concinnity_render/

csm.rs

//! Cascaded shadow map cascade computation. Produces a `ShadowUniforms` carrying
//! one orthographic light-view-projection matrix per cascade plus the view-space
//! far depth for each cascade (the fragment shader uses these to select which
//! cascade slice to sample).
//!
//! Algorithm (per-frame, called from each backend's draw loop):
//!
//!   1. Split the camera's [near, shadow_distance] depth range into N cascade
//!      sub-ranges using the practical PSSM blend
//!      (lambda * logarithmic + (1 - lambda) * linear).
//!   2. For each cascade, compute the 8 frustum corners at its near/far depths,
//!      then bound the corners with a sphere. The sphere bound makes the
//!      orthographic light frustum rotation-invariant, eliminating shimmer
//!      when the camera rotates.
//!   3. Snap the sphere centre, in world space along the light's right/up axes,
//!      to a per-cascade texel grid so the grid stays anchored in the world and
//!      individual texels don't crawl as the camera translates.
//!   4. Build a RH look_at from outside the sphere along the light direction
//!      and an ortho projection that exactly encloses the sphere.
//!
//! The math is shared across all three backends: Metal, Vulkan, and DirectX
//! all use RH view matrices with [0, 1] depth in their orthographic
//! projections, so the same VPs are valid for every backend's shadow sampling.

use crate::mat::{IDENTITY4, look_at, normalize3, ortho_rh};
use crate::render_types::{NUM_SHADOW_CASCADES, ShadowUniforms};
use concinnity_core::gfx::transform::mat4_mul;
use concinnity_core::math::vec3::{add, cross, dot, scale, sub};
use concinnity_core::math::{powf, round, sqrt, tan};

const SPLIT_LAMBDA: f32 = 0.5;

/// Fallback uniforms used when no shadow pass is active: identity VPs and a
/// single split at +inf so the fragment shader always picks cascade 0 with a
/// 1x1 fallback texture (returns "fully lit").
pub fn empty_shadow_uniforms() -> ShadowUniforms {
    ShadowUniforms {
        light_vps: [IDENTITY4; NUM_SHADOW_CASCADES],
        cascade_splits: [f32::INFINITY; NUM_SHADOW_CASCADES],
        active_cascades: NUM_SHADOW_CASCADES as u32,
        _pad: [0; 3],
    }
}

/// Camera, light, and shadow-configuration inputs to
/// [`compute_shadow_uniforms`].
#[derive(Clone, Copy)]
pub struct ShadowUniformInputs {
    /// Camera view matrix (column-major, RH, same convention as look_at).
    pub view: [[f32; 4]; 4],
    /// World-space camera position.
    pub cam_pos: [f32; 3],
    /// Vertical FOV in radians.
    pub fov_y_rad: f32,
    /// Viewport aspect ratio (width / height).
    pub aspect: f32,
    /// Camera near plane.
    pub near: f32,
    /// Far end of the last cascade. Cascades cover [near, shadow_distance].
    pub shadow_distance: f32,
    /// Unit vector pointing TOWARD the light. Same convention as
    /// `DirectionalLight.direction`; renormalised internally.
    pub light_dir_to_source: [f32; 3],
    /// Per-cascade texture resolution; used for texel snapping.
    pub shadow_map_size: u32,
    /// How many of the `NUM_SHADOW_CASCADES` slots are live (1..=4); only the
    /// first `active` are split + projected, the rest hold a negative split
    /// sentinel and an identity VP so the shader never selects them.
    pub active_cascades: u32,
}

/// Compute cascade VPs + split depths from camera + light parameters.
pub fn compute_shadow_uniforms(inputs: ShadowUniformInputs) -> ShadowUniforms {
    let ShadowUniformInputs {
        view,
        cam_pos,
        fov_y_rad,
        aspect,
        near,
        shadow_distance,
        light_dir_to_source,
        shadow_map_size,
        active_cascades,
    } = inputs;
    let shadow_far = shadow_distance.max(near + 1.0);
    let active = active_cascades.clamp(1, NUM_SHADOW_CASCADES as u32) as usize;

