//! Parameters of points on a surface, on the evaluator's own surface form (so the parameters
//! the plan stores are the ones the evaluators use), and the tolerance-driven divisions of a
//! face's parameter box.

use solidcraft_geom::Vec3;
use solidcraft_geom::tess::EvalSurface;

use super::size::Rules;

/// The parameter box of a surface and its periods.
#[derive(Clone, Copy, Debug)]
pub(crate) struct Domain {
    /// Bounded ranges (`None`: unbounded, as a plane's).
    pub range: [Option<(f64, f64)>; 2],
    pub period: [Option<f64>; 2],
}

pub(crate) fn domain(s: &EvalSurface) -> Domain {
    let tau = std::f64::consts::TAU;
    match s {
        EvalSurface::Plane { .. } => Domain { range: [None, None], period: [None, None] },
        EvalSurface::Nurbs { degree, knots, count, .. } => {
            let r = |d: usize| Some((*knots[d].get(degree[d])?, *knots[d].get(count[d])?));
            Domain { range: [r(0), r(1)], period: [None, None] }
        }
        EvalSurface::Revolved { profile, swap, .. } => {
            let r = (|| Some((*profile.knots.get(profile.degree)?, *profile.knots.get(profile.ctrl.len())?)))();
            let (a, b) = ((r, None), (Some((0.0, tau)), Some(tau)));
            let (u, v) = if *swap { (b, a) } else { (a, b) };
            Domain { range: [u.0, v.0], period: [u.1, v.1] }
        }
    }
}

impl Domain {
    pub(crate) fn clamp(&self, uv: [f64; 2]) -> [f64; 2] {
        let mut out = uv;
        for (d, x) in out.iter_mut().enumerate() {
            if let (Some((a, b)), None) = (self.range[d], self.period[d]) {
                *x = x.clamp(a.min(b), a.max(b));
            }
        }
        out
    }
}

/// Damped Gauss–Newton (Levenberg–Marquardt) for the parameters nearest to `p`, from `start`.
/// Returns the parameters and their distance to `p`.
fn newton(s: &EvalSurface, dom: &Domain, p: Vec3, start: [f64; 2]) -> Option<([f64; 2], f64)> {
    let mut uv = dom.clamp(start);
    let (mut q, mut su, mut sv) = s.derivs(uv[0], uv[1])?;
    let mut dist = q.dist(p);
    let mut lambda = 1e-6;
    for _ in 0..60 {
        let r = p - q;
        let (a, b, c) = (su.len2(), su.dot(sv), sv.len2());
        let (g0, g1) = (su.dot(r), sv.dot(r));
        let scale = a + c;
        if !(scale > 0.0) || !scale.is_finite() {
            break;
        }
        let (a2, c2) = (a + lambda * scale, c + lambda * scale);
        let det = a2 * c2 - b * b;
        if !(det.abs() > 0.0) {
            break;
        }
        let step = [(c2 * g0 - b * g1) / det, (a2 * g1 - b * g0) / det];
        let next = dom.clamp([uv[0] + step[0], uv[1] + step[1]]);
        let Some((nq, nsu, nsv)) = s.derivs(next[0], next[1]) else { break };
        let nd = nq.dist(p);
        if nd <= dist {
            let moved = (next[0] - uv[0]).abs() + (next[1] - uv[1]).abs();
            (uv, q, su, sv, dist) = (next, nq, nsu, nsv, nd);
            lambda = (lambda * 0.1).max(1e-12);
            if moved <= 1e-15 * (1.0 + uv[0].abs() + uv[1].abs()) {
                break;
            }
        } else {
            lambda *= 10.0;
            if lambda > 1e8 {
                break;
            }
        }
    }
    Some((uv, dist))
}

