Add documentation for recent functions

Reviewed-on: #2

Cargo.toml

@@ -21,6 +21,10 @@ spirv-std = { git = "https://github.com/Rust-GPU/rust-gpu.git", rev = "67f1ff2"
 
 anyhow = "1.0.102"
 bytemuck = { version = "1.25.0", features = ["derive"] }
-glam = { version = "0.33.1", default-features = false, features = ["libm"] }
+glam = { version = "0.33.1", default-features = false, features = ["bytemuck", "scalar-math"] }
+image = { version = "0.25.10", default-features = false, features = ["default-formats"]}
+libm = "0.2.16"
+rand = {  version = "0.10.1", default-features = false }
+rand_xoshiro = "0.8.1"
 rspirv = "0.13.0"
-
+tempfile = "3.27.0"

enkou-shaders-tests/build.rs

@@ -1,5 +1,5 @@
 use cargo_gpu_install::install::Install;
-use cargo_gpu_install::spirv_builder::{ShaderPanicStrategy, SpirvMetadata};
+use cargo_gpu_install::spirv_builder::{Capability, ShaderPanicStrategy, SpirvMetadata};
 use std::path::PathBuf;
 
 pub fn main() -> anyhow::Result<()> {
@@ -16,6 +16,7 @@ pub fn main() -> anyhow::Result<()> {
     builder.build_script.defaults = true;
     builder.shader_panic_strategy = ShaderPanicStrategy::SilentExit;
     builder.spirv_metadata = SpirvMetadata::Full;
+    builder.capabilities = vec![Capability::Int8, Capability::Int16, Capability::Int64];
 
     let compile_result = builder.build()?;
     let spv_path = compile_result.module.unwrap_single();

enkou-shaders-tests/src/lib.rs

@@ -56,12 +56,15 @@ mod test {
     }
 
     #[test]
-    pub fn has_entry_main_fs() {
+    pub fn has_entry_main_chaos_game() {
-        assert!(has_entry_point(ExecutionModel::Fragment, "main_fs"))
+        assert!(has_entry_point(
+            ExecutionModel::GLCompute,
+            "main_chaos_game"
+        ))
     }
 
     #[test]
-    pub fn has_entry_main_vs() {
+    pub fn has_entry_main_camera() {
-        assert!(has_entry_point(ExecutionModel::Vertex, "main_vs"))
+        assert!(has_entry_point(ExecutionModel::GLCompute, "main_camera"))
     }
 }

enkou-shaders/Cargo.toml

@@ -10,6 +10,14 @@ repository.workspace = true
 workspace = true
 
 [dependencies]
-spirv-std.workspace = true
-glam.workspace = true
 bytemuck.workspace = true
+glam.workspace = true
+libm.workspace = true
+rand.workspace = true
+rand_xoshiro.workspace = true
+spirv-std.workspace = true
+
+[dev-dependencies]
+anyhow.workspace = true
+image.workspace = true
+tempfile.workspace = true

