vec3.h

#pragma once
#include<cmath>
#include<iostream>
class vec3
{
public:
    double e[3];

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

    // 返回向量的 x、y、z 坐标的成员函数
    double x() const { return e[0]; }
    double y() const { return e[1]; }
    double z() const { return e[2]; }

    // 重载一元负运算符，返回当前向量的负向量
    vec3 operator-() const { return vec3(-e[0], -e[1], -e[2]); }

    // 重载下标运算符，允许通过下标访问向量的各个坐标分量
    // 返回索引i处元素的值，但不允许修改vec3对象。
    double operator[](int i) const { return e[i]; }
    // 可以通过下标修改向量的元素
    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];
    }
    static vec3 random()
    {
        return vec3(random_double(), random_double(), random_double());
    }
    static vec3 random(double min, double max)
    {
        return vec3(random_double(min, max), random_double(min, max), random_double(min, max));
    }
    bool near_zero() const
    {
        // Return true if the vector is close to zero in all dimensions.
        auto s = 1e-8;
        return (fabs(e[0]) < s) && (fabs(e[1]) < s) && (fabs(e[2]) < s);
    }
};
// point3 is just an alias for vec3, but useful for geometric clarity in the code.
using point3 = vec3;

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();
}
inline vec3 random_in_unit_sphere()
{
    while (true)
    {
        auto p = vec3::random(-1, 1);
        if (p.length_squared() < 1)
            return p;
    }
}
inline vec3 random_unit_vector()
{
    return unit_vector(random_in_unit_sphere());
}

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

inline vec3 random_on_hemisphere(const vec3& normal)
{
    vec3 on_unit_sphere = random_unit_vector();
    if (dot(on_unit_sphere, normal) > 0.0) // In the same hemisphere as the normal
        return on_unit_sphere;
    else
        return -on_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)
{
    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;
}