#include <iostream>
#include <string>
#include <math.h>

// define vector

class PhysicsVector {
public:
  PhysicsVector(std::string name,double x,double y,double z);
  void printVector();
  std::string name_out() {return name;};
  double x_out() {return x;};
  double y_out() {return y;};
  double z_out() {return z;};
  double magnitude();
  double direction_r();
  double direction_d();
private:
  std::string name;
  double x;
  double y;
  double z;
};

PhysicsVector::PhysicsVector(std::string name1 ,double x1,double y1,double z1)
  :name{name1},x{x1},y{y1},z{z1}
{
}

void PhysicsVector::printVector()
{
  std::cout << name << " = " << x << " i + " << y << " j + " << z << " k\n";  
}

double PhysicsVector::magnitude()
{
  return sqrt((x * x) + (y * y) +  (z * z));
}

double PhysicsVector::direction_r()
{
  return atan2(y,x);
}

double PhysicsVector::direction_d()
{
  return atan2(y,x) * 90.0 / asin(1.0);
}


PhysicsVector *addVectors(std::string name1, PhysicsVector *a,PhysicsVector *b)
{
  PhysicsVector *ret = new PhysicsVector(name1,a->x_out() + b->x_out(),a->y_out() + b->y_out(),a->z_out() + b->z_out());
  return ret;
}

PhysicsVector *subtractVectors(std::string name1, PhysicsVector *a,PhysicsVector *b)
{
  PhysicsVector *ret = new PhysicsVector(name1,a->x_out() - b->x_out(),a->y_out() - b->y_out(),a->z_out() - b->z_out());
  return ret;
}


double dotVectors(PhysicsVector *a,PhysicsVector *b)
{
  double ret;
  
  ret = a->x_out() * b->x_out() + a->y_out() * b->y_out() + a->z_out() * b->z_out();

  return ret;
}

PhysicsVector *crossVectors(std::string name1, PhysicsVector *a,PhysicsVector *b)
{
  PhysicsVector *ret = new PhysicsVector(name1, a->y_out() * b->z_out() - b->y_out() * a->z_out(), - (a->x_out() * b->z_out() - a->z_out() * b->x_out()), a->x_out() * b->y_out() - a->y_out() * b->x_out());
  return ret;
}



void print_magnitude(PhysicsVector *a)
{
  std::cout << "The magnitude of " << a->name_out() << " is " << a->magnitude() << "\n";
}

void print_dotVectors(PhysicsVector *a, PhysicsVector *b)
{
  std::cout << "The dot of " << a->name_out() << " and " << b->name_out() << " is " << dotVectors(a,b) << "\n";
}

void print_crossVectors_and_delete(std::string str, PhysicsVector *a, PhysicsVector *b)
{
  std::cout << "The cross of " << a->name_out() << " and " << b->name_out() << " is:\n";
  PhysicsVector *c = crossVectors(str,a,b);
  c->printVector();
  delete c;
}
void print_crossVectors_without_delete(std::string str, PhysicsVector *a, PhysicsVector *b)
{
  std::cout << "The cross of " << a->name_out() << " and " << b->name_out() << " is:\n";
  PhysicsVector *c = crossVectors(str,a,b);
  c->printVector();
}

void print_direction_r(PhysicsVector *a)
{
  std::cout << "The direction of " << a->name_out() << " in radians is " << a->direction_r() << "\n";
}

void print_direction_d(PhysicsVector *a)
{
  std::cout << "The direction of " << a->name_out() << " in degrees is " << a->direction_d() << "\n";
}

void prob_05();

int main()
{
  std::cout << "c++ output chapter 2\n";
   
  prob_05();
}

void prob_05()
{
  std::cout << "Problem 5\n";
  PhysicsVector *a = new PhysicsVector("a",4.0,-3.0,0.0);
  PhysicsVector *b = new PhysicsVector("b",6.0,8.0,0.0);
  PhysicsVector *c = addVectors("c",a,b);
  PhysicsVector *d = subtractVectors("d",b,a);
  PhysicsVector *e = subtractVectors("e",a,b);
  PhysicsVector f("f",2.0,-3.0,7.0);
  PhysicsVector g("g",12.0,45.0,-8.0);
  PhysicsVector h("h",-5.0,-3.0, 42.0);


  a->printVector();
  b->printVector();
  c->printVector();
  d->printVector();
  e->printVector();
  print_magnitude(a);
  print_magnitude(b);
  print_magnitude(c);
  print_magnitude(d);
  print_magnitude(e);
  print_direction_r(a);
  print_direction_r(b);
  print_direction_r(c);
  print_direction_r(d);
  print_direction_r(e);
  print_direction_d(a);
  print_direction_d(b);
  print_direction_d(c);
  print_direction_d(d);
  print_direction_d(e);



  print_dotVectors(a,a);
  print_dotVectors(a,b);
  print_dotVectors(b,a);
  print_dotVectors(a,c);
  print_dotVectors(d,a);
  print_dotVectors(a,e);
  print_dotVectors(e,a);
  
  print_crossVectors_and_delete("axa",a,a);
  print_crossVectors_and_delete("axb",a,b);
  print_crossVectors_and_delete("bxa",b,a);
  print_crossVectors_and_delete("axc",a,c);
  print_crossVectors_and_delete("dxa",d,a);
  print_crossVectors_and_delete("axe",a,e);
  print_crossVectors_and_delete("exa",e,a);

  print_crossVectors_without_delete("fxg",&f,&g);
  print_crossVectors_without_delete("fxh",&f,&h);
  print_crossVectors_without_delete("gxh",&g,&h);
  print_crossVectors_without_delete("gxf",&g,&f);
  print_crossVectors_without_delete("hxf",&h,&f);
  print_crossVectors_without_delete("hxg",&h,&g);

  delete a;
  delete b;
  delete c;
  delete d;
  delete e;

}