roxlap-core 0.14.0

//! KFA (animated kv6) bone solver — the bone-transform helpers
//! `genperp`, `mat0`, and `setlimb`.
//!
//! A KFA sprite is a hierarchy of bones; each bone carries an
//! optional [`Sprite`] (= one kv6 limb) plus a hinge tying it to
//! its parent. Per frame, the user updates `kfaval[i]` (a 16-bit
//! angle) for each animated bone; [`solve_kfa_limbs`] walks the hinge
//! tree in topological order and computes each limb's world transform
//! from its parent's. The caller then draws each posed limb via
//! [`crate::dda_sprite::draw_sprite_dda`].
//!
//! Animation-curve playback (advancing `kfaval[]` from a baked
//! keyframe sequence) lives in
//! [`roxlap_formats::kfa::KfaSprite::animsprite`] — call it to
//! advance `kfaval[]` from a baked curve, or poke `kfaval[]`
//! directly for procedural animation, then render here. The bone
//! posing this module computes is also exposed standalone as
//! [`solve_kfa_limbs`] for non-CPU backends (the GPU sprite pass).
//!
//! No oracle pose exercises KFA, so this module's correctness
//! gate is "looks right + tests verify the bone math". We can
//! tighten validation when a real `.kfa` asset lands.

#![allow(
    clippy::cast_possible_truncation,
    clippy::cast_possible_wrap,
    clippy::cast_sign_loss,
    clippy::cast_precision_loss,
    clippy::similar_names,
    clippy::too_many_arguments,
    clippy::doc_markdown,
    clippy::many_single_char_names,
    clippy::missing_panics_doc,
    clippy::float_cmp,
    clippy::useless_vec
)]

use roxlap_formats::kfa::{Hinge, KfaSprite, Point3};
use roxlap_formats::sprite::Sprite;
use roxlap_formats::xform::BoneXform;

/// 3×3 + translation matrix multiply. Composes transform
/// `(a_s, a_h, a_f, a_o)` with `(b_s, b_h, b_f, b_o)` into
/// `(c_s, c_h, c_f, c_o)`: `c_* = a_s·b_*.x + a_h·b_*.y + a_f·b_*.z`,
/// and `c_o` adds `a_o`. Used by [`setlimb`] to chain a child bone's
/// world transform onto its parent's.
#[allow(clippy::too_many_arguments)]
fn mat2(
    a_s: [f32; 3],
    a_h: [f32; 3],
    a_f: [f32; 3],
    a_o: [f32; 3],
    b_s: [f32; 3],
    b_h: [f32; 3],
    b_f: [f32; 3],
    b_o: [f32; 3],
) -> ([f32; 3], [f32; 3], [f32; 3], [f32; 3]) {
    let c_s = [
        a_s[0] * b_s[0] + a_h[0] * b_s[1] + a_f[0] * b_s[2],
        a_s[1] * b_s[0] + a_h[1] * b_s[1] + a_f[1] * b_s[2],
        a_s[2] * b_s[0] + a_h[2] * b_s[1] + a_f[2] * b_s[2],
    ];
    let c_h = [
        a_s[0] * b_h[0] + a_h[0] * b_h[1] + a_f[0] * b_h[2],
        a_s[1] * b_h[0] + a_h[1] * b_h[1] + a_f[1] * b_h[2],
        a_s[2] * b_h[0] + a_h[2] * b_h[1] + a_f[2] * b_h[2],
    ];
    let c_f = [
        a_s[0] * b_f[0] + a_h[0] * b_f[1] + a_f[0] * b_f[2],
        a_s[1] * b_f[0] + a_h[1] * b_f[1] + a_f[1] * b_f[2],
        a_s[2] * b_f[0] + a_h[2] * b_f[1] + a_f[2] * b_f[2],
    ];
    let c_o = [
        a_s[0] * b_o[0] + a_h[0] * b_o[1] + a_f[0] * b_o[2] + a_o[0],
        a_s[1] * b_o[0] + a_h[1] * b_o[1] + a_f[1] * b_o[2] + a_o[1],
        a_s[2] * b_o[0] + a_h[2] * b_o[1] + a_f[2] * b_o[2] + a_o[2],
    ];
    (c_s, c_h, c_f, c_o)
}