    // Practical PSSM splits over the `active` cascades. The unused tail keeps a
    // negative sentinel so the fragment shader's `view_depth < split` test never
    // selects a cascade the CPU did not render.
    let cascade_count = active as f32;
    let mut splits = [-1.0_f32; NUM_SHADOW_CASCADES];
    for (i, split) in splits.iter_mut().take(active).enumerate() {
        let p = (i + 1) as f32 / cascade_count;
        let log = near * powf(shadow_far / near, p);
        let lin = near + (shadow_far - near) * p;
        *split = SPLIT_LAMBDA * log + (1.0 - SPLIT_LAMBDA) * lin;
    }

    let l_to = normalize3(light_dir_to_source);

    // Camera basis from view matrix (column-major; look_at fills row 0 = right,
    // row 1 = up, row 2 = -forward into view[*][0], view[*][1], view[*][2]).
    let right = [view[0][0], view[1][0], view[2][0]];
    let up = [view[0][1], view[1][1], view[2][1]];
    let forward = [-view[0][2], -view[1][2], -view[2][2]];

    let tan_half_v = tan(fov_y_rad * 0.5);
    let tan_half_h = tan_half_v * aspect;

    let mut light_vps = [IDENTITY4; NUM_SHADOW_CASCADES];
    let mut prev_split = near;
    for i in 0..active {
        let near_d = prev_split;
        let far_d = splits[i];
        prev_split = far_d;

        // 8 frustum corners at near_d and far_d in world space.
        let h_near = near_d * tan_half_v;
        let w_near = near_d * tan_half_h;
        let h_far = far_d * tan_half_v;
        let w_far = far_d * tan_half_h;
        let cn = add(cam_pos, scale(forward, near_d));
        let cf = add(cam_pos, scale(forward, far_d));
        let corners: [[f32; 3]; 8] = [
            add(add(cn, scale(right, -w_near)), scale(up, -h_near)),
            add(add(cn, scale(right, w_near)), scale(up, -h_near)),
            add(add(cn, scale(right, w_near)), scale(up, h_near)),
            add(add(cn, scale(right, -w_near)), scale(up, h_near)),
            add(add(cf, scale(right, -w_far)), scale(up, -h_far)),
            add(add(cf, scale(right, w_far)), scale(up, -h_far)),
            add(add(cf, scale(right, w_far)), scale(up, h_far)),
            add(add(cf, scale(right, -w_far)), scale(up, h_far)),
        ];

        // Bounding sphere of the corners.
        let mut centre = [0.0_f32; 3];
        for c in &corners {
            centre[0] += c[0];
            centre[1] += c[1];
            centre[2] += c[2];
        }
        centre = scale(centre, 1.0 / 8.0);
        let mut r2 = 0.0_f32;
        for c in &corners {
            let d = sub(*c, centre);
            let dd = d[0] * d[0] + d[1] * d[1] + d[2] * d[2];
            if dd > r2 {
                r2 = dd;
            }
        }
        let radius = sqrt(r2).max(1e-3);

        // Stable up axis: avoid parallel to light direction.
        let up_l = if l_to[1].abs() > 0.95 {
            [1.0_f32, 0.0, 0.0]
        } else {
            [0.0_f32, 1.0, 0.0]
        };

        // Light-space basis matching `look_at` below: f points from the light
        // toward the scene, r and u span the shadow texel grid.
        let f = scale(l_to, -1.0);
        let r = normalize3(cross(f, up_l));
        let u = cross(r, f);

        // Texel-grid snap. Quantise the cascade centre along the light's right
        // and up axes to whole shadow texels so the texel grid stays anchored in
        // world space; the texels then stop crawling under camera translation
        // (the shadow stops chasing the camera). The snap must happen in world
        // space, before look_at: snapping the centre's light-space xy afterwards
        // is a no-op, because look_at always maps the centre onto the optical
        // axis (its light-space xy is identically zero).
        let texel_size = 2.0 * radius / shadow_map_size.max(1) as f32;
        let cx = dot(r, centre);
        let cy = dot(u, centre);
        let snap_dx = round(cx / texel_size) * texel_size - cx;
        let snap_dy = round(cy / texel_size) * texel_size - cy;
        let centre = add(add(centre, scale(r, snap_dx)), scale(u, snap_dy));

