spheres: enable intersect w/ transformed spheres.

rtchallenge/src/spheres.rs

@@ -8,6 +8,7 @@ use crate::{
 #[derive(Debug, PartialEq)]
 /// Sphere represents the unit-sphere (radius of unit 1.) at the origin 0., 0., 0.
 pub struct Sphere {
+    // TODO(wathiede): cache inverse to speed up intersect.
     pub transform: Matrix4x4,
 }
 
@@ -39,6 +40,7 @@ impl Default for Sphere {
 /// ```
 /// use rtchallenge::{
 ///     intersections::Intersection,
+///     matrices::Matrix4x4,
 ///     rays::Ray,
 ///     spheres::{intersect, Sphere},
 ///     tuples::Tuple,
@@ -76,8 +78,25 @@ impl Default for Sphere {
 ///     xs,
 ///     vec![Intersection::new(-6., &s), Intersection::new(-4., &s)]
 /// );
+///
+/// // Intersect a scaled sphere with a ray.
+/// let r = Ray::new(Tuple::point(0., 0., -5.), Tuple::vector(0., 0., 1.));
+/// let mut s = Sphere::default();
+/// s.transform = Matrix4x4::scaling(2., 2., 2.);
+/// let xs = intersect(&s, &r);
+/// assert_eq!(xs.len(), 2, "xs {:?}", xs);
+/// assert_eq!(xs[0].t, 3., "xs {:?}", xs);
+/// assert_eq!(xs[1].t, 7., "xs {:?}", xs);
+///
+/// // Intersect a translated sphere with a ray.
+/// let r = Ray::new(Tuple::point(0., 0., -5.), Tuple::vector(0., 0., 1.));
+/// let mut s = Sphere::default();
+/// s.transform = Matrix4x4::translation(5., 0., 0.);
+/// let xs = intersect(&s, &r);
+/// assert_eq!(xs.len(), 0);
 /// ```
 pub fn intersect<'s>(sphere: &'s Sphere, ray: &Ray) -> Vec<Intersection<'s>> {
+    let ray = ray.transform(sphere.transform.inverse());
     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);