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```
```use crate::{Vec3, Ray, RayIntersection, Intersect};

/// A sphere primitive.
pub struct Sphere {
origin: Vec3,
}

impl Sphere {
/// Create a new Sphere.
///
/// # Examples
/// ```
/// use obscura::{Sphere, Vec3};
///
/// let origin = Vec3::zero();
/// let x = Sphere::new(&origin, 1.0);
/// ```
pub fn new(origin: &Vec3, radius: f32) -> Sphere {
Sphere {
origin: Vec3::new(origin.x, origin.y, origin.z),
}
}
}

impl Intersect for Sphere {
/// Intersect ray with sphere.
/// Return t or t1,t2 where intersection point p = ray.origin + t * ray.direction
///
/// # Examples
/// ```
/// use obscura::{Sphere, Vec3, Ray, RayIntersection, Intersect};
///
/// let origin = Vec3::zero();
///
/// let target: Sphere = Sphere::new(
///     &Vec3::new(2.0, 0.0, 0.0),
///     1.0
/// );
///
/// // A ray that intersects the sphere twice.
/// let ray1: Ray = Ray::new(
///     &origin,
///     &Vec3::new(1.0, 0.0, 0.0)
/// );
///
/// if let RayIntersection::Hit(t1, t2) = Sphere::intersect(&target, &ray1) {
///     assert_eq!(t1, 1.0);
///     assert_eq!(t2, 3.0);
/// } else {
///     panic!("Oh no!");
/// }
///
/// // A ray which never intersects the sphere.
/// let ray2: Ray = Ray::new(
///     &origin,
///     &Vec3::new(0.0, 0.0, 1.0)
/// );
///
/// let result = Sphere::intersect(&target, &ray2);
/// assert_eq!(result, RayIntersection::Miss);
/// ```
fn intersect(&self, ray: &Ray) -> RayIntersection {
// http://viclw17.github.io/2018/07/16/raytracing-ray-sphere-intersection/

let target = self;

let a = Vec3::dot(&ray.direction, &ray.direction);
let b = 2.0 * Vec3::dot(
&ray.direction,
&Vec3::sub(&ray.origin, &target.origin)
);
let c = Vec3::dot(
&Vec3::sub(&ray.origin, &target.origin),
&Vec3::sub(&ray.origin, &target.origin)

let discriminant = b*b - 4.0*a*c;

if discriminant < 0.0 {

RayIntersection::Miss

} else if discriminant == 1.0 {

let t = (-b + f32::sqrt(discriminant)) / (2.0 * a);

RayIntersection::Tangent(t)

} else {

let t1 = ((-b) - f32::sqrt(discriminant)) / (2.0 * a);
let t2 = ((-b) + f32::sqrt(discriminant)) / (2.0 * a);

RayIntersection::Hit(t1, t2)

}
}
}```