Small optimization on sphere

main.cpp

@@ -25,14 +25,15 @@ color ray_color(const ray& r)
 double hit_sphere(const point3& center, double radius, const ray& r)
 {
     vec3 oc = r.origin - center;
-    double a = dot(r.direction, r.direction);
-    double b = 2.0 * dot(oc, r.direction);
-    double c = dot(oc,oc) - radius*radius;
-    double discriminant = b*b - 4*a*c;
+    double a = r.direction.length_squared();
+    double half_b = dot(oc, r.direction);
+    double c = oc.length_squared() - radius*radius;
+    double discriminant = half_b*half_b - a*c;
+
     if (discriminant < 0)
         return -1;
     else
-        return (-b - sqrt(discriminant)) / (2.0*a);
+        return (-half_b - sqrt(discriminant)) / a;
 }
 
 int main()

vec3.hpp

@@ -59,6 +59,12 @@ struct vec3 {
     {
         return sqrt(x*x + y*y + z*z);
     }
+
+    // Length squared, useful for some calculations
+    double length_squared() const
+    {
+        return x*x + y*y + z*z;
+    }
 };
 
 /* Type aliases */