/**************************************************************************
    
  algebra3.cpp, algebra3.h -  C++ Vector and Matrix Algebra routines           

  There are three vector classes and two matrix classes: vec2, vec3,
  vec4, mat3, and mat4.

  All the standard arithmetic operations are defined, with '*'
  for dot product of two vectors and multiplication of two matrices,
  and '^' for cross product of two vectors.

  Additional functions include length(), normalize(), homogenize for
  vectors, and print(), set(), apply() for all classes.

  There is a function transpose() for matrices, but note that it 
  does not actually change the matrix, 

  When multiplied with a matrix, a vector is treated as a row vector
  if it precedes the matrix (v*M), and as a column vector if it
  follows the matrix (M*v).

  Matrices are stored in row-major form.

  A vector of one dimension (2d, 3d, or 4d) can be cast to a vector
  of a higher or lower dimension.  If casting to a higher dimension,
  the new component is set by default to 1.0, unless a value is
  specified:
     vec3 a(1.0, 2.0, 3.0 );
     vec4 b( a, 4.0 );       // now b == {1.0, 2.0, 3.0, 4.0};
  When casting to a lower dimension, the vector is homogenized in
  the lower dimension.  E.g., if a 4d {X,Y,Z,W} is cast to 3d, the
  resulting vector is {X/W, Y/W, Z/W}.  It is up to the user to 
  insure the fourth component is not zero before casting.

  There are also the following function for building matrices:
     identity2D(), translation2D(), rotation2D(),
     scaling2D(),  identity3D(),    translation3D(),
     rotation3D(), rotation3Drad(),  scaling3D(),
     perspective3D()

  NOTE: When compiling for Windows, include this file first, to avoid
        certain name conflicts
 
  ---------------------------------------------------------------------
  
  Author: Jean-Francois DOUEg                   
  Revised: Paul Rademacher                                      
  Version 3.2 - Feb 1998
                                
**************************************************************************/

#ifndef _ALGEBRA3_H_
#define _ALGEBRA3_H_

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

// this line defines a new type: pointer to a function which returns a
// float and takes as argument a float
typedef float (*V_FCT_PTR) (float);

// min-max macros
#ifndef MIN
#define MIN(A,B) ((A) < (B) ? (A) : (B))
#define MAX(A,B) ((A) > (B) ? (A) : (B))
#endif

//#include <stream.h>
// error handling macro
//#define VEC_ERROR(E) { cerr << E; exit(1); }
/*#define << 
#define >>*/

#ifdef VEC_ERROR_FATAL
# ifndef VEC_ERROR
#  define VEC_ERROR(E) { printf( "VERROR %s\n", E ); exit(1); }
# endif
#else
# ifndef VEC_ERROR
#  define VEC_ERROR(E) { printf( "VERROR %s\n", E ); }
# endif
#endif

class vec2;
class vec3;
class vec4;
class mat3;
class mat4;

/*#ifndef X
enum {X,Y,Z,W};
#endif
*/

/*#ifndef R
enum {R,G,B,ALPHA};
#endif
*/

#ifndef M_PI
#define M_PI 3.141592654
#endif


enum { VX, VY, VZ, VW };	// axes
enum { PA, PB, PC, PD };	// planes
enum { RED, GREEN, BLUE, ALPHA };	// colors
enum { KA, KD, KS, ES };	// phong coefficients

/****************************************************************
*                                                               *
*               2D Vector                                       *
*                                                               *
****************************************************************/

class vec2 {
      protected:

	float n[2];

      public:

	// Constructors

	vec2(void);
	vec2(const float x, const float y);
	vec2(const float d);
	vec2(const vec2 & v);	// copy constructor
	vec2(const vec3 & v);	// cast v3 to v2
	vec2(const vec3 & v, int dropAxis);	// cast v3 to v2

	// Assignment operators

	vec2 & operator =(const vec2 & v);	// assignment of a vec2
	vec2 & operator +=(const vec2 & v);	// incrementation by a vec2
	vec2 & operator -=(const vec2 & v);	// decrementation by a vec2
	vec2 & operator *=(const float d);	// multiplication by a constant
	vec2 & operator /=(const float d);	// division by a constant
	float &operator [] (int i);	// indexing

	// special functions

	float length(void);	// length of a vec2
	float length2(void);	// squared length of a vec2
	vec2 & normalize(void);	// normalize a vec2
	vec2 & apply(V_FCT_PTR fct);	// apply a func. to each component
	void set(float x, float y);	// set vector

