bool hit_sphere(const vec3& center, float radius, const ray& r){
vec3 oc = r.origin() - center;
float a = dot(r.direction(), r.direction());
float b = 2.0 * dot(oc, r.direction());
float c = dot(oc,oc) - radius*radius;
float discriminant = b*b - 4*a*c;
return (discriminant>0);
}