indicatrix 0.9.0

//! Concave-facet tool volumes: the resolved primitives a stone is carved with.
//!
//! A concave (or "fantasy") facet is the surface a rotating or reciprocating
//! tool leaves behind. The kernel never sees a tier or a notation; it sees a
//! list of [`ToolPrimitive`]s, each a **convex** volume that is subtracted from
//! the flat stone. Convexity is what keeps ray intersection closed-form: every
//! primitive, swept or not, decomposes into a handful of convex pieces (ball,
//! cone frustum, wedge) whose union is itself convex, so the ray's interval
//! inside a tool is `[min c, max d]` over the pieces and no iterative solver is
//! needed.
//!
//! The layout is `repr(C)`, 80 bytes, 16-byte aligned and made only of
//! `u32`/`f32`, so it is [`bytemuck::Pod`] and mirrors the WGSL struct of the
//! same name byte for byte.

#![expect(
    clippy::many_single_char_names,
    reason = "ray and frame algebra (o, p, q, a, c, d, r, s, t, z) mirrors the derivation in the plan; longer names would hide the formulas"
)]
#![expect(
    clippy::pub_underscore_fields,
    clippy::used_underscore_binding,
    reason = "`_pad` is part of the specified 80-byte GPU layout and is read only to check it is zero"
)]

use crate::{geometry::plane::GpuFacetPlane, optics::raytracer::camera::Ray};
use glam::Vec3;

mod interval;
mod pack;

use interval::{ball_interval, frustum_interval, wedge_interval};
pub use pack::{
    GPU_MAX_TOOL_PRIMITIVES, TOOL_RECORD_VECS, pack_planes_and_tools, pack_tool_record,
    packed_entry_count,
};

/// Upper bound on tool primitives in one stone.
///
/// One `pub const` so every validator and the shader loop bound agree. Each
/// index is one placement, not one tier; it also sizes the fixed boundary array
/// in `intersect_stone`, which is why that function never allocates.
pub const MAX_TOOL_PRIMITIVES: usize = 128;

/// Shape of a tool.
#[repr(u32)]
#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
pub enum ToolKind {
    /// Sphere (`SPH`, a dimple).
    Ball = 0,
    /// Capped cylinder (`CYL`, and `CIR` as a short one).
    Cylinder = 1,
    /// Cone frustum (`CON`).
    Frustum = 2,
    /// Two frusta sharing a rim plane (`DSC`, a wheel with a bevelled rim).
    Bicone = 3,
}

impl TryFrom<u32> for ToolKind {
    type Error = u32;

    /// Decodes the wire/GPU value; an unknown value is returned as the error.
    fn try_from(value: u32) -> Result<Self, Self::Error> {
        match value {
            0 => Ok(Self::Ball),
            1 => Ok(Self::Cylinder),
            2 => Ok(Self::Frustum),
            3 => Ok(Self::Bicone),
            other => Err(other),
        }
    }
}

/// How a tool moves while it cuts; the swept volume is what is subtracted.
#[repr(u32)]
#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
pub enum ToolSweep {
    /// Pressed in without lateral motion.
    None = 0,
    /// Reciprocates along its own axis (Minkowski sum with an axial segment).
    AlongAxis = 1,
    /// Reciprocates across its axis along `sweep_dir` (Minkowski sum with a
    /// perpendicular segment).
    AcrossAxis = 2,
}

impl TryFrom<u32> for ToolSweep {
    type Error = u32;

    /// Decodes the wire/GPU value; an unknown value is returned as the error.
    fn try_from(value: u32) -> Result<Self, Self::Error> {
        match value {
            0 => Ok(Self::None),
            1 => Ok(Self::AlongAxis),
            2 => Ok(Self::AcrossAxis),
            other => Err(other),
        }
    }
}