	// friends

	friend vec2 operator -(const vec2 & v);	// -v1
	friend vec2 operator +(const vec2 & a, const vec2 & b);	// v1 + v2
	friend vec2 operator -(const vec2 & a, const vec2 & b);	// v1 - v2
	friend vec2 operator *(const vec2 & a, const float d);	// v1 * 3.0
	friend vec2 operator *(const float d, const vec2 & a);	// 3.0 * v1
	friend vec2 operator *(const mat3 & a, const vec2 & v);	// M . v
	friend vec2 operator *(const vec2 & v, mat3 & a);	// v . M
	friend float operator *(const vec2 & a, const vec2 & b);	// dot product
	friend vec2 operator /(const vec2 & a, const float d);	// v1 / 3.0
	friend vec3 operator ^(const vec2 & a, const vec2 & b);	// cross product
	friend int operator ==(const vec2 & a, const vec2 & b);	// v1 == v2 ?
	friend int operator !=(const vec2 & a, const vec2 & b);	// v1 != v2 ?
	//friend ostream& operator << (ostream& s, vec2& v);       // output to stream
	//friend istream& operator >> (istream& s, vec2& v);       // input from strm.
	friend void swap(vec2 & a, vec2 & b);	// swap v1 & v2
	friend vec2 min_vec(const vec2 & a, const vec2 & b);	// min(v1, v2)
	friend vec2 max_vec(const vec2 & a, const vec2 & b);	// max(v1, v2)
	friend vec2 prod(const vec2 & a, const vec2 & b);	// term by term *

	// necessary friend declarations

	friend class vec3;
};

/****************************************************************
*                                                               *
*               3D Vector                                       *
*                                                               *
****************************************************************/

class vec3 {
      protected:

	float n[3];

      public:

	// Constructors

	vec3(void);
	vec3(const float x, const float y, const float z);
	vec3(const float d);
	vec3(const vec3 & v);	// copy constructor
	vec3(const vec2 & v);	// cast v2 to v3
	vec3(const vec2 & v, float d);	// cast v2 to v3
	vec3(const vec4 & v);	// cast v4 to v3
	vec3(const vec4 & v, int dropAxis);	// cast v4 to v3

	// Assignment operators

	vec3 & operator =(const vec3 & v);	// assignment of a vec3
	vec3 & operator +=(const vec3 & v);	// incrementation by a vec3
	vec3 & operator -=(const vec3 & v);	// decrementation by a vec3
	vec3 & operator *=(const float d);	// multiplication by a constant
	vec3 & operator /=(const float d);	// division by a constant
	float &operator [] (int i);	// indexing

	// special functions

	float length(void);	// length of a vec3
	float length2(void);	// squared length of a vec3
	vec3 & normalize(void);	// normalize a vec3
	vec3 & homogenize(void);	// homogenize (div by Z)
	vec3 & apply(V_FCT_PTR fct);	// apply a func. to each component
	void set(float x, float y, float z);	// set vector
	void print(FILE * file, const char *name);	// print vector to a file

	// friends

	friend vec3 operator -(const vec3 & v);	// -v1
	friend vec3 operator +(const vec3 & a, const vec3 & b);	// v1 + v2
	friend vec3 operator -(const vec3 & a, const vec3 & b);	// v1 - v2
	friend vec3 operator *(const vec3 & a, const float d);	// v1 * 3.0
	friend vec3 operator *(const float d, const vec3 & a);	// 3.0 * v1
	friend vec3 operator *(const mat4 & a, const vec3 & v);	// M . v
	friend vec3 operator *(const vec3 & v, mat4 & a);	// v . M
	friend float operator *(const vec3 & a, const vec3 & b);	// dot product
	friend vec3 operator /(const vec3 & a, const float d);	// v1 / 3.0
	friend vec3 operator ^(const vec3 & a, const vec3 & b);	// cross product
	friend int operator ==(const vec3 & a, const vec3 & b);	// v1 == v2 ?
	friend int operator !=(const vec3 & a, const vec3 & b);	// v1 != v2 ?
	//friend ostream& operator << (ostream& s, vec3& v);       // output to stream
	//friend istream& operator >> (istream& s, vec3& v);       // input from strm.
	friend void swap(vec3 & a, vec3 & b);	// swap v1 & v2
	friend vec3 min_vec(const vec3 & a, const vec3 & b);	// min(v1, v2)
	friend vec3 max_vec(const vec3 & a, const vec3 & b);	// max(v1, v2)
	friend vec3 prod(const vec3 & a, const vec3 & b);	// term by term *

	// necessary friend declarations

	friend class vec2;
	friend class vec4;
	friend class mat3;
	friend vec2 operator *(const mat3 & a, const vec2 & v);	// linear transform
	friend vec3 operator *(const mat3 & a, const vec3 & v);	// linear transform
	friend mat3 operator *(mat3 & a, mat3 & b);	// matrix 3 product

