nextWeek: update moving_sphere.h

Improvements we made to sphere.h didn't make it into moving_sphere.h.
Fixing that here.

Author: hollasch

books/RayTracingTheNextWeek.html

@@ -206,10 +206,12 @@
         auto a = r.direction().length_squared();
         auto half_b = dot(oc, r.direction());
         auto c = oc.length_squared() - radius*radius;
+
         auto discriminant = half_b*half_b - a*c;
 
         if (discriminant > 0) {
             auto root = sqrt(discriminant);
+
             auto temp = (-half_b - root)/a;
             if (temp < t_max && temp > t_min) {
                 rec.t = temp;
@@ -221,6 +223,7 @@
                 rec.mat_ptr = mat_ptr;
                 return true;
             }
+
             temp = (-half_b + root) / a;
             if (temp < t_max && temp > t_min) {
                 rec.t = temp;

src/TheNextWeek/moving_sphere.h

@@ -56,15 +56,16 @@ bool moving_sphere::bounding_box(double t0, double t1, aabb& output_box) const {
 // replace "center" with "center(r.time())"
 bool moving_sphere::hit(const ray& r, double t_min, double t_max, hit_record& rec) const {
     vec3 oc = r.origin() - center(r.time());
-    auto a = dot(r.direction(), r.direction());
-    auto b = dot(oc, r.direction());
-    auto c = dot(oc, oc) - radius*radius;
+    auto a = r.direction().length_squared();
+    auto half_b = dot(oc, r.direction());
+    auto c = oc.length_squared() - radius*radius;
 
-    auto discriminant = b*b - a*c;
+    auto discriminant = half_b*half_b - a*c;
 
     if (discriminant > 0) {
+        auto root = sqrt(discriminant);
 
-        auto temp = (-b - sqrt(discriminant))/a;
+        auto temp = (-half_b - root)/a;
         if (temp < t_max && temp > t_min) {
             rec.t = temp;
             rec.p = r.at(rec.t);
@@ -74,7 +75,7 @@ bool moving_sphere::hit(const ray& r, double t_min, double t_max, hit_record& re
             return true;
         }
 
-        temp = (-b + sqrt(discriminant))/a;
+        temp = (-half_b + root)/a;
         if (temp < t_max && temp > t_min) {
             rec.t = temp;
             rec.p = r.at(rec.t);

src/TheNextWeek/sphere.h

@@ -23,6 +23,7 @@ class sphere: public hittable  {
         virtual bool hit(const ray& r, double tmin, double tmax, hit_record& rec) const;
         virtual bool bounding_box(double t0, double t1, aabb& output_box) const;
 
+    public:
         vec3 center;
         double radius;
         shared_ptr<material> mat_ptr;
@@ -41,6 +42,7 @@ bool sphere::hit(const ray& r, double t_min, double t_max, hit_record& rec) cons
     auto a = r.direction().length_squared();
     auto half_b = dot(oc, r.direction());
     auto c = oc.length_squared() - radius*radius;
+
     auto discriminant = half_b*half_b - a*c;
 
     if (discriminant > 0) {
@@ -68,6 +70,7 @@ bool sphere::hit(const ray& r, double t_min, double t_max, hit_record& rec) cons
             return true;
         }
     }
+
     return false;
 }