Simplifying the ray-sphere intersection code

src/main.rs

@@ -104,14 +104,14 @@ fn hit_sphere(
     ray: &Ray,
 ) -> f64 {
     let oc: DVec3 = ray.origin - *center;
-    let a = ray.direction.dot(ray.direction);
-    let b = 2.0 * oc.dot(ray.direction);
-    let c = oc.dot(oc) - radius * radius;
-    let discriminant = b * b - 4. * a * c;
+    let a = ray.direction.length_squared();
+    let half_b = oc.dot(ray.direction);
+    let c = oc.length_squared() - radius * radius;
+    let discriminant = half_b * half_b - a * c;
 
     if discriminant < 0. {
         -1.0
     } else {
-        (-b - discriminant.sqrt()) / (2.0 * a)
+        (-half_b - discriminant.sqrt()) / a
     }
 }