        // Build the light view from the snapped centre and an ortho projection
        // enclosing the sphere. The eye sits at +radius along the light
        // direction so the sphere centre maps to the middle of the depth range.
        //
        // The near plane is pushed back toward the light by `caster_extent` so
        // casters ABOVE this cascade's volume (tree canopies, tall building
        // tops, anything between the light and the sphere) still render into the
        // shadow map. Without it the near cascades, whose ortho boxes are only
        // `radius` deep along the light, clip any caster taller than the cascade;
        // as the camera moves, which casters fall inside each cascade changes,
        // so elevated shadows pop in and out and their edges slide with the
        // camera. The extension grows only the depth range, not the XY
        // footprint, so shadow-map resolution is unchanged.
        let caster_extent = shadow_far;
        let light_eye = add(centre, scale(l_to, radius));
        let light_view = look_at(light_eye, centre, up_l);
        let proj = ortho_rh(
            -radius,
            radius,
            -radius,
            radius,
            -caster_extent,
            2.0 * radius,
        );
        light_vps[i] = mat4_mul(proj, light_view);
    }

    ShadowUniforms {
        light_vps,
        cascade_splits: splits,
        active_cascades: active as u32,
        _pad: [0; 3],
    }
}

// Right-handed look-at producing a column-major view matrix matching the
// per-backend look_at helpers (Metal, Vulkan, DX all use the same convention).
#[cfg(test)]
mod tests {
    use super::*;

    fn ident_view() -> [[f32; 4]; 4] {
        // Camera at origin looking down -Z, up = +Y.
        look_at([0.0, 0.0, 0.0], [0.0, 0.0, -1.0], [0.0, 1.0, 0.0])
    }

    #[test]
    fn empty_uniforms_have_infinite_splits() {
        let u = empty_shadow_uniforms();
        for s in &u.cascade_splits {
            assert!(s.is_infinite());
        }
    }

    #[test]
    fn splits_are_strictly_increasing_within_range() {
        let u = compute_shadow_uniforms(ShadowUniformInputs {
            view: ident_view(),
            cam_pos: [0.0, 0.0, 0.0],
            fov_y_rad: core::f32::consts::FRAC_PI_2,
            aspect: 1.0,
            near: 0.1,
            shadow_distance: 80.0,
            light_dir_to_source: [0.0, 1.0, 0.0],
            shadow_map_size: 2048,
            active_cascades: 4,
        });
        for i in 1..NUM_SHADOW_CASCADES {
            assert!(
                u.cascade_splits[i] > u.cascade_splits[i - 1],
                "splits must increase: {:?}",
                u.cascade_splits
            );
        }
        assert!(u.cascade_splits[0] > 0.1);
        assert!((u.cascade_splits[NUM_SHADOW_CASCADES - 1] - 80.0).abs() < 1e-3);
    }

    #[test]
    fn fewer_active_cascades_fill_only_the_live_slots() {
        // With active_cascades = 2 the first two slots cover [near, shadow_far]
        // (last split == shadow distance) and the unused tail holds the negative
        // sentinel + identity VPs, so the shader never selects an unrendered slot.
        let u = compute_shadow_uniforms(ShadowUniformInputs {
            view: ident_view(),
            cam_pos: [0.0, 0.0, 0.0],
            fov_y_rad: core::f32::consts::FRAC_PI_2,
            aspect: 1.0,
            near: 0.1,
            shadow_distance: 80.0,
            light_dir_to_source: [0.0, 1.0, 0.0],
            shadow_map_size: 2048,
            active_cascades: 2,
        });
        assert_eq!(u.active_cascades, 2);
        assert!(u.cascade_splits[0] > 0.1);
        assert!(u.cascade_splits[1] > u.cascade_splits[0]);
        assert!((u.cascade_splits[1] - 80.0).abs() < 1e-3);
        // Unused tail: negative split sentinel + untouched identity VP.
        assert!(u.cascade_splits[2] < 0.0);
        assert!(u.cascade_splits[3] < 0.0);
        assert_eq!(u.light_vps[2], IDENTITY4);
        assert_eq!(u.light_vps[3], IDENTITY4);
        // Out-of-range counts clamp into 1..=4.
        let one = compute_shadow_uniforms(ShadowUniformInputs {
            view: ident_view(),
            cam_pos: [0.0, 0.0, 0.0],
            fov_y_rad: core::f32::consts::FRAC_PI_2,
            aspect: 1.0,
            near: 0.1,
            shadow_distance: 80.0,
            light_dir_to_source: [0.0, 1.0, 0.0],
            shadow_map_size: 2048,
            active_cascades: 0,
        });
        assert_eq!(one.active_cascades, 1);
        assert!((one.cascade_splits[0] - 80.0).abs() < 1e-3);
    }