};

/****************************************************************
*                                                               *
*               4D Vector                                       *
*                                                               *
****************************************************************/

class vec4 {
      protected:

	float n[4];

      public:

	// Constructors

	vec4(void);
	vec4(const float x, const float y, const float z, const float w);
	vec4(const float d);
	vec4(const vec4 & v);	// copy constructor
	vec4(const vec3 & v);	// cast vec3 to vec4
	vec4(const vec3 & v, const float d);	// cast vec3 to vec4

	// Assignment operators

	vec4 & operator =(const vec4 & v);	// assignment of a vec4
	vec4 & operator +=(const vec4 & v);	// incrementation by a vec4
	vec4 & operator -=(const vec4 & v);	// decrementation by a vec4
	vec4 & operator *=(const float d);	// multiplication by a constant
	vec4 & operator /=(const float d);	// division by a constant
	float &operator [] (int i);	// indexing

	// special functions

	float length(void);	// length of a vec4
	float length2(void);	// squared length of a vec4
	vec4 & normalize(void);	// normalize a vec4
	vec4 & apply(V_FCT_PTR fct);	// apply a func. to each component
	vec4 & homogenize(void);
	void print(FILE * file, const char *name);	// print vector to a file
	void set(float x, float y, float z, float a);

	// friends

	friend vec4 operator -(const vec4 & v);	// -v1
	friend vec4 operator +(const vec4 & a, const vec4 & b);	// v1 + v2
	friend vec4 operator -(const vec4 & a, const vec4 & b);	// v1 - v2
	friend vec4 operator *(const vec4 & a, const float d);	// v1 * 3.0
	friend vec4 operator *(const float d, const vec4 & a);	// 3.0 * v1
	friend vec4 operator *(const mat4 & a, const vec4 & v);	// M . v
	friend vec4 operator *(const vec4 & v, mat4 & a);	// v . M
	friend float operator *(const vec4 & a, const vec4 & b);	// dot product
	friend vec4 operator /(const vec4 & a, const float d);	// v1 / 3.0
	friend int operator ==(const vec4 & a, const vec4 & b);	// v1 == v2 ?
	friend int operator !=(const vec4 & a, const vec4 & b);	// v1 != v2 ?
	//friend ostream& operator << (ostream& s, vec4& v);       // output to stream
	//friend istream& operator >> (istream& s, vec4& v);       // input from strm.
	friend void swap(vec4 & a, vec4 & b);	// swap v1 & v2
	friend vec4 min_vec(const vec4 & a, const vec4 & b);	// min(v1, v2)
	friend vec4 max_vec(const vec4 & a, const vec4 & b);	// max(v1, v2)
	friend vec4 prod(const vec4 & a, const vec4 & b);	// term by term *

	// necessary friend declarations

	friend class vec3;
	friend class mat4;
	friend vec3 operator *(const mat4 & a, const vec3 & v);	// linear transform
	friend mat4 operator *(mat4 & a, mat4 & b);	// matrix 4 product
};

/****************************************************************
*                                                               *
*              3x3 Matrix                                       *
*                                                               *
****************************************************************/

class mat3 {
      protected:

	vec3 v[3];

      public:

	// Constructors

	mat3(void);
	mat3(const vec3 & v0, const vec3 & v1, const vec3 & v2);
	mat3(const float d);
	mat3(const mat3 & m);

	// Assignment operators

	mat3 & operator   =(const mat3 & m);	// assignment of a mat3
	mat3 & operator +=(const mat3 & m);	// incrementation by a mat3
	mat3 & operator -=(const mat3 & m);	// decrementation by a mat3
	mat3 & operator *=(const float d);	// multiplication by a constant
	mat3 & operator /=(const float d);	// division by a constant
	vec3 & operator [] (int i);	// indexing

	// special functions

	mat3 transpose(void);	// transpose
	mat3 inverse(void);	// inverse
	mat3 & apply(V_FCT_PTR fct);	// apply a func. to each element
	void print(FILE * file, const char *name);	// print matrix to a file
	void set(const vec3 & v0, const vec3 & v1, const vec3 & v2);


