//! The relief shading model in Rust — the arithmetic `shader2d.wgsl` performs
 //! per pixel, so code outside the GPU can PREDICT the pixels instead of
 //! sketching them. Both branches: the free carves ([`carve_shade`]) and the
 //! plate's own perimeter roll ([`plate_surface`]), which do not composite the
 //! same way — a carve is a translucent overlay, a plate is a multiply on its
 //! own fill plus an additive specular.
 //!
 //! This exists because `cce-relief` drew its cross-sections with a stand-in
 //! (`lit = dot(normal, light) * 0.35`) that shares nothing with the shader but
 //! a light azimuth. A section drawn that way shows the geometry honestly and
 //! the shading not at all — it cannot tell you that a wall reads hot, which is
 //! the single most common thing you go to the editor to judge.
 //!
 //! **Drift is the hazard**, since WGSL and Rust cannot share a function body.
 //! Two defences: the light vector lives HERE and the finish in
 //! [`crate::scene::material`], and the renderer reads both from there
 //! (`window_runner`'s `plate_light`/`plate_mat`); and the constants below are
 //! checked against the shader's own source text by a unit test. Anything that
 //! is only a comment away from disagreeing is not shared.
 
 /// The finish — how a surface answers light — moved to `scene::material` as
 /// [`Finish`] (RFC material, § 11 (4)). `Material` survives here as an alias
 /// through step 2 so out-of-crate readers build untouched.
 pub use crate::scene::material::Finish;
 pub use crate::scene::material::Finish as Material;
 
 /// Ambient floor of the plate lighting model. Mirrors `PLATE_AMBIENT`.
 pub const PLATE_AMBIENT: f32 = 0.55;
 /// A carve's drop as a fraction of its wall width when the material pins no
 /// height (`layout::bevel_height`). Mirrors `RECESS_DEPTH`.
 pub const RECESS_DEPTH: f32 = 0.6;
 
 /// Amplitude of the bright crest hugging a raised plate's silhouette.
 /// Mirrors `PLATE_CREST`.
 pub const PLATE_CREST: f32 = 0.25;
 /// The far-edge shade line's strength relative to the glint. Mirrors
 /// `PLATE_SHADE_LINE`.
 pub const PLATE_SHADE_LINE: f32 = 0.5;
 /// The roll's descent is truncated at this fraction of the quadrant, so the
 /// profile ends on a bounded slope instead of plunging vertical at the
 /// silhouette. Mirrors `ROLL_CUT`.
 pub const ROLL_CUT: f32 = 0.8;
 
 /// The free-carve modes, matching the shader's `MODE_*`.
 #[derive(Clone, Copy, PartialEq, Eq, Debug)]
 pub enum CarveMode {
     Recess,
     Boss,
     Ridge,
     Trough,
 }
 
 /// The DE's light as a unit vector in screen space (+z out of the screen), at
 /// the fixed 45° elevation the renderer uses. The ONE definition, as with
 /// [`Finish::from_style`].
 pub fn light_vector() -> [f32; 3] {
     let az = crate::layout::light_source_position();
     let el = std::f32::consts::FRAC_PI_4;
     [az.cos() * el.cos(), -az.sin() * el.cos(), el.sin()]
 }
 
 /// Shading of the flat face — the denominator every carve is expressed
 /// relative to, so an untouched surface composites to exactly nothing.
 pub fn flat_shade(light: [f32; 3]) -> f32 {
     PLATE_AMBIENT + (1.0 - PLATE_AMBIENT) * light[2]
 }
 
 /// The analytic carve slope: smoothstep normally, smootherstep under a
 /// continuous-curvature `corner_shape`. Mirrors `carve_slope`'s analytic
 /// branch; a custom profile replaces it with the LUT, which callers model by
 /// passing their own slope function to [`carve_shade`].
 pub fn analytic_carve_slope(v: f32) -> f32 {
     if crate::layout::corner_shape() > 2.001 {
         let w = v * (1.0 - v);
         30.0 * w * w
     } else {
         6.0 * v * (1.0 - v)
     }
 }
 
