vec3.h

#ifndef VEC3_H
#define VEC3_H

#include<cmath>
#include<iostream>
using std::sqrt;

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} { } //构造函数
       
       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);
       }  

    public:
       double e[3];
};

using point3=vec3;
using color=vec3;



inline std::ostream& operator<<(std::ostream &out,const vec3& v){
    return out<<v.e[0]<<" "<<v.e[1]<<" "<<v.e[2];
}
//四则运算
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/(const vec3& v, double t) {
	return (1 / t) * v;
}
//点乘
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];
}
//叉乘
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]);
}
//单位向量
inline vec3 unit_vector(const vec3& v) {
	return v / v.length();
}

inline vec3 random_in_unit_sphere(){
           while(true) {
               auto p = vec3::random(-1,1);
               //std::cerr<<p.x()<<std::endl;
               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) // In the same hemisphere as the normal
        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) {
    auto cos_theta = fmin(dot(-uv, n), 1.0);
    vec3 r_out_perp =  etai_over_etat * (uv + cos_theta*n);
    vec3 r_out_parallel = -sqrt(fabs(1.0 - r_out_perp.length_squared())) * n;
    return r_out_perp + 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;
    }
}

#endif