// This ensures that this file is included at most once
// in any program, as there may be multiple include
// statements.
#pragma once

#include <string>

// Class declaration
class Vector_3d;

  ///////////////////////////
 // Function declarations //
///////////////////////////

  //////
 // These query the arguments, but do not change them
//////

// Calculate the inner product of u and v.
double inner( Vector_3d const &u,
              Vector_3d const &v );

// Calculate the norm (length) of u.
double norm( Vector_3d const &u );

// Calculate u + v.
Vector_3d add( Vector_3d const &u,
               Vector_3d const &v );

// Calculate a*u for a scalar 'a'.
Vector_3d mul( double    const  a,
               Vector_3d const &u );

// Calculate u*a for a scalar 'a'.
Vector_3d mul( Vector_3d const &u,
               double    const  a );

// Calculate -u.
Vector_3d negate( Vector_3d const &u );

// Calculate u - v.
Vector_3d sub( Vector_3d const &u,
               Vector_3d const &v );

// Calculate (1/a)*u for a non-zero scalar 'a'.
Vector_3d div( Vector_3d const &u,
               double    const  a );

// Calculate the projection of u onto v.
Vector_3d proj( Vector_3d const &u,
                Vector_3d const &v );

// Calculate the cross product u x v.
Vector_3d cross( Vector_3d const &u,
                 Vector_3d const &v );

// Determine whether u and v are equal.
bool equal( Vector_3d const &u,
            Vector_3d const &v );

// Return a string representation of u.
std::string to_string( Vector_3d const &u );

  //////
 // These modify the first vector passed
//////

// Normalize u if it is not the zero vector.
void normalize( Vector_3d &u );

// Add v to u.
void add_to( Vector_3d       &u,
             Vector_3d const &v );

// Subtract v from u.
void sub_from( Vector_3d       &u,
               Vector_3d const &v );

// Multiply u by the scalar a.
void mul_by( Vector_3d   &u,
             double const a );

// Divide u by the non-zero scalar a.
void div_by( Vector_3d   &u,
             double const a );

  ////////////////////////
 // Vector_3d class    //
////////////////////////

// Store the three components of a 3-dimensional vector.
class Vector_3d {
  public:
    double x_;
    double y_;
    double z_;
};