	// friends

	friend mat3 operator -(const mat3 & a);	// -m1
	friend mat3 operator +(const mat3 & a, const mat3 & b);	// m1 + m2
	friend mat3 operator -(const mat3 & a, const mat3 & b);	// m1 - m2
	friend mat3 operator *(mat3 & a, mat3 & b);	// m1 * m2
	friend mat3 operator *(const mat3 & a, const float d);	// m1 * 3.0
	friend mat3 operator *(const float d, const mat3 & a);	// 3.0 * m1
	friend mat3 operator /(const mat3 & a, const float d);	// m1 / 3.0
	friend int operator ==(const mat3 & a, const mat3 & b);	// m1 == m2 ?
	friend int operator !=(const mat3 & a, const mat3 & b);	// m1 != m2 ?
	//friend ostream& operator << (ostream& s, mat3& m);       // output to stream
	//friend istream& operator >> (istream& s, mat3& m);       // input from strm.
	friend void swap(mat3 & a, mat3 & b);	// swap m1 & m2

	// necessary friend declarations

	friend vec3 operator *(const mat3 & a, const vec3 & v);	// linear transform
	friend vec2 operator *(const mat3 & a, const vec2 & v);	// linear transform
};

/****************************************************************
*                                                               *
*              4x4 Matrix                                       *
*                                                               *
****************************************************************/

class mat4 {
      protected:
      public:

	vec4 v[4];


	// Constructors

	mat4(void);
	mat4(const vec4 & v0, const vec4 & v1, const vec4 & v2,
	      const vec4 & v3);
	mat4(const float d);
	mat4(const mat4 & m);
	mat4(const float a00, const float a01, const float a02,
	      const float a03, const float a10, const float a11,
	      const float a12, const float a13, const float a20,
	      const float a21, const float a22, const float a23,
	      const float a30, const float a31, const float a32,
	      const float a33);


	// Assignment operators

	mat4 & operator   =(const mat4 & m);	// assignment of a mat4
	mat4 & operator +=(const mat4 & m);	// incrementation by a mat4
	mat4 & operator -=(const mat4 & m);	// decrementation by a mat4
	mat4 & operator *=(const float d);	// multiplication by a constant
	mat4 & operator /=(const float d);	// division by a constant
	vec4 & operator [] (int i);	// indexing

	// special functions

	mat4 transpose(void);	// transpose
	mat4 inverse(void);	// inverse
	mat4 & apply(V_FCT_PTR fct);	// apply a func. to each element
	void print(FILE * file, const char *name);	// print matrix to a file
	void swap_rows(int i, int j);	// swap rows i and j
	void swap_cols(int i, int j);	// swap cols i and j

	// friends

	friend mat4 operator -(const mat4 & a);	// -m1
	friend mat4 operator +(const mat4 & a, const mat4 & b);	// m1 + m2
	friend mat4 operator -(const mat4 & a, const mat4 & b);	// m1 - m2
	friend mat4 operator *(mat4 & a, mat4 & b);	// m1 * m2
	friend mat4 operator *(const mat4 & a, const float d);	// m1 * 4.0
	friend mat4 operator *(const float d, const mat4 & a);	// 4.0 * m1
	friend mat4 operator /(const mat4 & a, const float d);	// m1 / 3.0
	friend int operator ==(const mat4 & a, const mat4 & b);	// m1 == m2 ?
	friend int operator !=(const mat4 & a, const mat4 & b);	// m1 != m2 ?
	//friend ostream& operator << (ostream& s, mat4& m);       // output to stream
	//friend istream& operator >> (istream& s, mat4& m);       // input from strm.
	friend void swap(mat4 & a, mat4 & b);	// swap m1 & m2

	// necessary friend declarations

	friend vec4 operator *(const mat4 & a, const vec4 & v);	// linear transform
	//friend vec4 operator * (const vec4& v, const mat4& a);       // linear transform
	friend vec3 operator *(const mat4 & a, const vec3 & v);	// linear transform
	friend vec3 operator *(const vec3 & v, const mat4 & a);	// linear transform
};

/****************************************************************
*                                                               *
*          2D functions and 3D functions                        *
*                                                               *
****************************************************************/

mat3 identity2D(void);		// identity 2D
mat3 translation2D(vec2 & v);	// translation 2D
mat3 rotation2D(vec2 & Center, const float angleDeg);	// rotation 2D
mat3 scaling2D(vec2 & scaleVector);	// scaling 2D
mat4 identity3D(void);		// identity 3D
mat4 translation3D(vec3 & v);	// translation 3D
mat4 rotation3D(vec3 & Axis, const float angleDeg);	// rotation 3D
mat4 rotation3Drad(vec3 & Axis, const float angleRad);	// rotation 3D
mat4 scaling3D(vec3 & scaleVector);	// scaling 3D
mat4 perspective3D(const float d);	// perspective 3D


vec3 operator *(const vec3 & v, mat3 & a);
vec2 operator *(const vec2 & v, mat3 & a);
vec3 operator *(const vec3 & v, mat4 & a);
vec4 operator *(const vec4 & v, mat4 & a);


#endif