/// Parameters of `p` (a point on the surface within `accept`), from `hint` when that
/// converges, else from the best starts of a grid over the surface's domain.
pub(crate) fn project(s: &EvalSurface, dom: &Domain, p: Vec3, hint: Option<[f64; 2]>, accept: f64) -> Option<[f64; 2]> {
    if let EvalSurface::Plane { origin, du, dv } = s {
        let r = p - *origin;
        let (a, b, c) = (du.len2(), du.dot(*dv), dv.len2());
        let det = a * c - b * b;
        if !(det.abs() > 0.0) {
            return None;
        }
        let (g0, g1) = (du.dot(r), dv.dot(r));
        let uv = [(c * g0 - b * g1) / det, (a * g1 - b * g0) / det];
        return (uv[0].is_finite() && uv[1].is_finite()).then_some(uv);
    }
    let mut best: Option<([f64; 2], f64)> = None;
    if let Some(h) = hint
        && let Some((uv, d)) = newton(s, dom, p, h)
    {
        if d <= accept {
            return Some(uv);
        }
        best = Some((uv, d));
    }
    let (ur, vr) = (dom.range[0]?, dom.range[1]?);
    const N: usize = 16;
    let mut starts: Vec<(f64, [f64; 2])> = Vec::with_capacity((N + 1) * (N + 1));
    for i in 0..=N {
        for j in 0..=N {
            let uv = [ur.0 + (ur.1 - ur.0) * i as f64 / N as f64, vr.0 + (vr.1 - vr.0) * j as f64 / N as f64];
            if let Some((q, _, _)) = s.derivs(uv[0], uv[1]) {
                starts.push(((q - p).len2(), uv));
            }
        }
    }
    starts.sort_by(|a, b| a.0.total_cmp(&b.0));
    for (_, start) in starts.iter().take(4) {
        if let Some((uv, d)) = newton(s, dom, p, *start)
            && best.is_none_or(|(_, bd)| d < bd)
        {
            best = Some((uv, d));
        }
    }
    best.filter(|(_, d)| *d <= accept).map(|(uv, _)| uv)
}

/// `x` moved by whole periods to lie within half a period of `near`.
pub(crate) fn unwrap(x: f64, near: f64, period: Option<f64>) -> f64 {
    match period {
        Some(p) if p > 0.0 => x - ((x - near) / p).round() * p,
        _ => x,
    }
}

/// Is the surface degenerate along direction `d` at `uv` (a pole: moving along `d` does not
/// move the point)?
pub(crate) fn degenerate(s: &EvalSurface, uv: [f64; 2], d: usize) -> bool {
    let Some((_, su, sv)) = s.derivs(uv[0], uv[1]) else { return false };
    let (this, other) = if d == 0 { (su, sv) } else { (sv, su) };
    this.len() <= 1e-9 * other.len().max(1e-12)
}

/// Division of `range` along direction `d` so that between neighbouring lines the surface sags
/// at most the tolerance from its chord, the chord is at most `h` long and the normal turns
/// within the rules' facet angle, checked along iso-lines across `across`; at most `max_lines`
/// lines, ends included.
pub(crate) fn divide(s: &EvalSurface, d: usize, range: (f64, f64), across: (f64, f64), rules: &Rules, h: f64, max_lines: usize) -> Vec<f64> {
    let (a0, a1) = range;
    if !(a1 > a0) {
        return vec![a0, a1];
    }
    let flat = limits(s, d, across, rules, h);
    // Start from quarter turns at most, so a closed iso-line is not taken for a flat one (a
    // plane's parameters are lengths and its lines are never closed).
    let initial = if matches!(s, EvalSurface::Plane { .. }) { 1 } else { ((a1 - a0) / std::f64::consts::FRAC_PI_2).ceil().clamp(1.0, 64.0) as u32 };
    // Both ends exactly (a0 + (a1 − a0) · 1 may round away from a1): the end lines are the
    // face's own parameter box, which the boundary nodes sit on.
    let starts: Vec<f64> = (0..=initial)
        .map(|i| {
            let t = f64::from(i) / f64::from(initial);
            a0 * (1.0 - t) + a1 * t
        })
        .collect();
    split(&starts, &flat, max_lines)
}