/// A convex tool volume subtracted from the stone, in model units.
///
/// One primitive per placement. Its facet id is `planes.len() + k` where `k` is
/// its position in the slice, so the struct carries no facet bookkeeping.
///
/// `align(16)` matches the WGSL storage-buffer rule for a struct of `vec4`s, so a
/// host `&[ToolPrimitive]` uploads with no repacking (80 is a multiple of 16, so
/// the attribute adds no padding and `Pod` still holds).
#[repr(C, align(16))]
#[derive(Debug, Clone, Copy, PartialEq, bytemuck::Pod, bytemuck::Zeroable)]
#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
pub struct ToolPrimitive {
    /// `ToolKind as u32`: 0 ball, 1 capped cylinder, 2 cone frustum, 3 bicone.
    pub kind: u32,
    /// `ToolSweep as u32`: 0 none, 1 along `axis`, 2 across `axis`.
    pub sweep_kind: u32,
    /// Must be zero (keeps the GPU layout and the cache hash canonical).
    pub _pad: [u32; 2],
    /// Centre `xyz`; `w` = radius at the centre (ball, cylinder, bicone rim).
    pub origin: [f32; 4],
    /// Unit axis `xyz`; `w` = half-length along the axis (0 for a ball).
    pub axis: [f32; 4],
    /// `x` = radius at `-half_length`, `y` = radius at `+half_length`, `z` =
    /// sweep half-stroke, `w` = 0.
    pub profile: [f32; 4],
    /// Unit sweep direction `xyz` (read only when `sweep_kind == 2`), `w` = 0.
    pub sweep_dir: [f32; 4],
}

/// Why a [`ToolPrimitive`] failed [`ToolPrimitive::validate`].
#[derive(Debug, Clone, PartialEq)]
#[non_exhaustive]
pub enum ToolPrimitiveError {
    /// Some float is NaN or infinite.
    NonFinite,
    /// A radius is negative, no radius is positive, or a length (half-length,
    /// half-stroke) is negative or, for a non-ball, zero.
    NonPositiveRadius,
    /// The axis, or the sweep direction when it is read, is not a unit vector
    /// to `1e-4` (or the sweep direction is not perpendicular to the axis).
    AxisNotUnit,
    /// `kind` is not a [`ToolKind`] value.
    UnknownKind(u32),
    /// `sweep_kind` is not a [`ToolSweep`] value.
    UnknownSweep(u32),
    /// A padding lane or a `w` lane that must be zero is not.
    PaddingNotZero,
}

impl std::fmt::Display for ToolPrimitiveError {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        match self {
            Self::NonFinite => f.write_str("tool primitive has a non-finite value"),
            Self::NonPositiveRadius => {
                f.write_str("tool primitive has an invalid radius or length")
            }
            Self::AxisNotUnit => f.write_str("tool primitive axis is not a unit vector"),
            Self::UnknownKind(k) => write!(f, "unknown tool kind {k}"),
            Self::UnknownSweep(k) => write!(f, "unknown tool sweep {k}"),
            Self::PaddingNotZero => f.write_str("tool primitive padding is not zero"),
        }
    }
}

impl std::error::Error for ToolPrimitiveError {}

/// The planes and tools that together bound a stone.
///
/// The single gate every "convex shortcut" tests via [`Self::is_convex`].
#[derive(Debug, Clone, Copy)]
pub struct StoneGeometry<'a> {
    /// The flat facets; `n . x + d <= 0` inside.
    pub planes: &'a [GpuFacetPlane],
    /// Convex volumes subtracted from the polyhedron the planes define.
    pub tools: &'a [ToolPrimitive],
}

impl<'a> StoneGeometry<'a> {
    /// A stone with no tools: every plane-only API wraps its slice in this.
    #[must_use]
    pub const fn planes_only(planes: &'a [GpuFacetPlane]) -> Self {
        Self { planes, tools: &[] }
    }

    /// `true` when there are no tools, i.e. the stone is the convex polyhedron.
    #[must_use]
    pub const fn is_convex(&self) -> bool {
        self.tools.is_empty()
    }

    /// Plane count plus tool count; tool `k` has facet id `planes.len() + k`.
    #[must_use]
    pub const fn facet_count(&self) -> usize {
        self.planes.len() + self.tools.len()
    }
}

/// One convex piece of a (possibly swept) tool.
///
/// Every tool decomposes into at most [`MAX_PIECES`] of these whose union is
/// the tool, which is how sweeps stay closed-form.
#[derive(Debug, Clone, Copy)]
enum Piece {
    Ball {
        c: Vec3,
        r: f32,
    },
    /// Frustum about `a` through `c`, radius `r0` at `-hl` and `r1` at `+hl`.
    Frustum {
        c: Vec3,
        a: Vec3,
        hl: f32,
        r0: f32,
        r1: f32,
    },
    /// The straight part of a stadium-section sweep: `|axial| <= hl`,
    /// `|along d| <= s`, `|across| <= r(axial)`.
    Wedge {
        c: Vec3,
        a: Vec3,
        d: Vec3,
        hl: f32,
        s: f32,
        r0: f32,
        r1: f32,
    },
}

