}
// 1D subpixel distance transform
fn esdt1d(
mut mask_xy_cursor: impl for<'a> NDCursor<
'a,
usize,
RefMut = (crate::img::BitmapEntry<'a>, (&'a mut f32, &'a mut f32)),
>,
// FIXME(eddyb) provide this through the cursor, maybe?
length: usize,
reuse_bufs_1d: &mut ReusableBuffers1d,
) {
// FIXME(eddyb) this is a pretty misleading name.
const INF: f32 = 1e10;
let cm = &mut reuse_bufs_1d.critical_minima;
cm.clear();
{
let (mask, (&mut dx, &mut dy)) = mask_xy_cursor.get_mut();
cm.push(CriticalMinimum {
v: 0,
z: -INF,
f: if mask.get() { INF } else { dy.powi(2) },
b: dx,
t: dy,
});
mask_xy_cursor.advance(1);
}
// Scan along array and build list of critical minima
for q in 1..length {
// Perpendicular
let (mask, (&mut dx, &mut dy)) = mask_xy_cursor.get_mut();
let fq = if mask.get() { INF } else { dy.powi(2) };
mask_xy_cursor.advance(1);
// Parallel
let qs = q as f32 + dx;
let q2 = qs.powi(2);
// Remove any minima eclipsed by this one
let mut s;
loop {
let r = &cm[cm.len() - 1];
s = (fq - r.f + q2 - r.b.powi(2)) / (qs - r.b) / 2.0;
if !(s <= r.z) {
break;
}
cm.pop();
if cm.len() == 0 {
break;
}
}
// Add to minima list
cm.push(CriticalMinimum {
v: q,
z: s,
f: fq,
b: qs,
t: dy,
});
}
mask_xy_cursor.reset(0);
// Resample array based on critical minima
{
let mut k = 0;
for q in 0..length {
// Skip eclipsed minima
while k + 1 < cm.len() && cm[k + 1].z < q as f32 {
k += 1;
}
let r = &cm[k];
// Distance from integer index to subpixel location of minimum
let rq = r.b - q as f32;
let (mut mask, (dx, dy)) = mask_xy_cursor.get_mut();
*dx = rq;
*dy = r.t;
// Mark cell as having propagated
if r.v != q {
mask.set(false);
}
mask_xy_cursor.advance(1);
}
}
}