/// Given a non-zero axis vector `a`, build two unit vectors `b`, `c`
/// such that `(a, b, c)` is a right-handed orthogonal frame with `a` as
/// the primary axis (`a` is not normalised; `b` and `c` are). A zero
/// input returns `([0; 3], [0; 3])`.
///
/// `b` is formed by zeroing `a`'s smallest-magnitude component and
/// normalising the perpendicular it leaves; `c = a × b` completes the
/// frame. Zeroing the smallest component keeps the perpendicular
/// well-conditioned.
fn genperp(a: [f32; 3]) -> ([f32; 3], [f32; 3]) {
    if a == [0.0, 0.0, 0.0] {
        return ([0.0; 3], [0.0; 3]);
    }
    // Pick the smallest-magnitude axis to zero out in `b`, so the
    // remaining two components dominate and the cross-product
    // `c = a × b` stays well-conditioned.
    let ax = a[0].abs();
    let ay = a[1].abs();
    let az = a[2].abs();
    let b = if ax < ay && ax < az {
        let t = 1.0 / (a[1] * a[1] + a[2] * a[2]).sqrt();
        [0.0, a[2] * t, -a[1] * t]
    } else if ay < az {
        let t = 1.0 / (a[0] * a[0] + a[2] * a[2]).sqrt();
        [-a[2] * t, 0.0, a[0] * t]
    } else {
        let t = 1.0 / (a[0] * a[0] + a[1] * a[1]).sqrt();
        [a[1] * t, -a[0] * t, 0.0]
    };
    let c = [
        a[1] * b[2] - a[2] * b[1],
        a[2] * b[0] - a[0] * b[2],
        a[0] * b[1] - a[1] * b[0],
    ];
    (b, c)
}

/// Given orthonormal frames `B` and `C` (each a 3×3 basis + origin),
/// find the rigid transform `A` with `A · B = C`. Since `B` is
/// orthonormal, `A = C · Bᵀ`: each column of `A` is `C`'s column
/// re-expressed in `B`'s frame, and the origin follows by subtracting
/// `A · B_o`. Used by [`limb_xform`] to find the rotation mapping a
/// bone's parent-side hinge frame onto its child-side frame.
fn mat0(
    b_s: [f32; 3],
    b_h: [f32; 3],
    b_f: [f32; 3],
    b_o: [f32; 3],
    c_s: [f32; 3],
    c_h: [f32; 3],
    c_f: [f32; 3],
    c_o: [f32; 3],
) -> ([f32; 3], [f32; 3], [f32; 3], [f32; 3]) {
    // Each output column = C's column re-expressed in B's frame
    // (= C · Bᵀ, B orthonormal).
    let ts = [
        b_s[0] * c_s[0] + b_h[0] * c_h[0] + b_f[0] * c_f[0],
        b_s[0] * c_s[1] + b_h[0] * c_h[1] + b_f[0] * c_f[1],
        b_s[0] * c_s[2] + b_h[0] * c_h[2] + b_f[0] * c_f[2],
    ];
    let th = [
        b_s[1] * c_s[0] + b_h[1] * c_h[0] + b_f[1] * c_f[0],
        b_s[1] * c_s[1] + b_h[1] * c_h[1] + b_f[1] * c_f[1],
        b_s[1] * c_s[2] + b_h[1] * c_h[2] + b_f[1] * c_f[2],
    ];
    let tf = [
        b_s[2] * c_s[0] + b_h[2] * c_h[0] + b_f[2] * c_f[0],
        b_s[2] * c_s[1] + b_h[2] * c_h[1] + b_f[2] * c_f[1],
        b_s[2] * c_s[2] + b_h[2] * c_h[2] + b_f[2] * c_f[2],
    ];
    let to = [
        c_o[0] - b_o[0] * ts[0] - b_o[1] * th[0] - b_o[2] * tf[0],
        c_o[1] - b_o[0] * ts[1] - b_o[1] * th[1] - b_o[2] * tf[1],
        c_o[2] - b_o[0] * ts[2] - b_o[1] * th[2] - b_o[2] * tf[2],
    ];
    (ts, th, tf, to)
}

#[inline]
fn pt(p: Point3) -> [f32; 3] {
    [p.x, p.y, p.z]
}

/// Compute child limb `i`'s world transform from its parent's, via the
/// hinge connecting them, and write it into `limbs[i]`. Thin wrapper
/// over [`limb_xform`] (the pure math).
fn setlimb(limbs: &mut [Sprite], hinges: &[Hinge], i: usize, parent: usize, xform: &BoneXform) {
    let p = &limbs[parent];
    let (cs, ch, cf, co) = limb_xform((p.s, p.h, p.f, p.p), &hinges[i], xform);
    let child = &mut limbs[i];
    child.s = cs;
    child.h = ch;
    child.f = cf;
    child.p = co;
}

/// The pure `setlimb` math: a child bone's world `(s, h, f, p)` from its
/// parent's world transform, the connecting `hinge`, and the bone's local
/// [`BoneXform`]. Split out from [`setlimb`] (which writes into the
/// `Sprite` list) so it can be reasoned about / tested in isolation.
fn limb_xform(
    parent: ([f32; 3], [f32; 3], [f32; 3], [f32; 3]),
    hinge: &Hinge,
    xform: &BoneXform,
) -> ([f32; 3], [f32; 3], [f32; 3], [f32; 3]) {
    let (parent_s, parent_h, parent_f, parent_p) = parent;