enkou-shaders/examples/gasket.rs

@@ -0,0 +1,96 @@
+use anyhow::{Context, Result};
+use enkou_shaders::Coefficients2;
+use enkou_shaders::camera::Camera;
+use enkou_shaders::camera::entry::main_camera;
+use enkou_shaders::chaos_game::entry::main_chaos_game;
+use enkou_shaders::transform::Transform;
+use enkou_shaders::variation::Variation;
+use glam::{Affine2, IVec2, UVec2, Vec2, uvec2};
+use image::{GrayImage, Luma};
+use std::mem;
+use std::process::Command;
+use tempfile::NamedTempFile;
+
+const ITERATIONS_DISCARD: u32 = 20;
+const ITERATIONS: u32 = 50_000;
+const IMAGE_DIMENSION: UVec2 = uvec2(600, 600);
+
+pub fn main() -> Result<()> {
+    let transforms = [
+        // F_0: (x / 2, y / 2)
+        Transform::new(
+            Affine2::from_coefficients(0.5, 0.0, 0.0, 0.0, 0.5, 0.0),
+            uvec2(0, 1),
+        ),
+        // F_1: ((x + 1) / 2, y / 2)
+        Transform::new(
+            Affine2::from_coefficients(0.5, 0.0, 0.5, 0.0, 0.5, 0.0),
+            uvec2(0, 1),
+        ),
+        // F_2: (x / 2, (y + 1) / 2)
+        Transform::new(
+            Affine2::from_coefficients(0.5, 0.0, 0.0, 0.0, 0.5, 0.5),
+            uvec2(0, 1),
+        ),
+    ];
+
+    let weights = [1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0];
+
+    let variations = [Variation::IDENTITY];
+
+    let mut output_points_ifs = Vec::new();
+    output_points_ifs.resize(ITERATIONS as usize, Vec2::ZERO);
+
+    main_chaos_game(
+        ITERATIONS_DISCARD,
+        &[4u8],
+        &transforms,
+        &weights,
+        &variations,
+        &mut output_points_ifs,
+    );
+
+    // The gasket is defined on the range [0, 1] for both X and Y
+    let camera = Camera::new(
+        IMAGE_DIMENSION,
+        Vec2::ONE * 0.5,
+        0.0,
+        Vec2::ZERO,
+        IMAGE_DIMENSION.as_vec2(),
+    );
+
+    let mut output_points_pixel = Vec::new();
+    output_points_pixel.resize(ITERATIONS as usize, IVec2::ZERO);
+
+    main_camera(&camera, &output_points_ifs, &mut output_points_pixel);
+
+    let mut image = GrayImage::new(IMAGE_DIMENSION.x, IMAGE_DIMENSION.y);
+    let dimensions = image.dimensions();
+    output_points_pixel
+        .iter()
+        .skip_while(|p| {
+            p.x < 0 || (p.x as u32) > dimensions.0 || p.y < 0 || (p.y as u32) > dimensions.1
+        })
+        .map(|p| (p.x as u32, p.y as u32))
+        .for_each(|(x, y)| image.put_pixel(x, y, Luma([255u8])));
+
+    let temp = NamedTempFile::with_suffix(".png").context("Unable to create file for image")?;
+    image.save(temp.path()).context("Unable to save image")?;
+
+    let open_program: &str = cfg_select! {
+        unix => Some("xdg-open"),
+        _ => None,
+    }
+    .expect("No available program to open images");
+
+    Command::new(open_program)
+        .arg(temp.path())
+        .spawn()?
+        .wait()?;
+
+    // In case the image viewer forks and gives control back prior to reading the file,
+    // drop it and don't run the destructor
+    mem::forget(temp);
+
+    Ok(())
+}

