//! Boundary following on the pixel-crack grid.
//!
//! Vertices are pixel corners `(x, y)` with `0 ≤ x ≤ w`, `0 ≤ y ≤ h`. Every edge between an inside
//! and an outside pixel becomes a directed edge with the inside pixel on its right (y down), so
//! outer boundaries run clockwise and holes counter-clockwise. At a saddle (two inside pixels
//! touching only diagonally) the walk turns right, which keeps diagonal neighbours apart — the
//! same 4-connectivity used to label components.

/// A closed boundary loop.
#[derive(Clone, Debug, PartialEq)]
pub struct Loop {
    /// Corner vertices in order (the loop closes back to the first).
    pub pts: Vec<(i32, i32)>,
    /// Twice the signed area (positive = outer boundary, negative = hole).
    pub area2: i64,
}

/// One 4-connected component of the mask: its outer loop and holes.
#[derive(Clone, Debug, PartialEq)]
pub struct Component {
    pub outer: Loop,
    pub holes: Vec<Loop>,
    /// Inside pixel count.
    pub pixels: usize,
}

const R: u8 = 1;
const D: u8 = 2;
const L: u8 = 4;
const U: u8 = 8;

fn right_of(d: u8) -> u8 {
    match d {
        R => D,
        D => L,
        L => U,
        _ => R,
    }
}

fn step(d: u8) -> (i32, i32) {
    match d {
        R => (1, 0),
        D => (0, 1),
        L => (-1, 0),
        _ => (0, -1),
    }
}

/// 4-connected component labels (`u32::MAX` outside) and per-component pixel counts.
fn label(mask: &[bool], w: usize, h: usize) -> (Vec<u32>, Vec<usize>) {
    let mut comp = vec![u32::MAX; w * h];
    let mut sizes = Vec::new();
    let mut stack = Vec::new();
    for s in 0..w * h {
        if !mask[s] || comp[s] != u32::MAX {
            continue;
        }
        let id = sizes.len() as u32;
        let mut n = 0usize;
        comp[s] = id;
        stack.push(s);
        while let Some(i) = stack.pop() {
            n += 1;
            let (x, y) = (i % w, i / w);
            let mut go = |j: usize| {
                if mask[j] && comp[j] == u32::MAX {
                    comp[j] = id;
                    stack.push(j);
                }
            };
            if x > 0 {
                go(i - 1);
            }
            if x + 1 < w {
                go(i + 1);
            }
            if y > 0 {
                go(i - w);
            }
            if y + 1 < h {
                go(i + w);
            }
        }
        sizes.push(n);
    }
    (comp, sizes)
}

/// Trace every component of `mask` (row-major, `w × h`).
pub fn trace_mask(mask: &[bool], w: usize, h: usize) -> Vec<Component> {
    assert_eq!(mask.len(), w * h);
    let (comp, sizes) = label(mask, w, h);
    let vw = w + 1;
    let mut dirs = vec![0u8; vw * (h + 1)];
    let inside = |x: isize, y: isize| x >= 0 && y >= 0 && (x as usize) < w && (y as usize) < h && mask[y as usize * w + x as usize];
    for y in 0..h {
        for x in 0..w {
            if !mask[y * w + x] {
                continue;
            }
            let (xi, yi) = (x as isize, y as isize);
            if !inside(xi, yi - 1) {
                dirs[y * vw + x] |= R;
            }
            if !inside(xi + 1, yi) {
                dirs[y * vw + x + 1] |= D;
            }
            if !inside(xi, yi + 1) {
                dirs[(y + 1) * vw + x + 1] |= L;
            }
            if !inside(xi - 1, yi) {
                dirs[(y + 1) * vw + x] |= U;
            }
        }
    }
    let mut outers: Vec<Option<Loop>> = vec![None; sizes.len()];
    let mut holes: Vec<Vec<Loop>> = vec![Vec::new(); sizes.len()];
    for start in 0..dirs.len() {
        // Every loop has an R edge (the top edge of some inside pixel); start there so the loop
        // closes exactly (right-turn rule at the start vertex, too).
        while dirs[start] & R != 0 {
            let (sx, sy) = ((start % vw) as i32, (start / vw) as i32);
            let owner = comp[sy as usize * w + sx as usize];
            dirs[start] &= !R;
            let mut pts = vec![(sx, sy)];
            let (mut x, mut y) = (sx + 1, sy);
            let mut d = R;
            let mut area2: i64 = 0;
            let mut prev = (sx, sy);
            loop {
                area2 += prev.0 as i64 * y as i64 - x as i64 * prev.1 as i64;
                prev = (x, y);
                let v = y as usize * vw + x as usize;
                let at_start = (x, y) == (sx, sy);
                let mut cand = dirs[v];
                if at_start {
                    cand |= R;
                }
                let next = if cand.count_ones() == 1 {
                    cand
                } else if cand & right_of(d) != 0 {
                    right_of(d)
                } else if cand & d != 0 {
                    d
                } else {
                    // left turn
                    right_of(right_of(right_of(d)))
                };
                if at_start && next == R {
                    break;
                }
                if next == 0 || dirs[v] & next == 0 {
                    // Malformed (cannot happen for a valid mask); stop safely.
                    break;
                }
                dirs[v] &= !next;
                // Keep only turn vertices.
                if next != d {
                    pts.push((x, y));
                }
                let (dx, dy) = step(next);
                x += dx;
                y += dy;
                d = next;
            }
            let l = Loop { pts, area2 };
            if owner == u32::MAX {
                continue;
            }
            if l.area2 > 0 {
                outers[owner as usize] = Some(l);
            } else {
                holes[owner as usize].push(l);
            }
        }
    }
    let mut out = Vec::with_capacity(sizes.len());
    for (i, o) in outers.into_iter().enumerate() {
        if let Some(outer) = o {
            out.push(Component { outer, holes: std::mem::take(&mut holes[i]), pixels: sizes[i] });
        }
    }
    out
}