#include <stdio.h>
#include <math.h>
#include <stdlib.h>

// define vector
 
typedef struct vec {
  double x;
  double y;
  double z;
} vector;

// function prototype
double cvt_feet_to_meters(double feet);
double cvt_meters_to_feet(double meters);
void print_vector(char *str , vector *x);
void print_dot(char *str,vector *a,vector *b);
double magnitude(vector *x);
void print_vector_magnitude(char *str,vector *x);
double direction_2d(vector *x);
void print_vector_direction_2d(char *str,vector *x);
void prob_05();
void prob_02();
void prob_03();
double dot(vector *x, vector *y);
vector *cross(vector *x, vector *y);
void print_cross_and_free(char *str , vector *a,vector *b);

int main()
{
  printf("c output chapter 2\n"); 
  prob_05();
}

void prob_05()
{
  vector a;
  vector b;
  vector c;   // a + b
  vector d;   // b - a
  vector e;   // a - b
  vector f;
  vector g;
  vector h;

  a.x = 4.0;
  a.y = -3.0;
  a.z = 0.0;

  b.x = 6.0;
  b.y = 8.0;
  b.z = 0.0;

  printf("Problem 5\n");

  c.x = a.x + b.x;
  c.y = a.y + b.y;
  c.z = a.z + b.z;

  d.x = b.x - a.x;
  d.y = b.y - a.y;
  d.z = b.z - a.z;

  e.x = a.x - b.x;
  e.y = a.y - b.y;
  e.z = a.z - b.z;

  f.x = 2.0;
  f.y = -3.0;
  f.z = 7.0;

  g.x = 12.0;
  g.y = 45.0;
  g.z = -8.0;

  h.x = -5.0;
  h.y = -3.0;
  h.z = 42.0;

  print_vector("a",&a);
  print_vector("b",&b);
  print_vector("c",&c);
  print_vector("d",&d);
  print_vector("e",&e);

  print_dot("a.a",&a,&a);
  print_dot("a.b",&a,&b);
  print_dot("b.a",&b,&a);
  print_dot("a.c",&a,&c);
  print_dot("d.a",&d,&a);
  print_dot("a.e",&a,&e);
  print_dot("e.a",&e,&a);

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

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


}


double dot(vector *a, vector *b)
{
  double ret;
  ret = a->x * b->x + a->y * b->y + a->z * b->z;
  return ret;
}

void print_dot(char* str,vector *a, vector *b)
{
  printf("dot %s = %8.4f\n",str,dot(a,b));
}

vector *cross(vector *a, vector *b)
{
  vector *ret;
  ret = (vector *) malloc(sizeof(vector));
  ret->x = a->y * b->z - b->y * a->z;
  ret->y = -( a->x * b->z - b->x * a->z);
  ret->z = a->x * b->y - b->x * a->y;
  return ret;
}

void print_cross_and_free(char *str , vector *a,vector *b)
{
  vector *it;

  it = cross(a,b);
  printf("cross %s = %8.4f i + %8.4f j + %8.4f k\n",str,it->x,it->y,it->z);
  free(it);
}

void print_vector(char *str , vector *x)
{
  printf("vector %s = %8.4f i + %8.4f j + %8.4f k\n",str,x->x,x->y,x->z);
  print_vector_magnitude(str,x);
  print_vector_direction_2d(str,x);

}

void print_vector_magnitude(char *str,vector *x)
{
  printf("vector %s's magnitude is %8.4f\n",str,magnitude(x));
}

void print_vector_direction_2d(char *str,vector *x)
{
  printf("vector %s's direction (radians) is %8.4f\n",str,direction_2d(x));
  printf("vector %s's direction (degrees) is %8.4f\n",str,direction_2d(x) * 45.0 / atan(1.0));
}

double magnitude(vector *x)
{
  return sqrt(x->x * x->x + x->y * x->y + x->z * x->z);
}

double direction_2d(vector *x)
{
  return atan2(x->y, x->x);
}