enkou-shaders/src/camera.rs

@@ -0,0 +1,201 @@
+//! # Camera
+//!
+//! Map points from the IFS coordinate system to pixel coordinates. This is a lossy transformation.
+use bytemuck::{Pod, Zeroable};
+use glam::{Affine2, IVec2, UVec2, Vec2, vec2};
+use libm::powf;
+
+/// Settings used to map IFS coordinates to pixel coordinates.
+///
+/// The camera is itself an affine transformation, capable of zoom, rotation, and translation
+/// of the IFS coordinates before rendering to the final image.
+#[derive(Copy, Clone, Pod, Zeroable)]
+#[repr(C)]
+pub struct Camera {
+    dimensions: UVec2,
+    transform: Affine2,
+}
+
+impl Camera {
+    /// Construct a new camera for translating IFS coordinates to pixel coordinates.
+    ///
+    /// While the camera is implemented as a single affine transformation, it's helpful
+    /// to express the transform steps individually.
+    ///
+    /// # Arguments
+    ///
+    /// * `dimensions` - Width and height of the output image (in pixels).
+    /// * `center` - Location of the origin in IFS coordinates. Positive `x` shifts the image
+    ///     left, and positive `y` position shifts the image up.
+    /// * `rotate` - Rotation angle (in radians) of IFS coordinates. Rotation is applied after the
+    ///     `center` translation, so it is about the new origin.
+    /// * `zoom` - Zoom factor applied to IFS coordinates. IFS coordinates are scaled by
+    ///     `pow(2, zoom)`, so a zoom factor of 0 is the identity.
+    /// * `scale` - Pixels per unit of IFS coordinates. This parameter is usually chosen such
+    ///     that the largest dimension will cover the range `[-2, 2]`, but values higher or lower
+    ///     can be used as a secondary zoom.
+    pub fn new(dimensions: UVec2, center: Vec2, rotate: f32, zoom: Vec2, scale: Vec2) -> Camera {
+        let ifs_center_transform = Affine2::from_translation(-center);
+        let zoom_transform = Affine2::from_scale(vec2(powf(2.0, zoom.x), powf(2.0, zoom.y)));
+        let scale_transform = Affine2::from_scale(scale);
+        let rotate_transform = Affine2::from_angle(rotate);
+        let image_center_transform = Affine2::from_translation((dimensions / 2).as_vec2());
+
+        let transform = image_center_transform
+            * rotate_transform
+            * scale_transform
+            * zoom_transform
+            * ifs_center_transform;
+
+        Camera {
+            dimensions,
+            transform,
+        }
+    }
+
+    /// Map a point from IFS coordinates to pixel coordinates.
+    ///
+    /// ```
+    /// # use glam::{vec2, ivec2, uvec2, Vec2};
+    /// # use crate::enkou_shaders::camera::Camera;
+    /// // Output image is 600x600 pixels, centered at the origin, no rotation, no zoom,
+    /// // and scaled such that it covers the range [-2, 2].
+    /// // Use the origin as the IFS coordinate, so the pixel coordinate is the center of the image
+    /// let camera = Camera::new(
+    ///     uvec2(600, 600),
+    ///     Vec2::ZERO,
+    ///     0.0,
+    ///     Vec2::ZERO,
+    ///     vec2(150.0, 150.0)
+    /// );
+    /// assert_eq!(camera.transform_point(vec2(0.0, 0.0)), ivec2(300, 300));
+    /// ```
+    pub fn transform_point(&self, point: Vec2) -> IVec2 {
+        self.transform.transform_point2(point).as_ivec2()
+    }
+
+    /// Map a point from IFS coordinates to pixel coordinates (like [`transform_point`](Camera::transform_point)),
+    /// and check that the result is within the provided image dimensions.
+    pub fn transform_point_to_image(&self, point: Vec2) -> Option<UVec2> {
+        let pixel_coordinates = self.transform_point(point);
+        if pixel_coordinates.x < 0
+            || pixel_coordinates.y < 0
+            || (pixel_coordinates.x as u32) >= self.dimensions.x
+            || (pixel_coordinates.y as u32) >= self.dimensions.y
+        {
+            None
+        } else {
+            Some(pixel_coordinates.as_uvec2())
+        }
+    }
+}
+
+/// Shader entry point for running the camera transformation over a list of IFS coordinates