    #[test]
    fn near_clamped_to_avoid_degenerate_log() {
        // shadow_distance smaller than near is clamped to near + 1.0 so the
        // logarithmic split term stays finite.
        let u = compute_shadow_uniforms(ShadowUniformInputs {
            view: ident_view(),
            cam_pos: [0.0, 0.0, 0.0],
            fov_y_rad: core::f32::consts::FRAC_PI_2,
            aspect: 1.0,
            near: 5.0,
            shadow_distance: 1.0,
            light_dir_to_source: [0.0, 1.0, 0.0],
            shadow_map_size: 2048,
            active_cascades: 4,
        });
        for s in &u.cascade_splits {
            assert!(s.is_finite() && *s > 0.0);
        }
    }

    #[test]
    fn cascade_vps_finite_for_typical_inputs() {
        let u = compute_shadow_uniforms(ShadowUniformInputs {
            view: ident_view(),
            cam_pos: [10.0, 5.0, -3.0],
            fov_y_rad: core::f32::consts::FRAC_PI_4,
            aspect: 16.0 / 9.0,
            near: 0.1,
            shadow_distance: 80.0,
            light_dir_to_source: [-0.4, 0.7, 0.3],
            shadow_map_size: 2048,
            active_cascades: 4,
        });
        for vp in &u.light_vps {
            for col in vp {
                for v in col {
                    assert!(v.is_finite(), "non-finite element in light_vp");
                }
            }
        }
    }

    #[test]
    fn point_inside_first_cascade_projects_into_unit_box() {
        // A point a few metres in front of the camera should project into the
        // first cascade's light NDC, inside the [-1, 1] xy box (depth [0, 1]).
        let u = compute_shadow_uniforms(ShadowUniformInputs {
            view: ident_view(),
            cam_pos: [0.0, 0.0, 0.0],
            fov_y_rad: core::f32::consts::FRAC_PI_4,
            aspect: 16.0 / 9.0,
            near: 0.1,
            shadow_distance: 80.0,
            light_dir_to_source: [0.0, 1.0, 0.0],
            shadow_map_size: 2048,
            active_cascades: 4,
        });
        // World point 2m in front of camera (looking down -Z).
        let p = [0.0_f32, 0.0, -2.0, 1.0];
        let vp = u.light_vps[0];
        let mut clip = [0.0_f32; 4];
        for row in 0..4 {
            clip[row] =
                vp[0][row] * p[0] + vp[1][row] * p[1] + vp[2][row] * p[2] + vp[3][row] * p[3];
        }
        let ndc = [clip[0] / clip[3], clip[1] / clip[3], clip[2] / clip[3]];
        assert!(ndc[0].abs() <= 1.0, "x out of range: {}", ndc[0]);
        assert!(ndc[1].abs() <= 1.0, "y out of range: {}", ndc[1]);
        assert!(
            ndc[2] >= -0.05 && ndc[2] <= 1.05,
            "depth out of range: {}",
            ndc[2]
        );
    }

    // Project a fixed world point into cascade 0's shadow map and return its
    // texel coordinates for a camera at `cam` (looking down -Z).
    fn cascade0_texel(cam: [f32; 3], world_p: [f32; 3], light: [f32; 3], size: u32) -> (f32, f32) {
        let view = look_at(cam, [cam[0], cam[1], cam[2] - 1.0], [0.0, 1.0, 0.0]);
        let u = compute_shadow_uniforms(ShadowUniformInputs {
            view,
            cam_pos: cam,
            fov_y_rad: core::f32::consts::FRAC_PI_4,
            aspect: 16.0 / 9.0,
            near: 0.1,
            shadow_distance: 80.0,
            light_dir_to_source: light,
            shadow_map_size: size,
            active_cascades: 4,
        });
        let vp = u.light_vps[0];
        let p = [world_p[0], world_p[1], world_p[2], 1.0];
        let mut clip = [0.0_f32; 4];
        for row in 0..4 {
            clip[row] =
                vp[0][row] * p[0] + vp[1][row] * p[1] + vp[2][row] * p[2] + vp[3][row] * p[3];
        }
        let uvx = (clip[0] / clip[3] * 0.5 + 0.5) * size as f32;
        let uvy = (-clip[1] / clip[3] * 0.5 + 0.5) * size as f32;
        (uvx, uvy)
    }

