# Ray Tracing in a Weekend Part 2 - The vec3 class

## The vec3 class

In part 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 introduces the vec3 class used to perform calculations with 3-dimensional vectors and access them as x, y, z-coordinates or r, g, b-color values.

The code below is complete, but feel free to download the complete repo from https://github.com/celeph/ray-tracing-in-a-weekend.

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 >= 0; j--) {
for (int i = 0; i < 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";
}
}
}


Makefile


CC = g++
CFLAGS = -g
INCFLAGS = -I./

RM = /bin/rm -f
all: vec3-example

vec3-example: vec3-example.o
$(CC)$(CFLAGS) -o vec3-example vec3-example.o

vec3-example.o: vec3-example.cpp
$(CC)$(CFLAGS) $(INCFLAGS) -c vec3-example.cpp clean:$(RM) *.o vec3-example *.ppm

run: vec3-example
./vec3-example > vec3-example.ppm


## vec3 with Javascript and 2D Canvas

Here’s also the same example in Javascript. I apologize if the Javascript code is not super fancy or modern. I know kids these days do a lot differently. :)

class vec3 {
constructor(e0,e1,e2) {
this.e = [];
this.e[0] = parseFloat(e0);
this.e[1] = parseFloat(e1);
this.e[2] = parseFloat(e2);
}

get x() { return this.e[0]; }
get y() { return this.e[1]; }
get z() { return this.e[2]; }
get r() { return this.e[0]; }
get g() { return this.e[1]; }
get b() { return this.e[2]; }

toString() { return '('+this.e[0]+','+this.e[1]+','+this.e[2]+')'; }

if (summand.constructor.name == this.constructor.name) { // perform vec3 + vec3
return new vec3(this.e[0]+summand.e[0], this.e[1]+summand.e[1], this.e[2]+summand.e[2]);
} else { // perform vec3 + float
summand = parseFloat(summand);
return new vec3(this.e[0]+summand, this.e[1]+summand, this.e[2]+summand);
}
}

sub(subtrahend) {
if (subtrahend.constructor.name == this.constructor.name) { // perform vec3 - vec3
return new vec3(this.e[0]-subtrahend.e[0], this.e[1]-subtrahend.e[1], this.e[2]-subtrahend.e[2]);
} else { // perform vec3 - float
subtrahend = parseFloat(subtrahend);
return new vec3(this.e[0]-subtrahend, this.e[1]-subtrahend, this.e[2]-subtrahend);
}
}

mul(factor) {
if (factor.constructor.name == this.constructor.name) { // perform vec3 * vec3
return new vec3(this.e[0]*factor.e[0], this.e[1]*factor.e[1], this.e[2]*factor.e[2]);
} else { // perform vec3 * float
factor = parseFloat(factor);
return new vec3(this.e[0]*factor, this.e[1]*factor, this.e[2]*factor);
}
}

div(divisor) {
if (divisor.constructor.name == this.constructor.name) { // perform vec3 / vec3
return new vec3(this.e[0]/divisor.e[0], this.e[1]/divisor.e[1], this.e[2]/divisor.e[2]);
} else { // perform vec3 / float
divisor = 1/parseFloat(divisor);
return this.mul(divisor);
}
}

dot(v2) {
if (v2.constructor.name == this.constructor.name) { // perform vec3 dot vec3
return this.e[0]*v2.e[0] + this.e[1]*v2.e[1] + this.e[2]*v2.e[2];
} else return this;
}

cross(v2) {
if (v2.constructor.name == this.constructor.name) { // perform vec3 cross vec3
return new vec3( (this.e[1]*v2.e[2] - this.e[2]*v2.e[1]),
(-(this.e[0]*v2.e[2] - this.e[2]*v2.e[0])),
(this.e[0]*v2.e[1] - this.e[1]*v2.e[0]) );
} else return this;
}

length() {
return Math.sqrt(this.e[0]*this.e[0] + this.e[1]*this.e[1] + this.e[2]*this.e[2]);
}

squared_length() {
return this.e[0]*this.e[0] + this.e[1]*this.e[1] + this.e[2]*this.e[2];
}

make_unit_vector() {
var k = 1.0 / this.length();
return this.mul(k);
}

unit_vector() {
return this.div(this.length());
}
}

var example = {
main: function() {
var c = document.getElementById('example');
var ctx = c.getContext('2d');

var nx = 200;
var ny = 100;
for (var j = ny-1; j >= 0; j--) {
for (var i = 0; i < nx; i++) {
var color = new vec3(parseFloat(i)/parseFloat(nx), parseFloat(j)/parseFloat(ny), 0.2);
color = color.mul(255.99);
ctx.fillStyle = 'rgb('+parseInt(color.r)+','+parseInt(color.g)+','+parseInt(color.b)+')';
ctx.fillRect(i, ny-j, 1, 1);
}
}
}
};
window.onload = function() { example.main(); };