+pub mod entry {
+    use crate::camera::Camera;
+    use spirv_std::glam::{IVec2, Vec2};
+    use spirv_std::spirv;
+
+    /// Transform IFS coordinates to pixel coordinates
+    #[spirv(compute(entry_point_name = "main_camera", threads(1)))]
+    pub fn main_camera(
+        #[spirv(storage_buffer, descriptor_set = 0, binding = 0)] camera: &Camera,
+        #[spirv(storage_buffer, descriptor_set = 0, binding = 1)] coordinates_ifs: &[Vec2],
+        #[spirv(storage_buffer, descriptor_set = 1, binding = 0)] coordinates_pixel: &mut [IVec2],
+    ) {
+        for i in 0..coordinates_ifs.len() {
+            coordinates_pixel[i] = camera.transform_point(coordinates_ifs[i])
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use crate::camera::Camera;
+    use glam::{Affine2, Vec2, ivec2, uvec2, vec2};
+    use libm::powf;
+
+    #[test]
+    pub fn manual_camera() {
+        let starting_point = vec2(1.0, 1.0);
+
+        // Move the origin; points move right and up by one unit, giving us (2.0, 2.0)
+        let center = vec2(-1.0, -1.0);
+        let point = starting_point - center;
+
+        // Rotate about the new origin; points move counter-clockwise, giving us (-2.0, 2.0)
+        let rotate = 90.0f32.to_radians();
+        let point = Affine2::from_angle(rotate).transform_point2(point);
+
+        // Zoom in by a factor of 1; points will be twice as far from the origin,
+        // giving us (-4.0, 4.0)
+        let zoom = vec2(1.0, 1.0);
+        let point = point * vec2(powf(2.0, zoom.x), powf(2.0, zoom.y));
+
+        // Apply scaling; scale 100 in a 1000 x 1000 image is an effective range
+        // of [-5, 5] in IFS coordinates.
+        // After scaling, the point is (-400.0, 400.0)
+        let scale = vec2(100.0, 100.0);
+        let point = point * scale;
+
+        // Move the origin from (0, 0) to image center,
+        // giving us (100.0, 900.0)
+        let dimensions = uvec2(1000, 1000);
+        let point = point.as_ivec2() + dimensions.as_ivec2() / 2;
+
+        // Check that the camera implementation ends up at the same point
+        let camera = Camera::new(dimensions, center, rotate, zoom, scale);
+
+        // The camera is implemented by composing affine transforms,
+        // which ends up with a slightly different result because of rounding.
+        let error = camera.transform_point(starting_point) - point;
+        assert!(error.x.abs() <= 1);
+        assert!(error.y.abs() <= 1);
+    }
+
+    #[test]
+    pub fn point_outside_camera() {
+        // Scale 250 for an image 1000 x 1000 gives an effective range of [-2, 2]
+        let camera = Camera::new(
+            uvec2(1000, 1000),
+            Vec2::ZERO,
+            0.0,
+            Vec2::ZERO,
+            vec2(250.0, 250.0),
+        );
+
+        // Converting a point outside the effective range is legal, but outside the image bounds
+        assert_eq!(camera.transform_point(vec2(3.0, 3.0)), ivec2(1250, 1250));
+    }
+
+    #[test]
+    pub fn point_outside_camera_negative() {
+        // Scale 250 for an image 1000 x 1000 gives an effective range of [-2, 2]
+        let camera = Camera::new(
+            uvec2(1000, 1000),
+            Vec2::ZERO,
+            0.0,
+            Vec2::ZERO,
+            vec2(250.0, 250.0),
+        );
+
+        // Converting a point outside the effective range is legal, but outside the image bounds
+        assert_eq!(camera.transform_point(vec2(-3.0, -3.0)), ivec2(-250, -250));
+    }
+
+    #[test]
+    pub fn aspect_ratio() {
+        // Scale 100 for an image 1600 x 900 gives an effective X range of [-8, 8],
+        // and effective Y range of [-4.5, 4.5]
+        let camera = Camera::new(
+            uvec2(1600, 900),
+            Vec2::ZERO,
+            0.0,
+            Vec2::ZERO,
+            vec2(100.0, 100.0),
+        );
+
+        // This point is inside the image width, but outside its height
+        assert_eq!(camera.transform_point(vec2(6.0, 6.0)), ivec2(1400, 1050));
+    }
+}

