vec3.hpp

#ifndef VEC3_hpp
#define VEC3_hpp

#include <cmath>

using std::sqrt;
#include <iostream>

class vec3
{
public:
    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 sqrt(length_squared());
    }

    double length_squared() const
    {
        return e[0] * e[0] + e[1] * e[1] + e[2] * e[2];
    }
    bool near_zero() const {
        // Return true if the vector is close to zero in all dimensions.
        const auto s = 1e-8;
        return fabs(e[0]) < s && fabs(e[1]) < s && fabs(e[2]) < s;
    }

    inline friend std::ostream& operator<<(std::ostream& out, const vec3& v);
    inline friend vec3 operator+(const vec3& u, const vec3& v);
    inline friend vec3 operator-(const vec3& u, const vec3& v);
    inline friend vec3 operator*(const vec3& u, const vec3& v);
    inline friend vec3 operator*(double t, const vec3& v);
    inline friend vec3 operator*(const vec3& v, double t);
    inline friend vec3 operator/(vec3 v, double t);

    inline friend vec3 cross(const vec3& u, const vec3& v);
    inline friend double dot(const vec3& u, const vec3& v);
    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));
    }

    double e[3];
};
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 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() {
    return unit_vector(random_in_unit_sphere());
}

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;
}

vec3 refract(const vec3& uv, const vec3& n, double etai_over_etat) {
    double cos_theta = fmin(dot(-uv, n), 1.0);
    vec3 r_out_prep = etai_over_etat * (uv + cos_theta * n);
    vec3 r_out_parallel = -sqrt(fabs(1.0 - r_out_prep.length_squared())) * n;
    return r_out_prep + r_out_parallel;
}

vec3 random_in_unit_disk() {
    while (true) {
        auto p = vec3(random_double(-1, 1), random_double(-1, 1), 0);
        if (p.length_squared() >= 1) continue;
        return p;
    }
}

using point3 = vec3;
using color = vec3;

#endif