spheres: implement basic unit sphere and intersect.

rtchallenge/src/spheres.rs

@@ -0,0 +1,59 @@
+use crate::{
+    rays::Ray,
+    tuples::{dot, Tuple},
+};
+
+#[derive(Default)]
+pub struct Sphere {}
+pub struct Intersection {}
+
+/// Intersect a ray with a sphere.
+///
+/// # Examples
+/// ```
+/// use rtchallenge::{
+///     rays::Ray,
+///     spheres::{intersect, Sphere},
+///     tuples::Tuple,
+/// };
+///
+/// // A ray intersects a sphere in two points.
+/// let r = Ray::new(Tuple::point(0., 0., -5.), Tuple::vector(0., 0., 1.));
+/// let s = Sphere::default();
+/// let xs = intersect(&s, &r);
+/// assert_eq!(xs, vec![4., 6.]);
+///
+/// // A ray intersects a sphere at a tangent.
+/// let r = Ray::new(Tuple::point(0., 2., -5.), Tuple::vector(0., 0., 1.));
+/// let s = Sphere::default();
+/// let xs = intersect(&s, &r);
+/// assert_eq!(xs, vec![]);
+///
+/// // A ray originates inside a sphere.
+/// let r = Ray::new(Tuple::point(0., 0., 0.), Tuple::vector(0., 0., 1.));
+/// let s = Sphere::default();
+/// let xs = intersect(&s, &r);
+/// assert_eq!(xs, vec![-1., 1.]);
+///
+/// // A sphere is behind a ray.
+/// let r = Ray::new(Tuple::point(0., 0., 5.), Tuple::vector(0., 0., 1.));
+/// let s = Sphere::default();
+/// let xs = intersect(&s, &r);
+/// assert_eq!(xs, vec![-6., -4.]);
+/// ```
+
+pub fn intersect(_sphere: &Sphere, ray: &Ray) -> Vec<f32> {
+    let sphere_to_ray = ray.origin - Tuple::point(0., 0., 0.);
+    let a = dot(ray.direction, ray.direction);
+    let b = 2. * dot(ray.direction, sphere_to_ray);
+    let c = dot(sphere_to_ray, sphere_to_ray) - 1.;
+    let discriminant = b * b - 4. * a * c;
+    if discriminant < 0. {
+        vec![]
+    } else {
+        vec![
+            (-b - discriminant.sqrt()) / (2. * a),
+            (-b + discriminant.sqrt()) / (2. * a),
+        ]
+    }
+}