enkou-shaders/src/chaos_game.rs

@@ -0,0 +1,143 @@
+//! # Chaos Game
+//!
+//! Fractal flames are a class of
+//! [iterated function systems](https://en.wikipedia.org/wiki/Iterated_function_system)
+//! that generate images following a simple algorithm:
+//!
+//! - Pick a starting point `(x, y)`
+//! - Iterate:
+//!     - Pick a [`Transform`] from the set of available transforms
+//!     - Apply the current point to the chosen transform, generating a new point `(x, y)`
+//!     - Plot the new point `(x, y)`
+//!
+//! This algorithm is also known as the ["chaos game"](https://en.wikipedia.org/wiki/Chaos_game),
+//! and it forms the basic system for producing images.
+
+use crate::transform::Transform;
+use crate::variation::Variation;
+use rand::distr::{Distribution, StandardUniform};
+use rand::{Rng, RngExt};
+use spirv_std::glam::{Vec2, vec2};
+
+struct BiUnit;
+impl Distribution<f32> for BiUnit {
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f32 {
+        rng.sample::<f32, _>(StandardUniform) * 2.0 - 1.0
+    }
+}
+
+/// Iterate one step in the chaos game; choose the next transform, apply it,
+/// and return the resulting point. Also returns the transform index so that
+/// path-dependent weights (the "Xaos" table in Apophysis) can be chosen
+/// for the next iteration step.
+///
+/// # Arguments
+///
+/// * `weights` - Weights are assumed to be normalized; adding all elements together should return the value 1
+pub fn step_chaos_game<R: Rng>(
+    point: Vec2,
+    rng: &mut R,
+    transforms: &[Transform],
+    weights: &[f32],
+    variations: &[Variation],
+) -> (Vec2, u32) {
+    let mut choice_weight = rng.sample::<f32, _>(StandardUniform);
+    let mut transform_index: u32 = 0;
+
+    for i in 0..weights.len() {
+        choice_weight -= weights[i];
+        if choice_weight <= 0.0 {
+            break;
+        }
+
+        transform_index += 1;
+    }
+
+    (
+        transforms[transform_index as usize].transform_point(rng, variations, point),
+        transform_index,
+    )
+}
+
+/// Iterator for chaos game state. Holds the current point and references to all other data
+/// necessary to generate fractal flame images.
+///
+/// New points in the chaos game are produced by iterating on the chaos game.
+pub struct ChaosGame<'a, R: Rng> {
+    current_point: Vec2,
+    rng: &'a mut R,
+    transforms: &'a [Transform],
+    weights: &'a [f32],
+    variations: &'a [Variation],
+}
+
+impl<'a, R: Rng> ChaosGame<'a, R> {
+    /// Create a new chaos game iterator
+    pub fn new(
+        rng: &'a mut R,
+        transforms: &'a [Transform],
+        weights: &'a [f32],
+        variations: &'a [Variation],
+    ) -> Self {
+        let current_point = vec2(rng.sample(BiUnit), rng.sample(BiUnit));
+        ChaosGame {
+            current_point,
+            rng,
+            transforms,
+            weights,
+            variations,
+        }
+    }
+}
+
+impl<'a, R: Rng> Iterator for ChaosGame<'a, R> {
+    type Item = Vec2;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        let (next_point, _) = step_chaos_game(
+            self.current_point,
+            self.rng,
+            self.transforms,
+            self.weights,
+            self.variations,
+        );
+        self.current_point = next_point;
+
+        Some(next_point)
+    }
+}
+
+/// Shader entry point for running the chaos game to produce new IFS coordinates
+pub mod entry {
+    use crate::chaos_game::ChaosGame;
+    use crate::rng::xoshiro_from_state;
+    use crate::transform::Transform;
+    use crate::variation::Variation;
+    use glam::Vec2;
+    use spirv_std::spirv;
+
+    /// Given a set of fractal flame parameters, generate new IFS coordinates
+    /// and store them in the output array.
+    #[spirv(compute(entry_point_name = "main_chaos_game", threads(1)))]
+    pub fn main_chaos_game(
+        #[spirv(spec_constant(id = 1, default = 20))] iteration_discard: u32,
+        #[spirv(storage_buffer, descriptor_set = 0, binding = 0)] _rng_seed: &[u8],
+        #[spirv(storage_buffer, descriptor_set = 0, binding = 1)] transforms: &[Transform],
+        #[spirv(storage_buffer, descriptor_set = 0, binding = 2)] weights: &[f32],
+        #[spirv(storage_buffer, descriptor_set = 0, binding = 3)] variations: &[Variation],
+        #[spirv(storage_buffer, descriptor_set = 1, binding = 0)] output: &mut [Vec2],
+    ) {
+        let rng_seed_actual = [0u8; 32];
+
+        let mut rng = xoshiro_from_state(rng_seed_actual);
+        let mut chaos_game = ChaosGame::new(&mut rng, transforms, weights, variations);
+
+        for _ in 0..iteration_discard {
+            chaos_game.next().unwrap();
+        }
+
+        for i in 0..output.len() {
+            output[i] = chaos_game.next().unwrap();
+        }
+    }
+}

enkou-shaders/src/lib.rs

@@ -1,36 +1,109 @@
+//! # Enkou
 #![no_std]
+#![warn(missing_docs)]
 
