brep_kernel/intersect/

curve_surface_intersection.rs

use crate::curve::interior_knot_count;
use crate::{project_point_to_surface, NurbsCurve, NurbsSurface, Vec3};
use serde::Serialize;

const EPSILON: f64 = crate::tolerance::FP_FLOOR;

use crate::spatial::Aabb as Bounds;


/// The box of the carrier's control points, in their order; the first control
/// point that is not a point is the error. Read without collecting them: it
/// is paid on every call, and a view ray through a fitted carrier of a gear
/// asks it thousands of times.
fn surface_bounds(surface: &NurbsSurface) -> Result<Bounds, String> {
    let mut bounds = Bounds::from_points([]);
    for point in surface.control_points.iter().flatten() {
        let point = point.point()?;
        bounds.minimum.x = bounds.minimum.x.min(point.x);
        bounds.minimum.y = bounds.minimum.y.min(point.y);
        bounds.minimum.z = bounds.minimum.z.min(point.z);
        bounds.maximum.x = bounds.maximum.x.max(point.x);
        bounds.maximum.y = bounds.maximum.y.max(point.y);
        bounds.maximum.z = bounds.maximum.z.max(point.z);
    }
    Ok(bounds)
}


/// The box of each knot-span patch's control points: the surface over span
/// `[u_i, u_i+1) x [v_j, v_j+1)` lies in the convex hull of the
/// `(p + 1) x (q + 1)` control points that support it (positive weights), so
/// a curve segment clear of every span box is clear of the surface.
///
/// The whole-net box cannot say that for a carrier that winds: an eight-turn
/// helical tube's box is the whole coil, every sample segment of a ray through
/// the coil passes it, and every one seeded a Newton that starts from a global
/// projection onto a 1280-point net — 21 of the 26 s the 2026-09-26 coil
/// fillet report's interference check took, for about one hit in forty seeds.
fn span_bounds(surface: &NurbsSurface) -> Result<Vec<Bounds>, String> {
    let (p, q) = (surface.degree_u, surface.degree_v);
    let rows = surface.control_points.len();
    let columns = surface.control_points.first().map_or(0, Vec::len);
    let spans = |knots: &[f64], degree: usize, count: usize| -> Vec<usize> {
        (degree..count).filter(|&i| i + 1 < knots.len() && knots[i] < knots[i + 1]).collect()
    };
    let (spans_u, spans_v) = (spans(&surface.knots_u, p, rows), spans(&surface.knots_v, q, columns));
    // A malformed net has no span structure to trust: the whole-net box stands.
    if spans_u.is_empty() || spans_v.is_empty() {
        return Ok(vec![surface_bounds(surface)?]);
    }
    let mut boxes = Vec::with_capacity(spans_u.len() * spans_v.len());
    for &i in &spans_u {
        for &j in &spans_v {
            let mut bounds = Bounds::from_points([]);
            for row in &surface.control_points[i - p..=i] {
                for control in &row[j - q..=j] {
                    let point = control.point()?;
                    bounds.minimum.x = bounds.minimum.x.min(point.x);
                    bounds.minimum.y = bounds.minimum.y.min(point.y);
                    bounds.minimum.z = bounds.minimum.z.min(point.z);
                    bounds.maximum.x = bounds.maximum.x.max(point.x);
                    bounds.maximum.y = bounds.maximum.y.max(point.y);
                    bounds.maximum.z = bounds.maximum.z.max(point.z);
                }
            }
            boxes.push(bounds);
        }
    }
    Ok(boxes)
}

fn fit_parameter(value: f64, minimum: f64, maximum: f64, closed: bool) -> f64 {
    crate::projection::fit_parameter(value, minimum, maximum, closed)
}

fn solve_three(matrix: [[f64; 3]; 3], rhs: Vec3) -> Option<[f64; 3]> {
    let a = matrix;
    let determinant = a[0][0] * (a[1][1] * a[2][2] - a[1][2] * a[2][1])
        - a[0][1] * (a[1][0] * a[2][2] - a[1][2] * a[2][0])
        + a[0][2] * (a[1][0] * a[2][1] - a[1][1] * a[2][0]);
    let scale: f64 = a.iter().flatten().map(|value| value.abs()).sum();
    if determinant.abs() <= 1e-14 * scale.max(1.0).powi(3) {
        return None;
    }
    let x = (rhs.x * (a[1][1] * a[2][2] - a[1][2] * a[2][1])
        - a[0][1] * (rhs.y * a[2][2] - a[1][2] * rhs.z)
        + a[0][2] * (rhs.y * a[2][1] - a[1][1] * rhs.z))
        / determinant;
    let y = (a[0][0] * (rhs.y * a[2][2] - a[1][2] * rhs.z)
        - rhs.x * (a[1][0] * a[2][2] - a[1][2] * a[2][0])
        + a[0][2] * (a[1][0] * rhs.z - rhs.y * a[2][0]))
        / determinant;
    let z = (a[0][0] * (a[1][1] * rhs.z - rhs.y * a[2][1])
        - a[0][1] * (a[1][0] * rhs.z - rhs.y * a[2][0])
        + rhs.x * (a[1][0] * a[2][1] - a[1][1] * a[2][0]))
        / determinant;
    Some([x, y, z])
}