/// `lines` (increasing, ends included) with every interval that fails the same limits as
/// [`divide`] split until it passes: lines taken from a face's edge nodes meet the edges node for
/// node, but nothing else checks how far the surface turns between them inside the face.
pub(crate) fn refine(s: &EvalSurface, d: usize, lines: &[f64], across: (f64, f64), rules: &Rules, h: f64, max_lines: usize) -> Vec<f64> {
    let flat = limits(s, d, across, rules, h);
    split(lines, &flat, max_lines)
}

/// Depth-first bisection of the intervals between `starts` until `flat` holds for each.
fn split(starts: &[f64], flat: &dyn Fn(f64, f64) -> bool, max_lines: usize) -> Vec<f64> {
    let Some(&first) = starts.first() else { return Vec::new() };
    let mut out = vec![first];
    let mut stack: Vec<(f64, f64, u32)> = starts.windows(2).rev().map(|w| (w[0], w[1], 0)).collect();
    while let Some((a, b, depth)) = stack.pop() {
        if depth >= 20 || out.len() + stack.len() >= max_lines.max(2) || flat(a, b) {
            out.push(b);
        } else {
            let m = 0.5 * (a + b);
            stack.push((m, b, depth + 1));
            stack.push((a, m, depth + 1));
        }
    }
    out
}

/// Whether the surface between the parameter points `a` and `b` is within the tolerance (at
/// their middle), the side length `h` and the facet angle: no point is needed between them.
pub(crate) fn fine_between(s: &EvalSurface, rules: &Rules, h: f64, a: [f64; 2], b: [f64; 2]) -> bool {
    let at = |q: [f64; 2]| s.derivs(q[0], q[1]);
    let (Some((pa, _, _)), Some((pb, _, _))) = (at(a), at(b)) else { return true };
    if pa.dist(pb) > h * (1.0 + 1e-9) {
        return false;
    }
    let mid = [0.5 * (a[0] + b[0]), 0.5 * (a[1] + b[1])];
    let sag = at(mid).map_or(0.0, |(m, _, _)| m.dist((pa + pb) * 0.5));
    if sag > rules.tol {
        return false;
    }
    // At a pole the normal is undefined: take it from just inside the segment.
    let normal = |q: [f64; 2], toward: [f64; 2]| {
        let n = |q: [f64; 2]| at(q).and_then(|(_, su, sv)| su.cross(sv).normalized());
        n(q).or_else(|| n([q[0] + 1e-4 * (toward[0] - q[0]), q[1] + 1e-4 * (toward[1] - q[1])]))
    };
    match (rules.turn, normal(a, b), normal(b, a)) {
        (Some(t), Some(na), Some(nb)) => !t.exceeds(na.dot(nb).clamp(-1.0, 1.0).acos(), sag),
        _ => true,
    }
}

/// Whether the surface between the iso-lines at `a` and `b` (direction `d`, sampled along
/// iso-lines across `across`) is within the tolerance, the side length `h` and the facet angle.
fn limits<'a>(s: &'a EvalSurface, d: usize, across: (f64, f64), rules: &'a Rules, h: f64) -> impl Fn(f64, f64) -> bool + 'a {
    let tol = rules.tol;
    let uv = move |x: f64, y: f64| if d == 0 { (x, y) } else { (y, x) };
    let at = move |x: f64, y: f64| {
        let (u, v) = uv(x, y);
        s.derivs(u, v).map(|(p, _, _)| p)
    };
    let normal = move |x: f64, y: f64| {
        let (u, v) = uv(x, y);
        s.derivs(u, v).and_then(|(_, su, sv)| su.cross(sv).normalized())
    };
    const ACROSS: usize = 5;
    let ys: Vec<f64> = (0..ACROSS).map(|k| across.0 + (across.1 - across.0) * k as f64 / (ACROSS - 1) as f64).collect();
    move |a: f64, b: f64| {
        ys.iter().all(|&y| {
            let (Some(pa), Some(pb)) = (at(a, y), at(b, y)) else { return true };
            if pa.dist(pb) > h * (1.0 + 1e-9) {
                return false;
            }
            let sag = [0.25, 0.5, 0.75].iter().filter_map(|f| at(a + (b - a) * f, y)).map(|q| q.dist_to_segment(pa, pb)).fold(0.0, f64::max);
            if sag > tol {
                return false;
            }
            // At a pole the normal is undefined: take it from just inside the segment.
            let na = normal(a, y).or_else(|| normal(a + 1e-4 * (b - a), y));
            let nb = normal(b, y).or_else(|| normal(b - 1e-4 * (b - a), y));
            match (rules.turn, na, nb) {
                (Some(t), Some(na), Some(nb)) => !t.exceeds(na.dot(nb).clamp(-1.0, 1.0).acos(), sag),
                _ => true,
            }
        })
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use solidcraft_geom::tess::EvalCurve;