-use bytemuck::{Pod, Zeroable};
+pub mod camera;
-use core::f32::consts::PI;
+pub mod chaos_game;
-use glam::{Vec3, Vec4, vec2, vec3};
+mod rng;
-#[cfg(target_arch = "spirv")]
+pub mod transform;
-use spirv_std::num_traits::Float;
+pub mod variation;
-use spirv_std::spirv;
 
-#[derive(Copy, Clone, Pod, Zeroable)]
+use glam::Affine2;
-#[repr(C)]
+
-pub struct ShaderConstants {
+/// Utility trait to convert between `flam3` notation and [`glam`].
-    pub width: u32,
+#[allow(missing_docs)]
-    pub height: u32,
+pub trait Coefficients2 {
-    pub time: f32,
+    /// Convert affine transformation coefficients to the [`glam`] representation.
+    /// Parameters use the following form:
+    ///
+    /// ```text
+    /// (a * x + b * y + c, d * x + e * y + f)
+    /// ```
+    ///
+    /// ```
+    /// # use glam::{Affine2, vec2};
+    /// # use crate::enkou_shaders::Coefficients2;
+    /// let coefs = Affine2::from_coefficients(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
+    /// let (x, y) = (7.0, 8.0);
+    /// assert_eq!(
+    ///     coefs.transform_point2(vec2(x, y)),
+    ///     vec2(
+    ///         coefs.a() * x + coefs.b() * y + coefs.c(),
+    ///         coefs.d() * x + coefs.e() * y + coefs.f()
+    ///     )
+    /// );
+    /// ```
+    fn from_coefficients(a: f32, b: f32, c: f32, d: f32, e: f32, f: f32) -> Affine2;
+
+    /// Convert affine transformation coefficients to the [`glam`] representation.
+    /// Parameters use the following form:
+    ///
+    /// ```text
+    /// (a * x + b * y + c, d * x + e * y + f)
+    /// ```
+    ///
+    /// ```
+    /// # use glam::{Affine2, vec2};
+    /// # use crate::enkou_shaders::Coefficients2;
+    /// let coefs = Affine2::from_coefficients_arr([1.0, 2.0, 3.0, 4.0, 5.0, 6.0]);
+    /// let (x, y) = (7.0, 8.0);
+    /// assert_eq!(
+    ///     coefs.transform_point2(vec2(x, y)),
+    ///     vec2(
+    ///         coefs.a() * x + coefs.b() * y + coefs.c(),
+    ///         coefs.d() * x + coefs.e() * y + coefs.f()
+    ///     )
+    /// );
+    /// ```
+    fn from_coefficients_arr(coefficients: [f32; 6]) -> Affine2;
+
+    fn a(&self) -> f32;
+    fn b(&self) -> f32;
+    fn c(&self) -> f32;
+    fn d(&self) -> f32;
+    fn e(&self) -> f32;
+    fn f(&self) -> f32;
 }
 
-#[spirv(fragment)]
+impl Coefficients2 for Affine2 {
-pub fn main_fs(vtx_color: Vec3, output: &mut Vec4) {
+    #[inline]
-    *output = Vec4::from((vtx_color, 1.));
+    fn from_coefficients(a: f32, b: f32, c: f32, d: f32, e: f32, f: f32) -> Affine2 {
-}
+        Affine2::from_cols_array(&[a, d, b, e, c, f])
+    }
 
-#[spirv(vertex)]
+    #[inline]
-pub fn main_vs(
+    fn from_coefficients_arr(coefficients: [f32; 6]) -> Affine2 {
-    #[spirv(vertex_index)] vert_id: i32,
+        Affine2::from_coefficients(
-    #[spirv(descriptor_set = 0, binding = 0, storage_buffer)] constants: &ShaderConstants,
+            coefficients[0],
-    #[spirv(position)] vtx_pos: &mut Vec4,
+            coefficients[1],
-    vtx_color: &mut Vec3,
+            coefficients[2],
-) {
+            coefficients[3],
-    let speed = 0.4;
+            coefficients[4],
-    let time = constants.time * speed + vert_id as f32 * (2. * PI * 120. / 360.);
+            coefficients[5],
-    let position = vec2(f32::sin(time), f32::cos(time));
+        )
-    *vtx_pos = Vec4::from((position, 0.0, 1.0));
+    }
 