/// Most pieces any tool needs (a bicone swept across: two frusta, twice, plus
/// two wedges).
const MAX_PIECES: usize = 6;

/// Fixed-capacity piece list, so decomposing a tool never allocates.
struct Pieces {
    items: [Piece; MAX_PIECES],
    len: usize,
}

impl Pieces {
    const fn new() -> Self {
        Self {
            items: [Piece::Ball {
                c: Vec3::ZERO,
                r: 0.0,
            }; MAX_PIECES],
            len: 0,
        }
    }

    fn push(&mut self, p: Piece) {
        debug_assert!(
            self.len < MAX_PIECES,
            "tool decomposes into too many pieces"
        );
        if self.len < MAX_PIECES {
            self.items[self.len] = p;
            self.len += 1;
        }
    }

    fn as_slice(&self) -> &[Piece] {
        &self.items[..self.len]
    }
}

/// A straight run of the axial radius profile: `z` in `[z_lo, z_hi]`, radius
/// `r_lo -> r_hi`.
#[derive(Clone, Copy)]
struct Segment {
    z_lo: f32,
    z_hi: f32,
    r_lo: f32,
    r_hi: f32,
}

impl Piece {
    /// Entry/exit parameters of `ray` inside the piece.
    fn interval(&self, ray: Ray) -> Option<(f32, f32)> {
        match *self {
            Self::Ball { c, r } => ball_interval(ray, c, r),
            Self::Frustum { c, a, hl, r0, r1 } => frustum_interval(ray, c, a, hl, r0, r1),
            Self::Wedge {
                c,
                a,
                d,
                hl,
                s,
                r0,
                r1,
            } => wedge_interval(ray, c, a, d, hl, s, r0, r1),
        }
    }

    /// A signed distance estimate (negative inside, zero on the surface; never
    /// larger in magnitude than the true distance for a point inside, and the
    /// correct sign everywhere) and the outward unit normal of the face that
    /// attains it.
    #[expect(
        clippy::manual_midpoint,
        reason = "pinned reference arithmetic: plain f32 `0.5 * (a + b)` (`f32::midpoint` widens through f64)"
    )]
    #[allow(
        clippy::suboptimal_flops,
        reason = "pinned reference arithmetic: unfused products (`mul_add` rounds once and moves the last bit)"
    )]
    fn sd_normal(&self, p: Vec3) -> (f32, Vec3) {
        match *self {
            Self::Ball { c, r } => {
                let q = p - c;
                let len = q.length();
                (len - r, if len > 1e-12 { q / len } else { Vec3::Z })
            }
            Self::Frustum { c, a, hl, r0, r1 } => {
                let q = p - c;
                let z = q.dot(a);
                let perp = q - a * z;
                let rho = perp.length();
                let rho_hat = if rho > 1e-12 {
                    perp / rho
                } else {
                    a.any_orthonormal_vector()
                };
                let (cap_sd, cap_n) = if z >= 0.0 { (z - hl, a) } else { (-z - hl, -a) };
                let dr = r1 - r0;
                let len = (4.0 * hl).mul_add(hl, dr * dr).sqrt();
                let rm = 0.5 * (r0 + r1);
                let side_sd = z.mul_add(-dr, (rho - rm) * 2.0 * hl) / len;
                let side_n = rho_hat * (2.0 * hl / len) - a * (dr / len);
                if side_sd > cap_sd {
                    (side_sd, side_n)
                } else {
                    (cap_sd, cap_n)
                }
            }
            Self::Wedge {
                c,
                a,
                d,
                hl,
                s,
                r0,
                r1,
            } => {
                let q = p - c;
                let w = a.cross(d);
                let z = q.dot(a);
                let x = q.dot(d);
                let y = q.dot(w);
                let k = (r1 - r0) / (2.0 * hl);
                let rm = 0.5 * (r0 + r1);
                let kappa = 1.0 / k.mul_add(k, 1.0).sqrt();
                let mut best = if z >= 0.0 { (z - hl, a) } else { (-z - hl, -a) };
                let along = if x >= 0.0 { (x - s, d) } else { (-x - s, -d) };
                if along.0 > best.0 {
                    best = along;
                }
                let slant_pos = ((y - rm - k * z) * kappa, (w - a * k) * kappa);
                if slant_pos.0 > best.0 {
                    best = slant_pos;
                }
                let slant_neg = ((-y - rm - k * z) * kappa, (-w - a * k) * kappa);
                if slant_neg.0 > best.0 {
                    best = slant_neg;
                }
                best
            }
        }
    }
}