    #[test]
    fn texels_do_not_crawl_under_camera_translation() {
        // The chasing-shadow regression. A fixed world point must land on the
        // SAME sub-texel of the shadow map regardless of camera position: with
        // the texel grid anchored in world space, translating the camera shifts
        // the projected point by a whole number of texels only, so its
        // fractional texel position is invariant. (Before the world-space snap,
        // the centre was snapped after look_at, which is a no-op, and the grid
        // slid continuously with the camera -- the shadow "chased" it.)
        let light = [-0.4, 0.78, 0.5];
        let size = 2048u32;
        let world_p = [3.0_f32, 0.0, -5.0];

        // Two camera positions a fraction of a texel apart in world space.
        let a = cascade0_texel([0.0, 2.0, 0.0], world_p, light, size);
        let b = cascade0_texel([0.137, 2.0, 0.091], world_p, light, size);

        // The texel delta must be (within float error) a whole number of
        // texels: the fractional residual is the per-texel crawl.
        let dx = a.0 - b.0;
        let dy = a.1 - b.1;
        let rx = dx - dx.round();
        let ry = dy - dy.round();
        assert!(
            rx.abs() < 0.05,
            "shadow x crawls within a texel: residual {rx}"
        );
        assert!(
            ry.abs() < 0.05,
            "shadow y crawls within a texel: residual {ry}"
        );
    }

    // Project a world point through cascade 0's VP and return its light NDC.
    fn cascade0_ndc(cam: [f32; 3], world_p: [f32; 3], light: [f32; 3]) -> [f32; 3] {
        let view = look_at(cam, [cam[0], cam[1], cam[2] - 1.0], [0.0, 1.0, 0.0]);
        let u = compute_shadow_uniforms(ShadowUniformInputs {
            view,
            cam_pos: cam,
            fov_y_rad: core::f32::consts::FRAC_PI_4,
            aspect: 16.0 / 9.0,
            near: 0.1,
            shadow_distance: 80.0,
            light_dir_to_source: light,
            shadow_map_size: 2048,
            active_cascades: 4,
        });
        let vp = u.light_vps[0];
        let p = [world_p[0], world_p[1], world_p[2], 1.0];
        let mut clip = [0.0_f32; 4];
        for row in 0..4 {
            clip[row] =
                vp[0][row] * p[0] + vp[1][row] * p[1] + vp[2][row] * p[2] + vp[3][row] * p[3];
        }
        [clip[0] / clip[3], clip[1] / clip[3], clip[2] / clip[3]]
    }

    #[test]
    fn tall_casters_above_cascade_are_not_clipped() {
        // The disappearing-shadow regression. A caster high above the near
        // cascade (a tree canopy, a building top) must still fall inside the
        // cascade's light frustum so it renders into the shadow map; otherwise
        // its shadow vanishes the moment the receiver drops into a small near
        // cascade, and the clip boundary slides across the world as the camera
        // moves. The ortho near plane is extended toward the light for exactly
        // this. A caster 30m up sits well beyond the few-metre cascade-0 sphere
        // radius, so without the extension it projects to ndc.z < 0 (clipped).
        let cam = [0.0_f32, 0.0, 0.0];
        let light = [0.0_f32, 0.85, 0.3]; // mostly overhead
        let ndc = cascade0_ndc(cam, [0.0, 30.0, -3.0], light);
        assert!(
            ndc[0].abs() <= 1.0,
            "caster x outside footprint: {}",
            ndc[0]
        );
        assert!(
            ndc[1].abs() <= 1.0,
            "caster y outside footprint: {}",
            ndc[1]
        );
        assert!(
            (0.0..=1.0).contains(&ndc[2]),
            "tall caster clipped from shadow map: ndc.z = {}",
            ndc[2]
        );
    }
}