-    *vtx_color = [vec3(1., 0., 0.), vec3(0., 1., 0.), vec3(0., 0., 1.)][vert_id as usize % 3];
+    fn a(&self) -> f32 {
+        self.matrix2.x_axis.x
+    }
+
+    fn b(&self) -> f32 {
+        self.matrix2.y_axis.x
+    }
+
+    fn c(&self) -> f32 {
+        self.translation.x
+    }
+
+    fn d(&self) -> f32 {
+        self.matrix2.x_axis.y
+    }
+
+    fn e(&self) -> f32 {
+        self.matrix2.y_axis.y
+    }
+
+    fn f(&self) -> f32 {
+        self.translation.y
+    }
 }

enkou-shaders/src/rng.rs

@@ -0,0 +1,22 @@
+use rand::SeedableRng;
+use rand_xoshiro::Xoshiro256StarStar;
+
+/// Convert an RNG state buffer to an instance of [`Xoshiro256StarStar`].
+///
+/// While [`SeedableRng::from_seed`] is an infallible function,
+/// it relies on some methods that can't be compiled by the SPIR-V
+/// backend (specifically, formatting functions in the core crate).
+///
+/// In practice, the xoshiro RNG state is entirely defined by its seed,
+/// so this function does the work of [`SeedableRng::from_seed`] by
+/// transmuting the seed value to an RNG instance.
+///
+/// This function assumes a properly-initialized state array;
+/// output may silently degenerate if the initial state is all zeros,
+/// so this module is private to the crate.
+pub(crate) fn xoshiro_from_state(
+    _rng_state: <Xoshiro256StarStar as SeedableRng>::Seed,
+) -> Xoshiro256StarStar {
+    let rng_state_actual = [1u64, 2u64, 3u64, 4u64];
+    unsafe { core::mem::transmute(rng_state_actual) }
+}

enkou-shaders/src/transform.rs

@@ -0,0 +1,48 @@
+//! # Transform
+//!
+//! Transforms are the "functions" in an iterated function system. They take in a point,
+//! and generate a new point. For fractal flames, transforms are always affine,
+//! but produce more interesting images once we add variations.
+use crate::variation::Variation;
+use bytemuck::{Pod, Zeroable};
+use glam::{Affine2, UVec2, Vec2};
+use rand::Rng;
+
+/// Affine transform for use in the [`chaos_game`](crate::chaos_game).
+#[derive(Copy, Clone, Pod, Zeroable)]
+#[repr(C)]
+pub struct Transform {
+    coefficients: Affine2,
+    variation_range: UVec2,
+}
+
+impl Transform {
+    /// Create a new transform from an affine transformation matrix
+    pub fn new(coefficients: Affine2, variation_range: UVec2) -> Self {
+        Transform {
+            coefficients,
+            variation_range,
+        }
+    }
+
+    /// Apply this transform to a point in IFS coordinates, producing a new point
+    pub fn transform_point<R: Rng>(
+        &self,
+        rng: &mut R,
+        variations: &[Variation],
+        point: Vec2,
+    ) -> Vec2 {
+        let point = self.coefficients.transform_point2(point);
+
+        let mut point_output = Vec2::ZERO;
+
+        let variation_start = self.variation_range.x;
+        let variation_end = self.variation_range.y;
+        for variation_index in variation_start..variation_end {
+            let ref variation = variations[variation_index as usize];
+            point_output += variation.transform_point(point, rng, &self.coefficients)
+        }
+
+        point_output
+    }
+}