fn newton_curve_surface(
    curve: &NurbsCurve,
    surface: &NurbsSurface,
    seed: f64,
) -> Result<[f64; 3], String> {
    let [t0, t1] = curve.domain()?;
    let [u0, u1] = surface.domain_u()?;
    let [v0, v1] = surface.domain_v()?;
    let (closed_u, closed_v) = surface.closed_directions()?;
    let mut t = seed;
    let projection = project_point_to_surface(surface, curve.evaluate(t)?)?;
    let mut u = projection.u;
    let mut v = projection.v;
    for _ in 0..60 {
        let (curve_point, tangent) = curve.deriv1(t)?;
        let (surface_point, du, dv) = surface.deriv1(u, v)?;
        let residual = curve_point.sub(surface_point);
        if residual.length() <= EPSILON {
            return Ok([t, u, v]);
        }
        let Some([mut step_t, mut step_u, mut step_v]) = solve_three(
            [
                [tangent.x, -du.x, -dv.x],
                [tangent.y, -du.y, -dv.y],
                [tangent.z, -du.z, -dv.z],
            ],
            residual.scale(-1.0),
        ) else {
            if tangent.length_squared() <= EPSILON {
                return Ok([t, u, v]);
            }
            let next_t = (t - residual.dot(tangent) / tangent.length_squared()).clamp(t0, t1);
            if (next_t - t).abs() <= 1e-15 * (t1 - t0) {
                return Ok([t, u, v]);
            }
            t = next_t;
            // The next iterate's foot, continued from this one's: the Newton
            // is on ONE sheet, and the nearest point of the whole surface to
            // the stepped curve point can be on another.
            let projection =
                crate::projection::project_point_to_surface_from_seed(surface, curve.evaluate(t)?, [u, v])?;
            u = projection.u;
            v = projection.v;
            continue;
        };
        step_t = step_t.clamp(-(t1 - t0) / 4.0, (t1 - t0) / 4.0);
        step_u = step_u.clamp(-(u1 - u0) / 4.0, (u1 - u0) / 4.0);
        step_v = step_v.clamp(-(v1 - v0) / 4.0, (v1 - v0) / 4.0);
        let next_t = (t + step_t).clamp(t0, t1);
        let next_u = fit_parameter(u + step_u, u0, u1, closed_u);
        let next_v = fit_parameter(v + step_v, v0, v1, closed_v);
        let stalled = (next_t - t).abs() <= 1e-15 * (t1 - t0)
            && (next_u - u).abs() <= 1e-15 * (u1 - u0)
            && (next_v - v).abs() <= 1e-15 * (v1 - v0);
        t = next_t;
        u = next_u;
        v = next_v;
        if stalled {
            return Ok([t, u, v]);
        }
    }
    Ok([t, u, v])
}

#[derive(Clone, Copy, Debug, Serialize)]
pub struct CurveSurfaceIntersection {
    pub t: f64,
    pub u: f64,
    pub v: f64,
    pub point: Vec3,
    pub gap: f64,
    pub tangential: bool,
}

/// Whether the duplicate guard's parameter tolerance is capped by the curve's
/// domain. `BREP_CS_DUPLICATE_CAP=0` restores the uncapped tolerance, which at
/// a stationary parameter is 1e6 and swallows every other hit on the curve.
fn duplicate_cap_enabled() -> bool {
    switch!("BREP_CS_DUPLICATE_CAP", true)
}

pub fn intersect_curve_surface(
    curve: &NurbsCurve,
    surface: &NurbsSurface,
    tolerance: f64,
) -> Result<Vec<CurveSurfaceIntersection>, String> {
    let _lap = crate::projection_profile::Lap::enter(crate::projection_profile::LANE_INTERSECT_CURVE_SURFACE, surface);
    let seeds = sampled_seeds(curve, surface, tolerance)?;
    intersect_curve_surface_from_seeds(curve, surface, tolerance, seeds)
}

/// The general search's Newton seeds: the midpoint of every sample segment
/// of the curve whose box meets the surface's box and one of its span boxes.
fn sampled_seeds(curve: &NurbsCurve, surface: &NurbsSurface, tolerance: f64) -> Result<Vec<f64>, String> {
    let [t0, t1] = curve.domain()?;
    let surface_box = surface_bounds(surface)?.expanded(tolerance * 10.0);
    let sample_count =
        32usize.max((interior_knot_count(&curve.knots, curve.degree) + 1) * (curve.degree + 1) * 4);
    let mut samples = Vec::with_capacity(sample_count + 1);
    for index in 0..=sample_count {
        let t = t0 + (t1 - t0) * index as f64 / sample_count as f64;
        samples.push((t, curve.evaluate(t)?));
    }
    let span_boxes = span_bounds(surface)?;
    let mut seeds = Vec::new();
    for pair in samples.windows(2) {
        let segment_box = Bounds::from_points([pair[0].1, pair[1].1]).expanded(tolerance * 10.0);
        if segment_box.intersects_exact(surface_box)
            && span_boxes.iter().any(|span_box| segment_box.intersects_exact(span_box.expanded(tolerance * 10.0)))
        {
            seeds.push((pair[0].0 + pair[1].0) * 0.5);
        }
    }
    Ok(seeds)
}