    // Step 1: child-side anchor frame, with the animated translation added to
    // the child anchor (anchor-local).
    let qp0 = pt(hinge.p[0]);
    let qp = [
        qp0[0] + xform.t[0],
        qp0[1] + xform.t[1],
        qp0[2] + xform.t[2],
    ];
    let qs0 = pt(hinge.v[0]);
    let (qh0, qf0) = genperp(qs0);

    // Step 2: apply the hinge rotation by rotating the whole anchor frame
    // by the quaternion. A rotation about the hinge axis leaves `qs` fixed
    // and spins `(qh, qf)` in their plane — the legacy single-axis hinge
    // case (see `BoneXform::from_hinge_angle`); a free quaternion gives
    // full 3-DOF.
    let qs = xform.r.rotate(qs0);
    let qh = xform.r.rotate(qh0);
    let qf = xform.r.rotate(qf0);

    // Step 3: parent-side anchor frame.
    let pp = pt(hinge.p[1]);
    let ps = pt(hinge.v[1]);
    let (ph, pf) = genperp(ps);

    // Step 4: mat0 — find R such that R * (ps,ph,pf,pp) = (qs,qh,qf,qp).
    let (rs, rh, rf, ro) = mat0(ps, ph, pf, pp, qs, qh, qf, qp);

    // Step 5: mat2 — child_world = parent_world * R.
    let (cs, ch, cf, co) = mat2(parent_s, parent_h, parent_f, parent_p, rs, rh, rf, ro);

    // Step 6: non-uniform scale along the bone's local axes — the Sprite basis
    // vectors' length scales the kv6 (children inherit it via `mat2`).
    (
        [cs[0] * xform.s[0], cs[1] * xform.s[0], cs[2] * xform.s[0]],
        [ch[0] * xform.s[1], ch[1] * xform.s[1], ch[2] * xform.s[1]],
        [cf[0] * xform.s[2], cf[1] * xform.s[2], cf[2] * xform.s[2]],
        co,
    )
}

/// Pose every limb of a KFA sprite. Walks the hinge tree in
/// topological order (parents first) and writes each limb's world
/// `(s, h, f, p)` from its parent's via the per-limb `setlimb` math,
/// reading the current [`KfaSprite::kfaval`] angles. Mirror of the
/// bone-hierarchy transform solve.
///
/// Split out so non-CPU backends (e.g. the GPU instanced-sprite pass)
/// can run the exact same posing and then consume `kfa.limbs[*]`
/// transforms however they need (e.g. the renderer draws each limb via
/// [`crate::dda_sprite::draw_sprite_dda`]). The host typically calls
/// [`KfaSprite::animsprite`](roxlap_formats::kfa::KfaSprite::animsprite)
/// to advance `kfaval[]` first, then this to resolve world transforms.
pub fn solve_kfa_limbs(kfa: &mut KfaSprite) {
    // `hinge_sort` orders bones parents-before-children when walked in
    // reverse (parents sit at the high indices), so descending iteration
    // resolves each parent before its children.
    let n = kfa.hinge_sort.len();
    for k in (0..n).rev() {
        let j = kfa.hinge_sort[k];
        let parent = kfa.hinges[j].parent;
        if parent >= 0 {
            // Child bone: derive transform from parent using the bone's
            // resolved local TRS (`kfaval`). A non-zero `htype` means "no
            // rotation/transform".
            let htype = kfa.hinges[j].htype;
            let xform = if htype == 0 {
                kfa.kfaval[j]
            } else {
                BoneXform::IDENTITY
            };
            setlimb(&mut kfa.limbs, &kfa.hinges, j, parent as usize, &xform);
        } else {
            // Root bone: copy world basis from KfaSprite + apply
            // hinge.p[0] as the anchor offset.
            let s = kfa.s;
            let h = kfa.h;
            let f = kfa.f;
            let p_world = kfa.p;
            let tp = pt(kfa.hinges[j].p[0]);
            let limb = &mut kfa.limbs[j];
            limb.s = s;
            limb.h = h;
            limb.f = f;
            limb.p = [
                p_world[0] - tp[0] * s[0] - tp[1] * h[0] - tp[2] * f[0],
                p_world[1] - tp[0] * s[1] - tp[1] * h[1] - tp[2] * f[1],
                p_world[2] - tp[0] * s[2] - tp[1] * h[2] - tp[2] * f[2],
            ];
        }
    }
}