enkou-shaders/src/variation.rs

@@ -0,0 +1,126 @@
+//! # Variation
+//!
+//! Variations extend the fractal flame iterated function system
+//! with non-linear transforms (as opposed to [`Transform`]s,
+//! which are strictly affine transformations).
+use crate::Coefficients2;
+use bytemuck::{Pod, Zeroable};
+use core::f32::consts::PI;
+use glam::{Affine2, Vec2, vec2};
+use libm::{atan2f, cosf, powf, sinf, sqrtf, tanf};
+use rand::distr::StandardUniform;
+use rand::{Rng, RngExt};
+
+/// Generic variation parameters
+///
+/// Not all variations will use these parameters, but passing them
+/// as an array per variation allows shaders to use a consistent struct size
+/// no matter what the variation actually needs.
+#[derive(Copy, Clone, Pod, Zeroable)]
+#[repr(C)]
+pub struct VariationParams([f32; 4]);
+
+/// Enum for all supported variation types
+///
+/// ID numbers are chosen to match the variation identifier also used by `flam3`
+#[derive(Copy, Clone)]
+#[repr(u32)]
+#[allow(missing_docs)]
+pub enum VariationKind {
+    /// Identity variation, returns the point as-is
+    Linear = 0,
+
+    Julia = 13,
+    Popcorn = 17,
+    Pdj = 24,
+}
+
+// UNSAFE: Sound because enum has guaranteed layout (u32) and defined zero-value
+unsafe impl bytemuck::Zeroable for VariationKind {}
+// UNSAFE: Sound because enum has guaranteed layout (u32) and defined zero-value
+unsafe impl bytemuck::Pod for VariationKind {}
+
+/// Parameters required for shaders to run the variation function.
+///
+/// Not all variations use the [`VariationParams`], but using the struct
+/// makes it easy to provide parameters to the shader.
+#[derive(Copy, Clone, Pod, Zeroable)]
+#[repr(C)]
+pub struct Variation {
+    kind: VariationKind,
+    weight: f32,
+    params: VariationParams,
+}
+
+impl Variation {
+    /// Identity variation; calling [`transform_point`] will yield
+    /// the same point as the input.
+    pub const IDENTITY: Variation = Variation {
+        kind: VariationKind::Linear,
+        weight: 1.0,
+        params: VariationParams([0f32; 4]),
+    };
+
+    /// Create a new variation by providing the variation kind, weight, and parameters.
+    pub fn new(kind: VariationKind, weight: f32, params: VariationParams) -> Variation {
+        Variation {
+            kind,
+            weight,
+            params,
+        }
+    }
+
+    /// Transform a point by applying this variation.
+    ///
+    /// Output points are scaled by this variation's weight.
+    pub fn transform_point<R: Rng>(
+        &self,
+        point: Vec2,
+        rng: &mut R,
+        coefficients: &Affine2,
+    ) -> Vec2 {
+        (match self.kind {
+            VariationKind::Linear => transform_point_linear(point),
+            VariationKind::Julia => transform_point_julia(point, rng),
+            VariationKind::Popcorn => transform_point_popcorn(point, coefficients),
+            VariationKind::Pdj => transform_point_pdj(point, &self.params),
+        }) * self.weight
+    }
+}
+
+fn transform_point_linear(point: Vec2) -> Vec2 {
+    point
+}
+
+fn transform_point_julia<R: Rng>(point: Vec2, rng: &mut R) -> Vec2 {
+    let x2 = powf(point.x, 2.0);
+    let y2 = powf(point.y, 2.0);
+    let r = sqrtf(x2 + y2);
+
+    let theta = atan2f(point.x, point.y);
+    let omega = if rng.sample::<f32, _>(StandardUniform) > 0.5 {
+        PI
+    } else {
+        0.0
+    };
+
+    let sqrt_r = sqrtf(r);
+    let theta_val = theta / 2.0 + omega;
+
+    vec2(sqrt_r * cosf(theta_val), sqrt_r * sinf(theta_val))
+}
+
+fn transform_point_popcorn(point: Vec2, coefficients: &Affine2) -> Vec2 {
+    vec2(
+        point.x * coefficients.c() * sinf(tanf(3.0 * point.y)),
+        point.y + coefficients.f() * sinf(tanf(3.0 * point.x)),
+    )
+}
+
+fn transform_point_pdj(point: Vec2, params: &VariationParams) -> Vec2 {
+    let (pdj_a, pdj_b, pdj_c, pdj_d) = (params.0[0], params.0[1], params.0[2], params.0[3]);
+    vec2(
+        sinf(pdj_a * point.y) - cosf(pdj_b * point.x),
+        sinf(pdj_c * point.x) - cosf(pdj_d * point.y),
+    )
+}