snoopy/src/vec3.h

#pragma once

#include <cmath>
#include <iostream>

#include "rtweekend.h"

class vec3
{
public:
    inline static vec3 random()
    {
        return vec3(random_double(),random_double(),random_double());
    }

    inline static vec3 random(double min, double max)
    {
        return vec3(random_double(min,max),random_double(min,max),random_double(min,max));
    }

    vec3() : e{0,0,0} {}
    vec3(double e0, double e1, double e2) : e{e0, e1, e2} {}

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

    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 double t)
    {
        e[0] *= t;
        e[1] *= t;
        e[2] *= t;
        return *this;
    }

    vec3& operator/=(const double t)
    {
        return *this *= 1 / t;
    }

    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:
    double e[3];
};

// type aliases for vec3
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();
}

vec3 random_in_unit_sphere()
{
    while (true)
    {
        auto p = vec3::random(-1,1);
        if (p.length_squared() >= 1) continue;
        return p;
    }
}

vec3 random_unit_vector()
{
    auto a = random_double(0, 2*pi);
    auto z = random_double(-1,1);
    auto r = sqrt(1 - z*z);
    return vec3(r*cos(a), r*sin(a), z);
}

vec3 random_in_hemisphere(const vec3& normal)
{
    vec3 in_unit_sphere = random_in_unit_sphere();
    if (dot(in_unit_sphere, normal) > 0.0)
    {
        return in_unit_sphere;
    }
    else
    {
        return -in_unit_sphere;
    }
}

vec3 reflect(const vec3& v, const vec3& n)
{
    return v - 2*dot(v,n)*n;
}