    fn cylinder() -> EvalSurface {
        EvalSurface::Revolved {
            profile: EvalCurve { degree: 1, knots: vec![0.0, 0.0, 1.0, 1.0], ctrl: vec![[3.0, 0.0, 0.0, 1.0], [3.0, 0.0, 4.0, 1.0]] },
            origin: Vec3::ZERO,
            axis: Vec3::Z,
            transform: [[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0]],
            swap: false,
        }
    }

    #[test]
    fn projects_points_back_to_their_parameters() {
        let s = cylinder();
        let dom = domain(&s);
        for &(u, v) in &[(0.1, 0.2), (0.5, 3.0), (0.9, 6.0), (0.0, 1.0)] {
            let (p, _) = s.eval(u, v);
            let Some(uv) = project(&s, &dom, p, None, 1e-9) else { panic!("projects") };
            let (q, _) = s.eval(uv[0], uv[1]);
            assert!(q.dist(p) < 1e-9);
            assert!((uv[0] - u).abs() < 1e-9);
        }
        // Off the surface by more than `accept`: no parameters.
        assert!(project(&s, &dom, Vec3::new(5.0, 0.0, 1.0), None, 1e-3).is_none());
    }

    #[test]
    fn divides_the_turn_but_not_the_straight_direction() {
        let s = cylinder();
        let turn =
            divide(&s, 1, (0.0, std::f64::consts::TAU), (0.0, 1.0), &Rules { tol: 0.01, max_len: f64::INFINITY, turn: None }, f64::INFINITY, 10_000);
        let along =
            divide(&s, 0, (0.0, 1.0), (0.0, std::f64::consts::TAU), &Rules { tol: 0.01, max_len: f64::INFINITY, turn: None }, f64::INFINITY, 10_000);
        assert_eq!(along, vec![0.0, 1.0]);
        // Chord sag r(1 − cos(θ/2)) ≤ 0.01 with r = 3 needs θ ≤ 0.163: at least 39 segments.
        assert!(turn.len() >= 40 && turn.len() < 80, "{}", turn.len());
        // With a longest side the straight direction is divided too: 4 mm in sides ≤ 0.5.
        let along = divide(&s, 0, (0.0, 1.0), (0.0, std::f64::consts::TAU), &Rules { tol: 0.01, max_len: f64::INFINITY, turn: None }, 0.5, 10_000);
        assert_eq!(along.len(), 9);
    }

    /// The first and last lines are the range's ends to the last bit: the boundary nodes sit on
    /// them, and a line a rounding inside would be taken for an interior one (a drill point's
    /// cone, where a0 + (a1 − a0) is not a1).
    #[test]
    fn divides_with_the_ends_exactly() {
        let (a0, a1) = (-1.010485317689877, 1.083909784703316);
        let lines = divide(&cylinder(), 1, (a0, a1), (0.0, 1.0), &Rules { tol: 0.01, max_len: f64::INFINITY, turn: None }, f64::INFINITY, 10_000);
        assert_eq!(lines.first().copied(), Some(a0));
        assert_eq!(lines.last().copied(), Some(a1));
    }

    #[test]
    fn unwraps_across_the_period() {
        let tau = std::f64::consts::TAU;
        assert!((unwrap(0.1, tau - 0.1, Some(tau)) - (tau + 0.1)).abs() < 1e-12);
        assert_eq!(unwrap(0.1, 6.0, None), 0.1);
    }
}