# Ray Tracing 003: The vec3 Class

## The vec3 Class

In episode 1 I made a simple image by assigning rgb values to individual variables in a loop across the x- and y-coordinates.

This example produces the same image, but it introduces the vec3 class to perform calculations with 3-dimensional vectors. To keep it simple, this class can be used for x, y, z-coordinates as well as r, g, b-color values. There are getter methods for both x, y, and z as well as r, g, b.

The complete example is also available in my git repo at github.com/celeph/ray-tracing.

// vec3.h
#ifndef VEC3H
#define VEC3H

#include <math.h>
#include <stdlib.h>
#include <iostream>

class vec3 {
public:
float e[3];

vec3() {}
vec3(float e0, float e1, float e2) {
e[0] = e0;
e[1] = e1;
e[2] = e2;
}

inline float x() const { return e[0]; }
inline float y() const { return e[1]; }
inline float z() const { return e[2]; }

inline float r() const { return e[0]; }
inline float g() const { return e[1]; }
inline float b() const { return e[2]; }

inline const vec3& operator+() const { return *this; }
inline vec3 operator-() const { return vec3(-e[0], -e[1], -e[2]); }
inline float operator[](int i) const { return e[i]; }
inline float& operator[](int i) { return e[i]; }

inline vec3& operator+=(const vec3 &v2);
inline vec3& operator-=(const vec3 &v2);
inline vec3& operator*=(const vec3 &v2);
inline vec3& operator/=(const vec3 &v2);
inline vec3& operator*=(const float t);
inline vec3& operator/=(const float t);

inline float length() const {
return sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]);
}

inline float squared_length() const {
return e[0]*e[0] + e[1]*e[1] + e[2]*e[2];
}

inline void make_unit_vector();
};

inline std::istream& operator>>(std::istream &is, vec3 &t) {
is >> t.e[0] >> t.e[1] >> t.e[2];
return is;
}

inline std::ostream& operator<<(std::ostream &os, const vec3 &t) {
os << t.e[0] << " " << t.e[1] << " " << t.e[2];
return os;
}

inline void vec3::make_unit_vector() {
float k = 1.0 / sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]);
e[0] *= k;
e[1] *= k;
e[2] *= k;
}

inline vec3 operator+(const vec3 &v1, const vec3 &v2) {
return vec3(v1.e[0] + v2.e[0], v1.e[1] + v2.e[1], v1.e[2] + v2.e[2]);
}

inline vec3 operator-(const vec3 &v1, const vec3 &v2) {
return vec3(v1.e[0] - v2.e[0], v1.e[1] - v2.e[1], v1.e[2] - v2.e[2]);
}

inline vec3 operator*(const vec3 &v1, const vec3 &v2) {
return vec3(v1.e[0] * v2.e[0], v1.e[1] * v2.e[1], v1.e[2] * v2.e[2]);
}

inline vec3 operator/(const vec3 &v1, const vec3 &v2) {
return vec3(v1.e[0] / v2.e[0], v1.e[1] / v2.e[1], v1.e[2] / v2.e[2]);
}

inline vec3 operator*(float t, const vec3 &v) {
return vec3(t * v.e[0], t * v.e[1], t * v.e[2]);
}

inline vec3 operator/(const vec3 &v, float t) {
return vec3(v.e[0] / t, v.e[1] / t, v.e[2] / t);
}

inline vec3 operator*(const vec3 &v, float t) {
return vec3(t * v.e[0], t * v.e[1], t * v.e[2]);
}

inline float dot(const vec3 &v1, const vec3 &v2) {
return v1.e[0] * v2.e[0] + v1.e[1] * v2.e[1] + v1.e[2] * v2.e[2];
}

inline vec3 cross(const vec3 &v1, const vec3 &v2) {
return vec3(
(v1.e[1] * v2.e[2] - v1.e[2] * v2.e[1]),
(-(v1.e[0] * v2.e[2] - v1.e[2] * v2.e[0])),
(v1.e[0] * v2.e[1] - v1.e[1] * v2.e[0])
);
}

inline vec3& vec3::operator+=(const vec3 &v) {
e[0] += v.e[0];
e[1] += v.e[1];
e[2] += v.e[2];
return *this;
}

inline vec3& vec3::operator*=(const vec3 &v) {
e[0] *= v.e[0];
e[1] *= v.e[1];
e[2] *= v.e[2];
return *this;
}

inline vec3& vec3::operator/=(const vec3 &v) {
e[0] /= v.e[0];
e[1] /= v.e[1];
e[2] /= v.e[2];
return *this;
}

inline vec3& vec3::operator-=(const vec3 &v) {
e[0] -= v.e[0];
e[1] -= v.e[1];
e[2] -= v.e[2];
return *this;
}

inline vec3& vec3::operator*=(const float t) {
e[0] *= t;
e[1] *= t;
e[2] *= t;
return *this;
}

inline vec3& vec3::operator/=(const float t) {
float k = 1.0/t;
e[0] *= k;
e[1] *= k;
e[2] *= k;
return *this;
}

inline vec3 unit_vector(vec3 v) {
return v / v.length();
}
#endif

// vec3-example.cpp
#include <iostream>
#include "vec3.h"
int main() {
int nx = 200;
int ny = 100;
std::cout << "P3\n" << nx << " " << ny << "\n255\n";
for (int j = ny-1; j &gt;= 0; j--) {
for (int i = 0; i &lt; nx; i++) {
vec3 col( float(i) / float(nx), float(j) / float(ny), 0.2 );
int ir = int(255.99 * col[0]);
int ig = int(255.99 * col[1]);
int ib = int(255.99 * col[2]);
std::cout << ir << " " << ig << " " << ib << "\n";
}
}
}


## vec3 with Javascript and Canvas

The beauty of C++ is that it supports operator overloading and allows you to add two 3D vectors as easily as vsum = v1 + v2 or multiply them as easily as vproduct = v1 * v2. Similarly, you can perform operations like vsum += v etc. This makes it a perfect language choice for 3D or other type computation while keeping the code short and legible.