/// [`intersect_curve_surface`] from the caller's own Newton seeds (curve
/// parameters): the same Newton, gap filter, duplicate guard and tangency
/// reading as the general search, only the seeds differ. The classifier's
/// exact ray lane (`crate::exact_line_surface`) seeds it with the closed-form
/// roots of a straight segment against an analytic carrier.
pub(crate) fn intersect_curve_surface_from_seeds(
    curve: &NurbsCurve,
    surface: &NurbsSurface,
    tolerance: f64,
    seeds: Vec<f64>,
) -> Result<Vec<CurveSurfaceIntersection>, String> {
    let [t0, t1] = curve.domain()?;
    let mut results: Vec<CurveSurfaceIntersection> = Vec::new();
    for seed in seeds {
        let [t, u, v] = newton_curve_surface(curve, surface, seed)?;
        let on_curve = curve.evaluate(t)?;
        let on_surface = surface.evaluate(u, v)?;
        let gap = on_curve.sub(on_surface).length();
        if gap > tolerance {
            continue;
        }
        let tangent = curve.deriv1(t)?.1;
        // Two hits are the SAME hit when they are at the same PLACE, and the
        // chord test below is what measures that. This parameter test only has
        // to absorb two seeds landing on one root a few ulps apart — and it
        // converts the caller's 3D tolerance into a parameter tolerance by
        // dividing by the curve's speed, a quotient that is unbounded where the
        // speed is not. At a stationary parameter the `EPSILON` floor makes it
        // `1e-7 / 1e-12 * 10 = 1e6`, wider than any curve's domain, so every
        // earlier hit on the curve reads as a duplicate and a legitimate
        // intersection AT a cusp is discarded unless it happens to be first.
        // An involute flank's speed is `r_base * t`, so a gear profile carries
        // one such cusp per flank per tooth: this is the 2026-09-14 herringbone
        // report's root cause one lane over, where it is silent rather than
        // loud.
        //
        // The cap is the curve's OWN domain, which is the only scale this test
        // has: 1e-6 of it keeps the ulp-absorbing job (nine orders above the
        // `1e-15 * (t1 - t0)` stall the Newton above exits on, three above the
        // 1e-9 floor this rule already had) and drops the unbounded one. Two
        // seeds on the same cusp root can land further apart than that in
        // parameter, but not in space, and the chord test catches them.
        // Escape hatch for tamper-verification:
        // BREP_CS_DUPLICATE_CAP=0 restores the uncapped tolerance.
        let uncapped = ((tolerance / tangent.length().max(EPSILON)) * 10.0).max((t1 - t0) * 1e-9);
        let capped = uncapped.min((t1 - t0) * 1e-6);
        let parameter_tolerance = if duplicate_cap_enabled() { capped } else { uncapped };
        if let Some(result) = results.iter().find(|result| {
            (result.t - t).abs() <= parameter_tolerance
                || result.point.sub(on_curve).length() <= tolerance * 10.0
        }) {
            // The only drops the cap changes: a PARAMETER-only match (the two
            // hits are apart in space) that the capped tolerance would keep. A
            // hit dropped here leaves no trace anywhere else, so name it when
            // asked: `BREP_DEBUG_CS_DUPLICATE=1`. With the cap on this prints
            // nothing by construction; under `BREP_CS_DUPLICATE_CAP=0` it counts
            // what the cap recovers.
            let chord = result.point.sub(on_curve).length();
            let gap = (result.t - t).abs();
            if chord > tolerance * 10.0
                && gap > capped
                && std::env::var("BREP_DEBUG_CS_DUPLICATE").is_ok()
            {
                eprintln!(
                    "cs-duplicate: dropped t={t:.12} against t={:.12} gap={gap:.6e} ptol={parameter_tolerance:.6e} \
                     chord={chord:.6e} |tangent|={:.6e} domain=[{t0:.6},{t1:.6}] tolerance={tolerance:.3e}",
                    result.t,
                    tangent.length(),
                );
            }
            continue;
        }
        let normal = surface.normal(u, v).ok();
        let tangential = normal
            .and_then(|normal| {
                tangent
                    .normalized()
                    .ok()
                    .map(|unit| normal.dot(unit).abs() <= 1e-3)
            })
            .unwrap_or(false);
        results.push(CurveSurfaceIntersection {
            t,
            u,
            v,
            point: on_curve.add(on_surface).scale(0.5),
            gap,
            tangential,
        });
    }
    results.sort_by(|a, b| a.t.total_cmp(&b.t));
    Ok(results)
}