determine front/back faces

src/hittable.h

@@ -0,0 +1,23 @@
+#pragma once
+
+#include "ray.h"
+
+struct hit_record
+{
+    point3  p;
+    vec3    normal;
+    double  t;
+    bool    front_face;
+
+    inline void set_face_normal(const ray& r, const vec3& outward_normal)
+    {
+        front_face = dot(r.direction(), outward_normal) < 0;
+        normal = front_face ? outward_normal : -outward_normal;
+    }
+};
+
+class hittable
+{
+    public:
+        virtual bool hit(const ray& r, double tMin, double tMax, hit_record& rec) const = 0;
+};

src/sphere.h

@@ -0,0 +1,59 @@
+#pragma once
+
+#include "hittable.h"
+#include "vec3.h"
+
+class sphere : public hittable
+{
+    public:
+        sphere() {}
+        sphere(point3 centre, double r) : 
+            centre_(centre), 
+            radius_(r) {};
+
+        virtual bool hit(const ray& r, double t_min, double t_max, hit_record& rec) const;
+
+    private:
+        point3  centre_;
+        double  radius_;
+};
+
+bool sphere::hit(const ray& r, double t_min, double t_max, hit_record& rec) const 
+{
+    vec3 oc = r.origin() - centre_;
+    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;
+            rec.p = r.at(rec.t);
+
+            vec3 outward_normal = (rec.p - centre_) / radius_;
+            rec.set_face_normal(r, outward_normal);
+
+            return true;
+        }
+
+        temp = (-half_b + root) / a;
+        if (temp < t_max && temp > t_min)
+        {
+            rec.t = temp;
+            rec.p = r.at(rec.t);
+            
+            vec3 outward_normal = (rec.p - centre_) / radius_;
+            rec.set_face_normal(r, outward_normal);
+            
+            return true;
+        }
+    }
+
+    return false;
+}