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

    /// genperp produces an orthonormal basis with the input axis
    /// as the dominant direction.
    #[test]
    fn genperp_orthonormal() {
        let a = [1.0_f32, 0.0, 0.0];
        let (b, c) = genperp(a);
        // b · a = 0
        assert!((a[0] * b[0] + a[1] * b[1] + a[2] * b[2]).abs() < 1e-6);
        // c · a = 0
        assert!((a[0] * c[0] + a[1] * c[1] + a[2] * c[2]).abs() < 1e-6);
        // b · c = 0
        assert!((b[0] * c[0] + b[1] * c[1] + b[2] * c[2]).abs() < 1e-6);
        // |b| ≈ 1
        let lb = b[0] * b[0] + b[1] * b[1] + b[2] * b[2];
        assert!((lb - 1.0).abs() < 1e-5, "|b|² = {lb}");
        // |c| ≈ 1
        let lc = c[0] * c[0] + c[1] * c[1] + c[2] * c[2];
        assert!((lc - 1.0).abs() < 1e-5, "|c|² = {lc}");
    }

    /// genperp of zero vector returns zero vectors.
    #[test]
    fn genperp_zero() {
        let (b, c) = genperp([0.0, 0.0, 0.0]);
        assert_eq!(b, [0.0, 0.0, 0.0]);
        assert_eq!(c, [0.0, 0.0, 0.0]);
    }

    /// The single-axis hinge rotation in closed form (rotate `(qh, qf)`
    /// about `qs` by the Q15 angle, no translation / scale), kept as the
    /// reference the general `BoneXform` path must reproduce.
    fn legacy_limb_xform(
        parent: ([f32; 3], [f32; 3], [f32; 3], [f32; 3]),
        hinge: &Hinge,
        val: i16,
    ) -> ([f32; 3], [f32; 3], [f32; 3], [f32; 3]) {
        let (ps0, ph0, pf0, pp0) = parent;
        let qp = pt(hinge.p[0]);
        let qs = pt(hinge.v[0]);
        let (mut qh, mut qf) = genperp(qs);
        let ang = (i32::from(val) as f32) * (std::f32::consts::PI * 2.0 / 65536.0);
        let (c, s) = (ang.cos(), ang.sin());
        let (ih, jf) = (qh, qf);
        qh = [
            ih[0] * c - jf[0] * s,
            ih[1] * c - jf[1] * s,
            ih[2] * c - jf[2] * s,
        ];
        qf = [
            ih[0] * s + jf[0] * c,
            ih[1] * s + jf[1] * c,
            ih[2] * s + jf[2] * c,
        ];
        let pp = pt(hinge.p[1]);
        let ps = pt(hinge.v[1]);
        let (ph, pf) = genperp(ps);
        let (rs, rh, rf, ro) = mat0(ps, ph, pf, pp, qs, qh, qf, qp);
        mat2(ps0, ph0, pf0, pp0, rs, rh, rf, ro)
    }

    /// The new TRS solver, fed a rotation-only `BoneXform` from a hinge angle,
    /// reproduces the legacy single-axis `setlimb` to f32 epsilon — so the
    /// quaternion rewrite is behaviour-preserving for existing rigs.
    #[test]
    fn trs_solver_matches_the_legacy_hinge_rotation() {
        let axis = Point3 {
            x: 0.0,
            y: 0.0,
            z: 1.0,
        };
        let hinge = Hinge {
            parent: 0,
            p: [
                Point3 {
                    x: 0.0,
                    y: 0.0,
                    z: 0.0,
                },
                Point3 {
                    x: 6.0,
                    y: 0.0,
                    z: 0.0,
                },
            ],
            v: [axis, axis],
            vmin: i16::MIN,
            vmax: i16::MAX,
            htype: 0,
            filler: [0; 7],
        };
        // An identity (axis-aligned, origin) parent world transform.
        let parent = (
            [1.0, 0.0, 0.0],
            [0.0, 1.0, 0.0],
            [0.0, 0.0, 1.0],
            [0.0, 0.0, 0.0],
        );
        let close = |a: [f32; 3], b: [f32; 3]| (0..3).all(|i| (a[i] - b[i]).abs() < 1e-4);
        for val in [0i16, 8000, 16384, -16384, 30000, i16::MIN] {
            let want = legacy_limb_xform(parent, &hinge, val);
            let got = limb_xform(parent, &hinge, &BoneXform::from_hinge_angle(pt(axis), val));
            assert!(
                close(got.0, want.0),
                "s mismatch at {val}: {:?} vs {:?}",
                got.0,
                want.0
            );
            assert!(close(got.1, want.1), "h mismatch at {val}");
            assert!(close(got.2, want.2), "f mismatch at {val}");
            assert!(close(got.3, want.3), "p mismatch at {val}");
        }
    }
}