impl ToolPrimitive {
    const fn base(
        kind: ToolKind,
        centre: Vec3,
        axis: Vec3,
        rim: f32,
        half_length: f32,
        r: [f32; 2],
    ) -> Self {
        Self {
            kind: kind as u32,
            sweep_kind: ToolSweep::None as u32,
            _pad: [0; 2],
            origin: [centre.x, centre.y, centre.z, rim],
            axis: [axis.x, axis.y, axis.z, half_length],
            profile: [r[0], r[1], 0.0, 0.0],
            sweep_dir: [0.0; 4],
        }
    }

    /// A sphere. Its axis is `+Z` so an along-axis sweep has a direction.
    #[must_use]
    pub const fn ball(centre: Vec3, radius: f32) -> Self {
        Self::base(
            ToolKind::Ball,
            centre,
            Vec3::Z,
            radius,
            0.0,
            [radius, radius],
        )
    }

    /// A capped cylinder of `radius` and total length `2 * half_length`.
    #[must_use]
    pub const fn cylinder(centre: Vec3, axis: Vec3, radius: f32, half_length: f32) -> Self {
        Self::base(
            ToolKind::Cylinder,
            centre,
            axis,
            radius,
            half_length,
            [radius, radius],
        )
    }

    /// A cone frustum with radius `r_neg` at `-half_length` and `r_pos` at
    /// `+half_length`.
    #[must_use]
    #[expect(
        clippy::manual_midpoint,
        reason = "pinned reference arithmetic: plain f32 `0.5 * (r_neg + r_pos)`; `f32::midpoint` widens through f64"
    )]
    pub fn frustum(centre: Vec3, axis: Vec3, r_neg: f32, r_pos: f32, half_length: f32) -> Self {
        Self::base(
            ToolKind::Frustum,
            centre,
            axis,
            0.5 * (r_neg + r_pos),
            half_length,
            [r_neg, r_pos],
        )
    }

    /// Two frusta sharing a rim of `rim_radius` at the centre, tapering to a
    /// point at each end (`r_neg = r_pos = 0`).
    #[must_use]
    pub const fn bicone(centre: Vec3, axis: Vec3, rim_radius: f32, half_length: f32) -> Self {
        Self::base(
            ToolKind::Bicone,
            centre,
            axis,
            rim_radius,
            half_length,
            [0.0, 0.0],
        )
    }

    /// Returns the tool with a sweep applied: a half-stroke along the axis, or
    /// across it along `dir` (which must be a unit vector perpendicular to the
    /// axis; ignored for [`ToolSweep::AlongAxis`] and [`ToolSweep::None`]).
    #[must_use]
    pub fn with_sweep(mut self, sweep: ToolSweep, half_stroke: f32, dir: Vec3) -> Self {
        self.sweep_kind = sweep as u32;
        self.profile[2] = half_stroke;
        self.sweep_dir = if sweep == ToolSweep::AcrossAxis {
            [dir.x, dir.y, dir.z, 0.0]
        } else {
            [0.0; 4]
        };
        self
    }

    /// The decoded shape, `None` for an unknown `kind`.
    #[must_use]
    pub fn kind(&self) -> Option<ToolKind> {
        ToolKind::try_from(self.kind).ok()
    }

    /// The decoded sweep, `None` for an unknown `sweep_kind`.
    #[must_use]
    pub fn sweep(&self) -> Option<ToolSweep> {
        ToolSweep::try_from(self.sweep_kind).ok()
    }