 /// Specular term of a tilted surface under the DE light. Mirrors `roll_spec`.
 pub fn roll_spec(sv: [f32; 2], light: [f32; 3], mat: &Finish) -> f32 {
     let m = (sv[0] * sv[0] + sv[1] * sv[1]).sqrt();
     if m < 1e-5 {
         return 0.0;
     }
     let hv = {
         let h = [light[0], light[1], light[2] + 1.0];
         let n = (h[0] * h[0] + h[1] * h[1] + h[2] * h[2]).sqrt().max(1e-6);
         [h[0] / n, h[1] / n, h[2] / n]
     };
     let facing = [sv[0] / m, sv[1] / m];
     let cos_t = 1.0 / (1.0 + m * m).sqrt();
     let sin_t = m * cos_t;
     let hxy = (hv[0] * hv[0] + hv[1] * hv[1]).sqrt();
     let prof = cos_t * hv[2] + sin_t * hxy;
     let az = ((facing[0] * hv[0] + facing[1] * hv[1]) / hxy.max(1e-4)).clamp(0.0, 1.0);
     mat.spec * (prof.powf(mat.shininess) - hv[2].powf(mat.shininess)).max(0.0) * az * az
 }
 
 /// The glint's dark counterpart: [`roll_spec`] under the light's azimuth
 /// mirrored, so the same lobe lands on the edges facing away from the light,
 /// scaled by [`PLATE_SHADE_LINE`]. Mirrors `roll_shade_line`. Subtracted in
 /// colour units where the glint is added.
 pub fn roll_shade_line(sv: [f32; 2], light: [f32; 3], mat: &Finish) -> f32 {
     roll_spec(sv, [-light[0], -light[1], light[2]], mat) * PLATE_SHADE_LINE
 }
 
 /// The signed shading value one carve contributes at `u` across its wall —
 /// the shader's `v`, before the tint branch. Positive is a white screen over
 /// what is beneath, negative a black multiply; magnitude is the alpha.
 ///
 /// `facing` is the SDF gradient direction (unit, pointing OUT of the carve's
 /// box). `slope_at` is the profile's slope function — pass
 /// [`analytic_carve_slope`] for the default material, or the derivative of a
 /// custom height curve to model an installed LUT.
 ///
 /// `att` (the host-box roll fade) is left to the caller: it depends on where
 /// the carve sits inside its host, not on the profile.
 pub fn carve_shade(
     mode: CarveMode,
     u: f32,
     facing: [f32; 2],
     slope_at: &dyn Fn(f32) -> f32,
     light: [f32; 3],
     mat: &Finish,
 ) -> f32 {
     let u = u.clamp(0.0, 1.0);
     let (slope, curv) = match mode {
         // The straddling pair: ONE profile evaluation on the folded coordinate,
         // amplitude halved so the wall tilt matches a step's.
         CarveMode::Ridge | CarveMode::Trough => {
             let w = (2.0 * u).min(2.0 - 2.0 * u).clamp(0.0, 1.0);
             let up = if mode == CarveMode::Ridge { 1.0 } else { -1.0 };
             let rising = if u <= 0.5 { 1.0 } else { -1.0 } * up;
             (
                 rising * 0.5 * mat.carve_depth * 2.0 * slope_at(w),
                 -up * mat.curvature * (w * std::f32::consts::TAU).sin(),
             )
         }
         _ => {
             let dir = if mode == CarveMode::Boss { 1.0 } else { -1.0 };
             (
                 dir * mat.carve_depth * slope_at(u),
                 -dir * mat.curvature * (u * std::f32::consts::TAU).sin(),
             )
         }
     };
     let sv = [facing[0] * slope, facing[1] * slope];
     let n = {
         let len = (sv[0] * sv[0] + sv[1] * sv[1] + 1.0).sqrt();
         [sv[0] / len, sv[1] / len, 1.0 / len]
     };
     let ndl = (n[0] * light[0] + n[1] * light[1] + n[2] * light[2]).max(0.0);
     let diff = PLATE_AMBIENT + (1.0 - PLATE_AMBIENT) * ndl;
     let spec = roll_spec(sv, light, mat);
     (diff / flat_shade(light) - 1.0 + curv + spec) * mat.strength
 }
 
 /// The analytic roll slope at `f` (0 where the roll meets the face, 1 at the
 /// silhouette). Mirrors `roll_slope`'s analytic branch: the one-exponent
 /// generalisation of the circular quadrant, truncated at [`ROLL_CUT`].
 pub fn analytic_roll_slope(f: f32) -> f32 {
     let shape = crate::layout::corner_shape();
     let fc = f * ROLL_CUT;
     if shape > 2.001 {
         let h = (1.0 - fc.powf(shape)).max(1e-4).powf(1.0 / shape);
         (fc / h).powf(shape - 1.0)
     } else {
         fc / (1.0 - fc * fc).max(1e-4).sqrt()
     }
 }
 
