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/*
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 *
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