    /// Checks everything a producer must guarantee: every float finite, radii
    /// `>= 0` with one `> 0`, lengths `>= 0` (`> 0` for a non-ball), axis (and
    /// the sweep direction when read) unit to `1e-4` and perpendicular, pad and
    /// `w` lanes zero, kinds known.
    ///
    /// # Errors
    ///
    /// The first violated rule, as a [`ToolPrimitiveError`].
    pub fn validate(&self) -> Result<(), ToolPrimitiveError> {
        let all = self
            .origin
            .iter()
            .chain(&self.axis)
            .chain(&self.profile)
            .chain(&self.sweep_dir);
        if !all.into_iter().all(|v| v.is_finite()) {
            return Err(ToolPrimitiveError::NonFinite);
        }
        let kind = ToolKind::try_from(self.kind).map_err(ToolPrimitiveError::UnknownKind)?;
        let sweep =
            ToolSweep::try_from(self.sweep_kind).map_err(ToolPrimitiveError::UnknownSweep)?;
        if self._pad != [0; 2] || self.profile[3] != 0.0 || self.sweep_dir[3] != 0.0 {
            return Err(ToolPrimitiveError::PaddingNotZero);
        }
        let radii = [self.origin[3], self.profile[0], self.profile[1]];
        let hl = self.axis[3];
        let stroke = self.profile[2];
        if radii.iter().any(|&r| r < 0.0)
            || radii.iter().all(|&r| r <= 0.0)
            || hl < 0.0
            || (kind != ToolKind::Ball && hl <= 0.0)
            || (kind == ToolKind::Ball && hl != 0.0)
            || stroke < 0.0
        {
            return Err(ToolPrimitiveError::NonPositiveRadius);
        }
        let axis = self.axis_vec();
        if (axis.length() - 1.0).abs() > 1e-4 {
            return Err(ToolPrimitiveError::AxisNotUnit);
        }
        if sweep == ToolSweep::AcrossAxis {
            let dir = self.sweep_dir_vec();
            if (dir.length() - 1.0).abs() > 1e-4 || dir.dot(axis).abs() > 1e-4 {
                return Err(ToolPrimitiveError::AxisNotUnit);
            }
        }
        Ok(())
    }

    const fn centre(&self) -> Vec3 {
        Vec3::new(self.origin[0], self.origin[1], self.origin[2])
    }

    const fn axis_vec(&self) -> Vec3 {
        Vec3::new(self.axis[0], self.axis[1], self.axis[2])
    }

    const fn sweep_dir_vec(&self) -> Vec3 {
        Vec3::new(self.sweep_dir[0], self.sweep_dir[1], self.sweep_dir[2])
    }

    /// The profile as straight segments in axial coordinate, plus the index of
    /// the peak vertex (the plateau of an along-axis sweep sits there).
    fn segments(&self, kind: ToolKind) -> ([Segment; 2], usize, f32, f32) {
        let hl = self.axis[3];
        let rim = self.origin[3];
        let (rn, rp) = (self.profile[0], self.profile[1]);
        let seg = |z_lo, z_hi, r_lo, r_hi| Segment {
            z_lo,
            z_hi,
            r_lo,
            r_hi,
        };
        match kind {
            ToolKind::Ball | ToolKind::Cylinder => (
                [seg(-hl, hl, rim, rim), seg(0.0, 0.0, 0.0, 0.0)],
                1,
                hl,
                rim,
            ),
            ToolKind::Frustum => {
                let peak = if rp >= rn { (hl, rp) } else { (-hl, rn) };
                (
                    [seg(-hl, hl, rn, rp), seg(0.0, 0.0, 0.0, 0.0)],
                    1,
                    peak.0,
                    peak.1,
                )
            }
            ToolKind::Bicone => ([seg(-hl, 0.0, rn, rim), seg(0.0, hl, rim, rp)], 2, 0.0, rim),
        }
    }

