diff --git a/include/camera.h b/include/camera.h
index 0f68329..f8b423f 100644
--- a/include/camera.h
+++ b/include/camera.h
@@ -1,52 +1,29 @@
 #pragma once
 
-#include "rtweekend.h"
+#include "math.h"
+#include "vec3.h"
+#include "ray.h"
 #include "image.h"
 
 class camera
 {
-    public:
-        camera(
-            point3  lookfrom,
-            point3  lookat,
-            vec3    vup,
-            double  vfov,   // vertical field of view in degrees
-            double  aspect_ratio,
-            double  aperture,
-            double  focus_dist)
-        {
-            auto theta = degrees_to_radians(vfov);
-            auto h = tan(theta/2);
-            auto viewport_height = 2.0 * h;
-            auto viewport_width = aspect_ratio * viewport_height;
+public:
+    camera(
+        point3  lookfrom,
+        point3  lookat,
+        vec3    vup,
+        double  vfov,   // vertical field of view in degrees
+        double  aspect_ratio,
+        double  aperture,
+        double  focus_dist);
 
-            w_ = unit_vector(lookfrom - lookat);
-            u_ = unit_vector(cross(vup, w_));
-            v_ = cross(w_, u_);
+    ray get_ray(double s, double t) const; 
 
-            origin_ = lookfrom;
-            horizontal_ = focus_dist * viewport_width * u_;
-            vertical_ = focus_dist * viewport_height * v_;
-            lower_left_corner_ = origin_ - horizontal_/2 - vertical_/2 - focus_dist * w_;
-
-            lens_radius_ = aperture / 2;
-        }
-
-        ray get_ray(double s, double t) const 
-        {
-            vec3 rd = lens_radius_ * random_in_unit_disk();
-            vec3 offset = (u_ * rd.x()) + (v_ * rd.y());
-
-            return ray(
-                origin_ + offset,
-                lower_left_corner_ + s*horizontal_ + t*vertical_ - origin_ - offset);
-        }
-
-    private:
-        point3  origin_;
-        point3  lower_left_corner_;
-        vec3    horizontal_;
-        vec3    vertical_;
-        vec3    u_, v_, w_;
-        double  lens_radius_;
+private:
+    point3  origin_;
+    point3  lower_left_corner_;
+    vec3    horizontal_;
+    vec3    vertical_;
+    vec3    u_, v_, w_;
+    double  lens_radius_;
 };
diff --git a/include/material.h b/include/material.h
index fb8f666..78a2ef3 100644
--- a/include/material.h
+++ b/include/material.h
@@ -54,7 +54,7 @@ class metal : public material
         colour& attenuation, 
         ray& scattered) const 
     {
-        vec3 reflected = vec3::reflect(unit_vector(r_in.direction()), rec.normal);
+        vec3 reflected = reflect(normalize(r_in.direction()), rec.normal);
         scattered = ray(rec.p, reflected + fuzz_ * vec3::random_in_unit_sphere());
         attenuation = albedo_;
         return dot(scattered.direction(), rec.normal) > 0;
@@ -79,13 +79,13 @@ class dielectric : public material
         attenuation = colour(1.0,1.0,1.0);
         double etai_over_etat = rec.front_face ? (1.0 / refraction_index_) : refraction_index_;
 
-        vec3 unit_direction = unit_vector(r_in.direction());
+        vec3 unit_direction = normalize(r_in.direction());
 
         double cos_theta = fmin(dot(-unit_direction, rec.normal), 1.0);
         double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
         if (etai_over_etat * sin_theta > 1.0)
         {
-            vec3 reflected = vec3::reflect(unit_direction, rec.normal);
+            vec3 reflected = reflect(unit_direction, rec.normal);
             scattered = ray(rec.p, reflected);
             return true;
         }
@@ -93,12 +93,12 @@ class dielectric : public material
         double reflect_prob = schlick(cos_theta, etai_over_etat);
         if (math::random_double() < reflect_prob)
         {
-            vec3 reflected = vec3::reflect(unit_direction, rec.normal);
+            vec3 reflected = reflect(unit_direction, rec.normal);
             scattered = ray(rec.p, reflected);
             return true;
         }
 