 /// How squarely a rim faces the light's azimuth, 0..1 — the weight on the
 /// plate crest. Mirrors `crest_weight`. The crest used to be a flat
 /// `PLATE_CREST` on every side, which out-measured the far edges' diffuse
 /// fall-off everywhere along the roll, so a raised plate had a lit rim and no
 /// shadowed one; weighted, the down-light edges keep only their diffuse
 /// shading and read as the glint's dark counterpart. A light from straight
 /// overhead has no near or far side and keeps the crest everywhere.
 pub fn crest_weight(facing: [f32; 2], light: [f32; 3]) -> f32 {
     let m = (light[0] * light[0] + light[1] * light[1]).sqrt();
     if m < 1e-4 {
         return 1.0;
     }
     ((facing[0] * light[0] + facing[1] * light[1]) / m).max(0.0)
 }
 
 /// The plate's own surface colour across its perimeter roll — mode 1, which is
 /// NOT the free-carve branch and does not composite like one.
 ///
 /// A carve emits a translucent overlay; a plate emits its material directly, as
 /// a MULTIPLY on the face colour plus an additive specular. Expressed relative
 /// to the flat face (shade 1.0, specular 0.0) so the face keeps exactly the
 /// app's chosen colour — which is why a plate can be tinted freely and a carve
 /// cannot.
 ///
 /// `f` is 0 where the roll meets the face and 1 at the silhouette. Returns
 /// `None` past the silhouette, where the shader discards.
 pub fn plate_surface(
     base: [f32; 3],
     f: f32,
     facing: [f32; 2],
     roll_slope_at: &dyn Fn(f32) -> f32,
     light: [f32; 3],
     mat: &Finish,
 ) -> Option<[f32; 3]> {
     if !(0.0..=1.0).contains(&f) {
         return None;
     }
     let slope = roll_slope_at(f) * mat.roll_height;
     let sv = [facing[0] * slope, facing[1] * slope];
     let n = {
         let len = (sv[0] * sv[0] + sv[1] * sv[1] + 1.0).sqrt();
         [sv[0] / len, sv[1] / len, 1.0 / len]
     };
     let ndl = (n[0] * light[0] + n[1] * light[1] + n[2] * light[2]).max(0.0);
     let diff = PLATE_AMBIENT + (1.0 - PLATE_AMBIENT) * ndl;
     // The crest: the ambient-catching convex rim that makes glass read as glass.
     let extra = PLATE_CREST * f * f * f * crest_weight(facing, light);
     let shade = 1.0 + (diff / flat_shade(light) - 1.0 + extra) * mat.strength;
     let spec = (roll_spec(sv, light, mat) - roll_shade_line(sv, light, mat)) * mat.strength;
     Some([
         (base[0] * shade + spec).clamp(0.0, 1.0),
         (base[1] * shade + spec).clamp(0.0, 1.0),
         (base[2] * shade + spec).clamp(0.0, 1.0),
     ])
 }
 
 /// Composite one carve's shading over what is already there, the way the
 /// renderer's alpha blend does.
 ///
 /// This asymmetry is load-bearing and is why a wall's bright side always
 /// out-measures its dark side: brightening screens toward WHITE, darkening
 /// multiplies toward BLACK, so on a mid-grey surface the same |v| moves the
 /// pixel about twice as far up as down.
 pub fn composite(base: [f32; 3], v: f32) -> [f32; 3] {
     let a = v.abs().min(1.0);
     let target = if v >= 0.0 { 1.0f32 } else { 0.0f32 };
     [
         base[0] * (1.0 - a) + target * a,
         base[1] * (1.0 - a) + target * a,
         base[2] * (1.0 - a) + target * a,
     ]
 }
 
 #[cfg(test)]
 mod tests {
     use super::*;
 
     /// The shader's own source, so the constants below are checked against the
     /// thing they mirror rather than against a comment.
     const WGSL: &str = include_str!("../vk/shader2d.wgsl");
 
     fn wgsl_const(name: &str) -> f32 {
         let needle = format!("const {name}: f32 = ");
         let rest = WGSL
             .split(&needle)
             .nth(1)
             .unwrap_or_else(|| panic!("{name} not found in shader2d.wgsl"));
         let lit: String = rest.chars().take_while(|c| *c != ';').collect();
         lit.trim().parse().expect("numeric literal")
     }
 
     #[test]
     fn constants_match_the_shader() {
         assert_eq!(wgsl_const("PLATE_AMBIENT"), PLATE_AMBIENT);
         assert_eq!(wgsl_const("RECESS_DEPTH"), RECESS_DEPTH);
         assert_eq!(wgsl_const("PLATE_CREST"), PLATE_CREST);
         assert_eq!(wgsl_const("ROLL_CUT"), ROLL_CUT);
         assert_eq!(wgsl_const("PLATE_SHADE_LINE"), PLATE_SHADE_LINE);
     }
 