    /// Decomposes the (swept) tool into convex pieces whose union it is.
    ///
    /// Along-axis: the radius profile of a Minkowski sum with an axial segment
    /// is the sliding-window maximum of a concave profile, i.e. each rising run
    /// shifted by `-stroke`, each falling run by `+stroke`, and a cylinder of
    /// half-length `stroke` on the peak. Across-axis: every cross-section
    /// circle becomes a stadium, i.e. two shifted copies plus the wedge between
    /// them.
    #[expect(
        clippy::manual_midpoint,
        reason = "pinned reference arithmetic: plain f32 `0.5 * (z_lo + z_hi)`; `f32::midpoint` widens through f64"
    )]
    fn pieces(&self) -> Option<Pieces> {
        let kind = self.kind()?;
        let sweep = self.sweep()?;
        let c = self.centre();
        let a = self.axis_vec();
        let stroke = self.profile[2];
        let mut out = Pieces::new();
        let swept = sweep != ToolSweep::None && stroke > 0.0;
        if kind == ToolKind::Ball {
            let r = self.origin[3];
            if swept {
                let dir = if sweep == ToolSweep::AlongAxis {
                    a
                } else {
                    self.sweep_dir_vec()
                };
                out.push(Piece::Ball {
                    c: c - dir * stroke,
                    r,
                });
                out.push(Piece::Ball {
                    c: c + dir * stroke,
                    r,
                });
                out.push(Piece::Frustum {
                    c,
                    a: dir,
                    hl: stroke,
                    r0: r,
                    r1: r,
                });
            } else {
                out.push(Piece::Ball { c, r });
            }
            return Some(out);
        }
        let (segs, n, peak_z, peak_r) = self.segments(kind);
        let seg_piece = |s: &Segment, shift: Vec3| Piece::Frustum {
            c: c + a * (0.5 * (s.z_lo + s.z_hi)) + shift,
            a,
            hl: 0.5 * (s.z_hi - s.z_lo),
            r0: s.r_lo,
            r1: s.r_hi,
        };
        for s in &segs[..n] {
            if !swept {
                out.push(seg_piece(s, Vec3::ZERO));
            } else if sweep == ToolSweep::AlongAxis {
                let shift = if s.r_hi >= s.r_lo {
                    -a * stroke
                } else {
                    a * stroke
                };
                out.push(seg_piece(s, shift));
            } else {
                let dir = self.sweep_dir_vec();
                out.push(seg_piece(s, -dir * stroke));
                out.push(seg_piece(s, dir * stroke));
                out.push(Piece::Wedge {
                    c: c + a * (0.5 * (s.z_lo + s.z_hi)),
                    a,
                    d: dir,
                    hl: 0.5 * (s.z_hi - s.z_lo),
                    s: stroke,
                    r0: s.r_lo,
                    r1: s.r_hi,
                });
            }
        }
        if swept && sweep == ToolSweep::AlongAxis {
            out.push(Piece::Frustum {
                c: c + a * peak_z,
                a,
                hl: stroke,
                r0: peak_r,
                r1: peak_r,
            });
        }
        Some(out)
    }

    /// Analytic inside test, used by tests and debug assertions.
    #[must_use]
    pub fn contains(&self, p: Vec3) -> bool {
        self.pieces()
            .is_some_and(|ps| ps.as_slice().iter().any(|pc| pc.sd_normal(p).0 <= 0.0))
    }

    /// Smallest `|signed distance estimate|` over the pieces: never larger than
    /// the true distance to a piece surface, so a point with a large gap is
    /// safely away from every boundary. Test support.
    #[cfg(test)]
    fn boundary_gap(&self, p: Vec3) -> f32 {
        self.pieces().map_or(0.0, |ps| {
            ps.as_slice()
                .iter()
                .map(|pc| pc.sd_normal(p).0.abs())
                .fold(f32::INFINITY, f32::min)
        })
    }

    /// Outward normal of the TOOL at a surface point (callers negate it for the
    /// stone: the tool's outward normal points into the stone material, the
    /// stone's outward normal into the cavity).
    ///
    /// For a union the owner of the surface point is the piece whose surface it
    /// is closest to; at a seam between pieces that is a tie and the first
    /// piece wins, deterministically.
    #[must_use]
    pub fn outward_normal(&self, p: Vec3) -> Vec3 {
        let Some(ps) = self.pieces() else {
            return Vec3::Z;
        };
        let mut best = (f32::INFINITY, Vec3::Z);
        for pc in ps.as_slice() {
            let (sd, n) = pc.sd_normal(p);
            if sd.abs() < best.0 {
                best = (sd.abs(), n);
            }
        }
        best.1
    }

    /// Entry/exit parameters of the ray inside the tool, or `None`.
    ///
    /// `[min c, max d]` over the convex pieces; valid because the union of the
    /// pieces is convex (a Minkowski sum of a convex tool with a segment).
    #[must_use]
    pub fn ray_interval(&self, ray: Ray) -> Option<(f32, f32)> {
        let ps = self.pieces()?;
        let mut hull: Option<(f32, f32)> = None;
        for pc in ps.as_slice() {
            if let Some((c, d)) = pc.interval(ray) {
                hull = Some(hull.map_or((c, d), |(lo, hi)| (lo.min(c), hi.max(d))));
            }
        }
        hull
    }
}

#[cfg(test)]
mod gpu_twin_tests;
#[cfg(test)]
mod tests;