-        vec3 refracted = vec3::refract(unit_direction, rec.normal, etai_over_etat);
+        vec3 refracted = refract(unit_direction, rec.normal, etai_over_etat);
         scattered = ray(rec.p, refracted);
 
         return true;
diff --git a/include/scene.h b/include/scene.h
index dba330b..2a2f7c0 100644
--- a/include/scene.h
+++ b/include/scene.h
@@ -28,7 +28,7 @@ colour ray_colour(const ray& r, const hittable& world, int depth)
         return grey;
     }
 
-    vec3 unit_direction = unit_vector(r.direction());
+    vec3 unit_direction = normalize(r.direction());
     auto t = 0.5 * (unit_direction.y() + 1.0) + 0.5;
 
     return lerp(grey, pink, t);
diff --git a/include/vec3.h b/include/vec3.h
index 061c222..e591529 100755
--- a/include/vec3.h
+++ b/include/vec3.h
@@ -7,21 +7,12 @@
 class vec3
 {
 public:
-    inline static vec3 random()
-    {
-        return vec3(math::random_double(),math::random_double(),math::random_double());
-    }
-
-    inline static vec3 random(double min, double max)
-    {
-        return vec3(math::random_double(min,max),math::random_double(min,max),math::random_double(min,max));
-    }
-
+    static vec3 random();
+    static vec3 random(double min, double max);
     static vec3 random_in_unit_disk();
     static vec3 random_unit_vector();
     static vec3 random_in_unit_sphere();
-    static vec3 reflect(const vec3& v, const vec3& n);
-    static vec3 refract(const vec3& uv, const vec3& n, double etai_over_etat);
+    static vec3 random_in_hemisphere(const vec3& normal);
 
     vec3() : e{0,0,0} {}
     vec3(double e0, double e1, double e2) : e{e0, e1, e2} {}
@@ -29,43 +20,33 @@ public:
     double x() const { return e[0]; }
     double y() const { return e[1]; }
     double z() const { return e[2]; }
+    double length() const;
+    double length_squared() const;
 
     vec3 operator-() const { return vec3(-e[0], -e[1], -e[2]); }
     double operator[](int i) const { return e[i]; }
     double& operator[](int i) { return e[i]; }
 
-    vec3& operator+=(const vec3 &v)
-    {
-        e[0] += v.e[0];
-        e[1] += v.e[1];
-        e[2] += v.e[2];
-        return *this;
-    }
+    vec3& operator+=(const vec3 &v);
+    vec3& operator*=(const double t);
+    vec3& operator/=(const double t);
 
-    vec3& operator*=(const double t)
-    {
-        e[0] *= t;
-        e[1] *= t;
-        e[2] *= t;
-        return *this;
-    }
+    friend std::ostream& operator<<(std::ostream &out, const vec3 &v);
+    friend vec3 operator+(const vec3 &u, const vec3 &v);
+    friend vec3 operator-(const vec3 &u, const vec3 &v);
+    friend vec3 operator*(const vec3 &u, const vec3 &v);
+    friend vec3 operator*(double t, const vec3 &v);
+    friend vec3 operator*(const vec3 &v, double t);
+    friend vec3 operator/(vec3 v, double t);
 
-    vec3& operator/=(const double t)
-    {
-        return *this *= 1 / t;
-    }
+    friend vec3 lerp(const vec3 &a, const vec3 &b, double t);
+    friend vec3 reflect(const vec3& v, const vec3& n);
+    friend vec3 refract(const vec3& uv, const vec3& n, double etai_over_etat);
+    friend double dot(const vec3 &u, const vec3 &v);
+    friend vec3 cross(const vec3 &u, const vec3 &v);
+    friend vec3 normalize(vec3 v);
 
-    double length() const 
-    {
-        return std::sqrt(length_squared());
-    }
-
-    double length_squared() const
-    {
-        return e[0]*e[0] + e[1]*e[1] + e[2]*e[2];
-    }
-
-public:
+private:
     double e[3];
 };
 
@@ -73,64 +54,3 @@ public:
 using point3 = vec3; // 3D point
 using colour = vec3; // RGB colour
 