     /// The crest is light-facing: at the silhouette the edge toward the light
     /// shades brighter than the face and the edge away from it darker. Before
     /// the weight, the flat crest left the far edge at or above the face.
     #[test]
     fn far_edge_shades_darker_than_the_face() {
         let light = light_vector();
         let mat = Finish::from_style();
         let base = [0.5f32; 3];
         let lxy = [light[0], light[1]];
         let m = (lxy[0] * lxy[0] + lxy[1] * lxy[1]).sqrt();
         let near = [lxy[0] / m, lxy[1] / m];
         let far = [-near[0], -near[1]];
         let lit = plate_surface(base, 1.0, near, &analytic_roll_slope, light, &mat).unwrap();
         let dark = plate_surface(base, 1.0, far, &analytic_roll_slope, light, &mat).unwrap();
         assert!(lit[0] > base[0] + 0.02, "near edge {} vs face {}", lit[0], base[0]);
         assert!(dark[0] < base[0] - 0.02, "far edge {} vs face {}", dark[0], base[0]);
     }
 
     /// The plate's face must come through as exactly the app's colour, or a
     /// plate silently recolours whatever it is filled with.
     #[test]
     fn plate_face_is_untouched() {
         let light = light_vector();
         let mat = Finish::from_style();
         let base = [0.3f32, 0.4, 0.5];
         let out = plate_surface(base, 0.0, [-1.0, 0.0], &analytic_roll_slope, light, &mat).unwrap();
         for i in 0..3 {
             assert!((out[i] - base[i]).abs() < 1e-4, "face channel {i}: {} vs {}", out[i], base[i]);
         }
     }
 
     /// A flat surface must composite to nothing, or the cover quad tints
     /// everything it covers — the property the whole "relative to the flat
     /// face" formulation exists to guarantee.
     #[test]
     fn flat_ground_shades_to_zero() {
         let light = light_vector();
         let mat = Finish::from_style();
         for mode in [CarveMode::Recess, CarveMode::Boss, CarveMode::Ridge, CarveMode::Trough] {
             for u in [0.0f32, 1.0] {
                 let v = carve_shade(mode, u, [-1.0, 0.0], &analytic_carve_slope, light, &mat);
                 assert!(v.abs() < 1e-4, "{mode:?} at u={u} shaded {v}, expected 0");
             }
         }
     }
 
     /// A pinned height is geometry: a deeper carve tilts its wall more and
     /// shades harder, with nothing else changed.
     #[test]
     fn deeper_carve_shades_harder() {
         let light = light_vector();
         let shallow = Finish { carve_depth: 0.3, ..Finish::from_style() };
         let deep = Finish { carve_depth: 1.2, ..Finish::from_style() };
         let at = |m: &Finish| carve_shade(CarveMode::Recess, 0.5, [-1.0, 0.0], &analytic_carve_slope, light, m).abs();
         assert!(at(&deep) > at(&shallow) * 1.5, "deep {} vs shallow {}", at(&deep), at(&shallow));
         // And the flat plateaus still composite to nothing.
         assert!(carve_shade(CarveMode::Recess, 0.0, [-1.0, 0.0], &analytic_carve_slope, light, &deep).abs() < 1e-4);
     }
 
     /// Ridge and trough are the same wall with the height sign flipped, so
     /// their shading is opposite WHERE THE WALL IS STEEP.
     ///
     /// Not everywhere, which is worth stating because it is the first thing you
     /// would assume: the response has an EVEN component. Tilting a surface
     /// either way shortens the face-on `n.z` term and adds a non-negative
     /// specular, so near the plateau lips — where the directional part is
     /// nearly nothing — a ridge and a trough both darken slightly. That is the
     /// faint lip lobe visible on both, not an asymmetry bug.
     #[test]
     fn ridge_and_trough_oppose_where_the_wall_is_steep() {
         let light = light_vector();
         let mat = Finish::from_style();
         let sample = |m: CarveMode, u: f32| {
             carve_shade(m, u, [-1.0, 0.0], &analytic_carve_slope, light, &mat)
         };
         // Steepest point of the folded profile: w = 1 at u = 0.5 is the crest
         // (zero slope), so the extremes sit either side of it.
         let steep = (0..=100)
             .map(|i| i as f32 / 100.0)
             .max_by(|a, b| sample(CarveMode::Ridge, *a).abs().total_cmp(&sample(CarveMode::Ridge, *b).abs()))
             .unwrap();
         let (r, t) = (sample(CarveMode::Ridge, steep), sample(CarveMode::Trough, steep));
         assert!(r.abs() > 0.05, "ridge shading {r} at u={steep} is too faint to test");
         assert!(r * t < 0.0, "ridge {r} and trough {t} agree in sign at u={steep}");
     }
 }