/*vector3.h
3D vector algebra. Requires the GL/glut library
CS537
George Kamberov


  */
#include<iostream.h>
#include<GL/glut.h>

class vector3
{                                                                       
	public:                                                             //faster then ussing access functions

	double c[3];                                                        //components array

	/*																constructors                                     */


	vector3(void);														 //creates a zero vector
	vector3(double, double, double);                          //explicit defn
	vector3( double* array);                                       //converts an array into a  vector

	/*                                                            vector agebra                                         */

	friend vector3 operator* (double s, const vector3 vector);               //scaling
	friend vector3 cross_prod(const vector3 u, const vector3 v);             //cross product
	friend double dot_prod(const vector3 u, const vector3 v);                //dot product
	friend double norm(const vector3 u);                                     //returns |u|   
	friend vector3 normalize(const vector3 u);                               //returns u/|u|
	friend vector3 operator- (const vector3 u, const vector3 v);             //retruns u-v

	/*                                                             comparisons                                               */
   	friend bool operator== (const vector3 u, const vector3 v);      
	friend bool operator!=  (const vector3 u, const vector3 v);   
	friend bool colinear(const vector3 u, const vector3 v);            

	/*                                                              Misc                                                             */
    friend ostream& operator<< (ostream& co, const vector3& v);


 
};

class frame
{
  
  public:  
	vector3 u;
	vector3 v;
	vector3 n;


	/* constructors */

	frame(vector3 n, vector3 up);                  //builds a camera frame if n x up != 0 exits otherwise.

	/*    tests */

	friend double det(frame f);
	friend void error_message(frame f);
	friend bool right_oriented(frame f);
	friend bool onb(frame f);
};