-// utility functions
-
-inline std::ostream& operator<<(std::ostream &out, const vec3 &v) 
-{
-    return out << v.e[0] << ' ' << v.e[1] << ' ' << v.e[2];
-}
-
-inline vec3 operator+(const vec3 &u, const vec3 &v)
-{
-    return vec3(u.e[0] + v.e[0], u.e[1] + v.e[1], u.e[2] + v.e[2]);
-}
-
-inline vec3 operator-(const vec3 &u, const vec3 &v)
-{
-    return vec3(u.e[0] - v.e[0], u.e[1] - v.e[1], u.e[2] - v.e[2]);
-}
-
-inline vec3 operator*(const vec3 &u, const vec3 &v)
-{
-    return vec3(u.e[0] * v.e[0], u.e[1] * v.e[1], u.e[2] * v.e[2]);
-}
-
-inline vec3 operator*(double t, const vec3 &v)
-{
-    return vec3(t * v.e[0], t * v.e[1], t * v.e[2]);
-}
-
-inline vec3 operator*(const vec3 &v, double t)
-{
-    return t * v;
-}
-
-inline vec3 operator/(vec3 v, double t)
-{
-    return (1 / t) * v;
-}
-
-inline double dot(const vec3 &u, const vec3 &v)
-{
-    return u.e[0] * v.e[0]
-         + u.e[1] * v.e[1]
-         + u.e[2] * v.e[2];
-}
-
-inline vec3 cross(const vec3 &u, const vec3 &v)
-{
-    return vec3(u.e[1] * v.e[2] - u.e[2] * v.e[1],
-                u.e[2] * v.e[0] - u.e[0] * v.e[2],
-                u.e[0] * v.e[1] - u.e[1] * v.e[0]);
-}
-
-inline vec3 lerp(const vec3 &a, const vec3 &b, double t)
-{
-    return (1.0 - t) * a + t * b;
-}
-
-inline vec3 unit_vector(vec3 v)
-{
-    return v / v.length();
-}
-
diff --git a/src/camera.cpp b/src/camera.cpp
index 08151c7..463685c 100644
--- a/src/camera.cpp
+++ b/src/camera.cpp
@@ -15,8 +15,8 @@ camera::camera(
     auto viewport_height = 2.0 * h;
     auto viewport_width = aspect_ratio * viewport_height;
 
-    w_ = unit_vector(lookfrom - lookat);
-    u_ = unit_vector(cross(vup, w_));
+    w_ = normalize(lookfrom - lookat);
+    u_ = normalize(cross(vup, w_));
     v_ = cross(w_, u_);
 
     origin_ = lookfrom;
diff --git a/src/camera.h b/src/camera.h
deleted file mode 100644
index f8b423f..0000000
--- a/src/camera.h
+++ /dev/null
@@ -1,29 +0,0 @@
-#pragma once
-
-#include "math.h"
-#include "vec3.h"
-#include "ray.h"
-#include "image.h"
-
-class camera
-{
-public:
-    camera(
-        point3  lookfrom,
-        point3  lookat,
-        vec3    vup,
-        double  vfov,   // vertical field of view in degrees
-        double  aspect_ratio,
-        double  aperture,
-        double  focus_dist);
-
-    ray get_ray(double s, double t) const; 
-
-private:
-    point3  origin_;
-    point3  lower_left_corner_;
-    vec3    horizontal_;
-    vec3    vertical_;
-    vec3    u_, v_, w_;
-    double  lens_radius_;
-};
diff --git a/src/vec3.cpp b/src/vec3.cpp
index 08fd529..9b742d9 100644
--- a/src/vec3.cpp
+++ b/src/vec3.cpp
@@ -1,5 +1,15 @@
 #include "vec3.h"
 
+vec3 vec3::random()
+{
+    return vec3(math::random_double(),math::random_double(),math::random_double());
+}
+
+vec3 vec3::random(double min, double max)
+{
+    return vec3(math::random_double(min,max),math::random_double(min,max),math::random_double(min,max));
+}
+
 vec3 vec3::random_unit_vector()
 {
     auto a = math::random_double(0, 2 * math::pi);
@@ -8,20 +18,6 @@ vec3 vec3::random_unit_vector()
     return vec3(r*cos(a), r*sin(a), z);
 }
 
