// 3D SDF primitives
fn sdSphere(p: vec3<f32>, r: f32) -> f32 {
    return length(p) - r;
}

fn sdBox(p: vec3<f32>, b: vec3<f32>) -> f32 {
    let q = abs(p) - b;
    return length(max(q, vec3<f32>(0.0))) + min(max(q.x, max(q.y, q.z)), 0.0);
}

fn sdTorus(p: vec3<f32>, t: vec2<f32>) -> f32 {
    let q = vec2<f32>(length(p.xz) - t.x, p.y);
    return length(q) - t.y;
}

fn sdPlane(p: vec3<f32>, n: vec3<f32>, h: f32) -> f32 {
    return dot(p, n) + h;
}

// 2D SDF primitives
fn sdBox2D(p: vec2<f32>, b: vec2<f32>) -> f32 {
    let d = abs(p) - b;
    return length(max(d, vec2<f32>(0.0))) + min(max(d.x, d.y), 0.0);
}

fn sdEllipse(p: vec2<f32>, ab: vec2<f32>) -> f32 {
    var p_abs = abs(p);
    if (p_abs.x > p_abs.y) {
        p_abs = vec2<f32>(p_abs.y, p_abs.x);
    }
    let l = ab.y * ab.y - ab.x * ab.x;
    let m = ab.x * p_abs.x / l;
    let n = ab.y * p_abs.y / l;
    let m2 = m * m;
    let n2 = n * n;
    let c = (m2 + n2 - 1.0) / 3.0;
    let c3 = c * c * c;
    let d = c3 + m2 * n2;
    let g = m + m * n2;
    var co: f32;
    if (d < 0.0) {
        let h = acos((c3 + m2 * n2 * 2.0) / c3) / 3.0;
        let s = cos(h);
        let t = sin(h) * sqrt(3.0);
        co = (sqrt(-c * (s + t * 2.0) + m2) + sign(l) * sqrt(-c * (s - t * 2.0) + m2) + abs(g) / (sqrt(-c * (s + t * 2.0) + m2) * sqrt(-c * (s - t * 2.0) + m2)) - m) / 2.0;
    } else {
        let h = 2.0 * m * n * sqrt(d);
        let s = sign(c3 + m2 * n2 + h) * pow(abs(c3 + m2 * n2 + h), 1.0 / 3.0);
        let u = sign(c3 + m2 * n2 - h) * pow(abs(c3 + m2 * n2 - h), 1.0 / 3.0);
        let rx = -s - u + m2 * 2.0;
        let ry = (s - u) * sqrt(3.0);
        co = (ry / sqrt(sqrt(rx * rx + ry * ry) - rx) + 2.0 * g / sqrt(rx * rx + ry * ry) - m) / 2.0;
    }
    let si = sqrt(max(0.0, 1.0 - co * co));
    return length(p_abs - vec2<f32>(ab.x * co, ab.y * si)) * sign(p_abs.y * ab.x * co - p_abs.x * ab.y * si);
}