path: root/tests/box2d/glui/algebra3.h

/*

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

  GLUI User Interface Toolkit (LGPL)
  Copyright (c) 1998 Paul Rademacher

  WWW:    http://sourceforge.net/projects/glui/
  Forums: http://sourceforge.net/forum/?group_id=92496

  This library is free software; you can redistribute it and/or
  modify it under the terms of the GNU Lesser General Public
  License as published by the Free Software Foundation; either
  version 2.1 of the License, or (at your option) any later version.

  This library is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  Lesser General Public License for more details.

  You should have received a copy of the GNU Lesser General Public
  License along with this library; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

*/

/**************************************************************************
    
  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
  Revised: Nigel Stewart (GLUI Code Cleaning)
  
**************************************************************************/

#ifndef GLUI_ALGEBRA3_H
#define GLUI_ALGEBRA3_H

#include <cmath>
#include <cstdio>
#include <cstdlib>

// 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);

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

#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
{
  friend class vec3;

protected:

  float n[2];

public:

  // Constructors

  vec2();
  vec2(float x, float y);
  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 *= (float d);    // multiplication by a constant
  vec2  &operator /= (float d);    // division by a constant

  // special functions

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

  float &operator [] (int i);         // indexing
  const float &operator [] (int i) const;   // indexing

  // 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, float d);          // v1 * 3.0
  friend vec2  operator *  (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, const mat3 &a);    // v . M
  friend float operator *  (const vec2 &a, const vec2 &b);    // dot product
  friend vec2  operator /  (const vec2 &a, 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 *
};

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

class vec3
{
  friend class vec2;
  friend class vec4;
  friend class mat3;

protected:

  float n[3];

public:

  // Constructors

  vec3();
  vec3(float x, float y, float z);
  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 *= (float d);      // multiplication by a constant
  vec3  &operator /= (float d);      // division by a constant

  // special functions

  float  length()  const;                     // length of a vec3
  float  length2() const;                     // squared length of a vec3
  vec3&  normalize();                         // normalize a vec3
  vec3&  homogenize();                        // 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) const; // print vector to a file


  float &operator [] (int i);       // indexing
  const float &operator [] (int i) const; // indexing

  // 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, float d);        // v1 * 3.0
  friend vec3  operator *  (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, const mat4 &a);  // v . M
  friend float operator *