《Ray Tracing in One Weekend》全内反射光线追踪问题求助

我正在跟随《Ray Tracing in One Weekend》一书学习，在11.3节全内反射（Total internal reflection）部分遇到问题。生成的图像如下：

以下是球体相交检测代码，返回std::optional<Intersection>实例或std::nullopt：

std::optional<Intersection> Sphere::intersect(const Ray& r, double tMin, double tMax) const {
    vec o_c = this->center - r.origin();
    auto a = r.direction().length_squared() () 
    auto b = dot(r.direction(), o_c);
    auto c = o_c.length_squared() - radius * radius;
    
    auto d = b * b - a * c;
    // at^2 + tb + c = 0 not real solution
    if (d < 0) {
        return std::nullopt;
    }
    // Verify root in [tMin, tMax]   
    double dSqrt = std::sqrt(d);
    double root = (b - dSqrt) / a;
    if (root < tMin || root > tMax) {
        root = (b + dSqrt) / a;
        if (root < tMin || root > tMax) return std::nullopt;
    }
    Intersection i;
    i.t = root;
    i.point = r(i.t);
    i.normal = unit_vector(i.point - center);
    
    i.material = material;
    return i; 
};

以下是折射计算代码：

inline vec refraction(const vec& v, const vec& normal, double refraction_index) {
    vec rparal{ .0, .0, .0 };
    vec rperp{ .0, .0, .0 };
    bool front_face = (dot(v, normal) < 0);
    double ri = front_face ? 1.0 / refraction_index : refraction_index;
    vec outward_normal = front_face ? normal : -normal;
    
    double cos_tita = fmin(dot(-v, outward_normal ), 1.0);
    double sen_tita = sqrt(1 - cos_tita * cos_tita);
    
    if (ri * sen_tita > 1) {
        return reflect(v, outward_normal);
    }
    
    rperp = ri * (v + (dot(-v, outward_normal) * outward_normal)); 
    rparal = (-sqrt(abs(1 - rperp.length_squared()))) * outward_normal;
    return rparal + rperp;
};

以下是color_ray代码：

color color_ray(const Ray& r, int deep, const Geometry& g) {
    if (deep <= 0)
        return color(0, 0, 0);
    auto i = g.intersect(r, 0.001, infinity);
    if (i) {
        color intensity; 
        // Check if the material is reflective
        if (i->material->reflective) {
            vec reflectedVector = reflect(unit_vector(r.direction()), i->normal) + 
            (i->material->coef_Reflective * vec::random_Unit_vector());
            Ray reflected_Ray = Ray(i->point, reflectedVector);
            intensity = i->material->DifuseColor * color_ray(reflected_Ray, deep - 1, g); 
        // Check if the material is refractive
        } else if (i->material->refractive) {
           vec refractedVector = refraction(unit_vector(r.direction()), i->normal, 
                                 i->material>refraction_index);
       Ray refracted_Ray = Ray(i->point, refractedVector);
           intensity = color_ray(refracted_Ray , deep - 1, g);
        } else {
            intensity = i->material->DifuseColor * color_ray(Ray(i->point, i->normal + 
                    vec::randomUnitVector()), deep - 1, g);
        }
        return intensity;
    }
    
    vec unit_direction = unit_vector(r.direction());
    auto a = 0.5 * (unit_direction .y() + 1);
    return (1.0 - a) * color(1.0, 1.0, 1.0) + a * color(0.5, 0.7, 1.0);
};

预期得到的图像如下：

如需更多信息请告知，感谢帮助 :)

内容的提问来源于stack exchange，提问作者Lautaro10263