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//! Provides a `MetaBall` struct and functions for creating a `Sketch` from [MetaBalls](https://en.wikipedia.org/wiki/Metaballs)
use crate::float_types::{EPSILON, Real};
use crate::sketch::Sketch;
use crate::traits::CSG;
use geo::{
CoordsIter, Geometry, GeometryCollection, LineString, Polygon as GeoPolygon, coord,
};
use hashbrown::HashMap;
use std::fmt::Debug;
impl<S: Clone + Debug + Send + Sync> Sketch<S> {
/// Create a 2D metaball iso-contour in XY plane from a set of 2D metaballs.
/// - `balls`: array of (center, radius).
/// - `resolution`: (nx, ny) grid resolution for marching squares.
/// - `iso_value`: threshold for the iso-surface.
/// - `padding`: extra boundary beyond each ball's radius.
/// - `metadata`: optional user metadata.
pub fn metaballs(
balls: &[(nalgebra::Point2<Real>, Real)],
resolution: (usize, usize),
iso_value: Real,
padding: Real,
metadata: Option<S>,
) -> Sketch<S> {
let (nx, ny) = resolution;
if balls.is_empty() || nx < 2 || ny < 2 {
return Sketch::new();
}
// 1) Compute bounding box around all metaballs
let mut min_x = Real::MAX;
let mut min_y = Real::MAX;
let mut max_x = -Real::MAX;
let mut max_y = -Real::MAX;
for (center, r) in balls {
let rr = *r + padding;
if center.x - rr < min_x {
min_x = center.x - rr;
}
if center.x + rr > max_x {
max_x = center.x + rr;
}
if center.y - rr < min_y {
min_y = center.y - rr;
}
if center.y + rr > max_y {
max_y = center.y + rr;
}
}
let dx = (max_x - min_x) / (nx as Real - 1.0);
let dy = (max_y - min_y) / (ny as Real - 1.0);
// 2) Fill a grid with the summed "influence" minus iso_value
/// **Mathematical Foundation**: 2D metaball influence I(p) = r²/(|p-c|² + ε)
/// **Optimization**: Iterator-based computation with early termination for distant points.
fn scalar_field(balls: &[(nalgebra::Point2<Real>, Real)], x: Real, y: Real) -> Real {
balls
.iter()
.map(|(center, radius)| {
let dx = x - center.x;
let dy = y - center.y;
let distance_sq = dx * dx + dy * dy;
// Early termination for very distant points
let threshold_distance_sq = radius * radius * 1000.0;
if distance_sq > threshold_distance_sq {
0.0
} else {
let denominator = distance_sq + EPSILON;
(radius * radius) / denominator
}
})
.sum()
}
let mut grid = vec![0.0; nx * ny];
let index = |ix: usize, iy: usize| -> usize { iy * nx + ix };
for iy in 0..ny {
let yv = min_y + (iy as Real) * dy;
for ix in 0..nx {
let xv = min_x + (ix as Real) * dx;
let val = scalar_field(balls, xv, yv) - iso_value;
grid[index(ix, iy)] = val;
}
}
// 3) Marching squares -> line segments
let mut contours = Vec::<LineString<Real>>::new();
// Interpolator:
let interpolate = |(x1, y1, v1): (Real, Real, Real),
(x2, y2, v2): (Real, Real, Real)|
-> (Real, Real) {
let denom = (v2 - v1).abs();
if denom < EPSILON {
(x1, y1)
} else {
let t = -v1 / (v2 - v1); // crossing at 0
(x1 + t * (x2 - x1), y1 + t * (y2 - y1))
}
};
for iy in 0..(ny - 1) {
let y0 = min_y + (iy as Real) * dy;
let y1 = min_y + ((iy + 1) as Real) * dy;
for ix in 0..(nx - 1) {
let x0 = min_x + (ix as Real) * dx;
let x1 = min_x + ((ix + 1) as Real) * dx;
let v0 = grid[index(ix, iy)];
let v1 = grid[index(ix + 1, iy)];
let v2 = grid[index(ix + 1, iy + 1)];
let v3 = grid[index(ix, iy + 1)];
// classification
let mut c = 0u8;
if v0 >= 0.0 {
c |= 1;
}
if v1 >= 0.0 {
c |= 2;
}
if v2 >= 0.0 {
c |= 4;
}
if v3 >= 0.0 {
c |= 8;
}
if c == 0 || c == 15 {
continue; // no crossing
}
let corners = [(x0, y0, v0), (x1, y0, v1), (x1, y1, v2), (x0, y1, v3)];
let mut pts = Vec::new();
// function to check each edge
let mut check_edge = |mask_a: u8, mask_b: u8, a: usize, b: usize| {
let inside_a = (c & mask_a) != 0;
let inside_b = (c & mask_b) != 0;
if inside_a != inside_b {
let (px, py) = interpolate(corners[a], corners[b]);
pts.push((px, py));
}
};
check_edge(1, 2, 0, 1);
check_edge(2, 4, 1, 2);
check_edge(4, 8, 2, 3);
check_edge(8, 1, 3, 0);
// we might get 2 intersection points => single line segment
// or 4 => two line segments, etc.
// For simplicity, we just store them in a small open polyline:
if pts.len() >= 2 {
let mut pl = LineString::new(vec![]);
for &(px, py) in &pts {
pl.0.push(coord! {x: px, y: py});
}
// Do not close. These are just line segments from this cell.
contours.push(pl);
}
}
}
// 4) Convert these line segments into geo::LineStrings or geo::Polygons if closed.
// We store them in a GeometryCollection.
let mut gc = GeometryCollection::default();
let stitched = stitch(&contours);
for pl in stitched {
if pl.is_closed() && pl.coords_count() >= 4 {
let polygon = GeoPolygon::new(pl, vec![]);
gc.0.push(Geometry::Polygon(polygon));
}
}
Sketch::from_geo(gc, metadata)
}
}
// helper – quantise to avoid FP noise
#[inline]
fn key(x: Real, y: Real) -> (i64, i64) {
((x * 1e8).round() as i64, (y * 1e8).round() as i64)
}
/// stitch all 2-point segments into longer polylines,
/// close them when the ends meet
fn stitch(contours: &[LineString<Real>]) -> Vec<LineString<Real>> {
// adjacency map endpoint -> (line index, end-id 0|1)
let mut adj: HashMap<(i64, i64), Vec<(usize, usize)>> = HashMap::new();
for (idx, ls) in contours.iter().enumerate() {
let p0 = ls[0]; // first point
let p1 = ls[1]; // second point
adj.entry(key(p0.x, p0.y)).or_default().push((idx, 0));
adj.entry(key(p1.x, p1.y)).or_default().push((idx, 1));
}
let mut used = vec![false; contours.len()];
let mut chains = Vec::new();
for start in 0..contours.len() {
if used[start] {
continue;
}
used[start] = true;
// current chain of points
let mut chain = contours[start].0.clone();
// walk forward
loop {
let last = *chain.last().unwrap();
let Some(cands) = adj.get(&key(last.x, last.y)) else {
break;
};
let mut found = None;
for &(idx, end_id) in cands {
if used[idx] {
continue;
}
used[idx] = true;
// choose the *other* endpoint
let other = contours[idx][1 - end_id];
chain.push(other);
found = Some(());
break;
}
if found.is_none() {
break;
}
}
// close if ends coincide
if chain.len() >= 3 && (chain[0] != *chain.last().unwrap()) {
chain.push(chain[0]);
}
chains.push(LineString::new(chain));
}
chains
}