-vec3 vec3::reflect(const vec3& v, const vec3& n)
-{
-    return v - 2*dot(v,n)*n;
-}
-
-vec3 vec3::refract(const vec3& uv, const vec3& n, double etai_over_etat)
-{
-    auto cos_theta = dot(-uv, n);
-    vec3 r_out_parallel = etai_over_etat * (uv + cos_theta*n);
-    vec3 r_out_perp = -sqrt(1.0 - r_out_parallel.length_squared()) * n;
-
-    return r_out_parallel + r_out_perp;
-}
-
 vec3 vec3::random_in_unit_disk()
 {
     while(true)
@@ -42,7 +38,7 @@ vec3 vec3::random_in_unit_sphere()
     }
 }
 
-vec3 random_in_hemisphere(const vec3& normal)
+vec3 vec3::random_in_hemisphere(const vec3& normal)
 {
     vec3 in_unit_sphere = vec3::random_in_unit_sphere();
     if (dot(in_unit_sphere, normal) > 0.0)
@@ -55,3 +51,107 @@ vec3 random_in_hemisphere(const vec3& normal)
     }
 }
 
+vec3 normalize(vec3 v)
+{
+    return v / v.length();
+}
+
+double vec3::length() const
+{
+    return std::sqrt(length_squared());
+}
+
+double vec3::length_squared() const
+{
+    return e[0]*e[0] + e[1]*e[1] + e[2]*e[2];
+}
+
+vec3& vec3::operator+=(const vec3 &v)
+{
+    e[0] += v.e[0];
+    e[1] += v.e[1];
+    e[2] += v.e[2];
+    return *this;
+}
+
+vec3& vec3::operator*=(const double t)
+{
+    e[0] *= t;
+    e[1] *= t;
+    e[2] *= t;
+    return *this;
+}
+
+vec3& vec3::operator/=(const double t)
+{
+    return *this *= 1 / t;
+}
+
+std::ostream& operator<<(std::ostream &out, const vec3 &v)
+{
+    return out << v.e[0] << ' ' << v.e[1] << ' ' << v.e[2];
+}
+
+vec3 operator+(const vec3 &u, const vec3 &v)
+{
+    return vec3(u.e[0] + v.e[0], u.e[1] + v.e[1], u.e[2] + v.e[2]);
+}
+
+vec3 operator-(const vec3 &u, const vec3 &v)
+{
+    return vec3(u.e[0] - v.e[0], u.e[1] - v.e[1], u.e[2] - v.e[2]);
+}
+
+vec3 operator*(const vec3 &u, const vec3 &v)
+{
+    return vec3(u.e[0] * v.e[0], u.e[1] * v.e[1], u.e[2] * v.e[2]);
+}
+
+vec3 operator*(const vec3 &v, double t)
+{
+    return t * v;
+}
+
+vec3 operator*(double t, const vec3 &v)
+{
+    return vec3(t * v.e[0], t * v.e[1], t * v.e[2]);
+}
+
+vec3 operator/(vec3 v, double t)
+{
+    return (1 / t) * v;
+}
+
+vec3 lerp(const vec3 &a, const vec3 &b, double t)
+{
+    return (1.0 - t) * a + t * b;
+}
+
+double dot(const vec3 &u, const vec3 &v)
+{
+    return u[0] * v[0]
+         + u[1] * v[1]
+         + u[2] * v[2];
+}
+
+vec3 cross(const vec3 &u, const vec3 &v)
+{
+    return vec3(u.e[1] * v.e[2] - u.e[2] * v.e[1],
+                u.e[2] * v.e[0] - u.e[0] * v.e[2],
+                u.e[0] * v.e[1] - u.e[1] * v.e[0]);
+}
+
+vec3 reflect(const vec3& v, const vec3& n)
+{
+    return v - 2*dot(v,n)*n;
+}
+
+vec3 refract(const vec3& uv, const vec3& n, double etai_over_etat)
+{
+    auto cos_theta = dot(-uv, n);
+    vec3 r_out_parallel = etai_over_etat * (uv + cos_theta*n);
+    vec3 r_out_perp = -sqrt(1.0 - r_out_parallel.length_squared()) * n;
+
+    return r_out_parallel + r_out_perp;
+}
+