Intersection Tests

A ray–shape intersection answers a single question: at what distance t along a ray ro + rd * t does the ray first touch a given shape? That t is the workhorse behind ray casting, ray tracing, mouse picking, and every “what’s under this pointer in 3D” query — once you have it, you can shade by hit normal, place reflections, mask shadows, or build the next ray. Tests that produce two roots (sphere, box, cylinder) return (t_near, t_far) so you can also use them as solid volumes.

Every entry below is a single pure WGSL function in the registry. Pull one into a composition by slug and call it from your fragment stage:

let main = r#"
@fragment fn fs_main(in: VertexOutput) -> @location(0) vec4<f32> {
    let ndc = in.uv * 2.0 - vec2<f32>(1.0);
    let ro  = vec3<f32>(0.0, 0.0, -2.5);
    let rd  = normalize(vec3<f32>(ndc.x, -ndc.y, 1.5));
    let hit = ray_sphere(ro, rd, vec3<f32>(0.0), 0.85);
    if (hit.x < 0.0) { return vec4<f32>(0.10, 0.12, 0.18, 1.0); }
    let n = normalize((ro + rd * hit.x));
    return vec4<f32>(n * 0.5 + vec3<f32>(0.5), 1.0);
}
"#;
let shader = Shader::new(&["intersect/ray_sphere", main])?;

Each preview below uses a fixed pinhole camera (ro = (0, 0, -2.5), forward +z) and shades by hit normal, hit distance, or the slab (t_near, t_far) depending on what each test returns.

ray_box

Ray vs axis-aligned box centered at center with half-extents b, using the slab method. Returns (t_near, t_far) or (-1, -1) on miss.

fn ray_box(ro: vec3<f32>, rd: vec3<f32>, center: vec3<f32>, b: vec3<f32>) -> vec2<f32>

ray_capsule

Ray vs capsule between endpoints pa and pb with radius r. Returns the nearest positive t on hit, or -1 on miss.

fn ray_capsule(ro: vec3<f32>, rd: vec3<f32>, pa: vec3<f32>, pb: vec3<f32>, r: f32) -> f32

ray_cylinder

Ray vs an infinite cylinder along the +y axis, centered at the origin, with radius r. Returns (t_near, t_far) or (-1, -1) on miss.

fn ray_cylinder(ro: vec3<f32>, rd: vec3<f32>, r: f32) -> vec2<f32>

ray_disk

Ray vs a finite disk at center with unit normal n and radius r. Returns the hit distance t, or -1 on miss.

fn ray_disk(ro: vec3<f32>, rd: vec3<f32>, center: vec3<f32>, n: vec3<f32>, r: f32) -> f32

ray_plane

Ray vs an infinite plane with unit normal n and origin-distance d. Returns t (which may be negative if the plane is behind the ray), or the sentinel 1e30 when the ray is parallel to the plane.

fn ray_plane(ro: vec3<f32>, rd: vec3<f32>, n: vec3<f32>, d: f32) -> f32

ray_sphere

Ray vs sphere at center with radius radius. Assumes rd is unit length. Returns (t_near, t_far) or (-1, -1) on miss.

fn ray_sphere(ro: vec3<f32>, rd: vec3<f32>, center: vec3<f32>, radius: f32) -> vec2<f32>

ray_triangle

Möller–Trumbore ray–triangle intersection against vertices a, b, c. Returns vec4(t, u, v, 1) on hit (where (u, v) are barycentric coordinates), or (-1, -1, -1, -1) on miss.

fn ray_triangle(ro: vec3<f32>, rd: vec3<f32>, a: vec3<f32>, b: vec3<f32>, c: vec3<f32>) -> vec4<f32>