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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 * (const vec3 &a, const vec3 &b); // dot product
friend vec3 operator / (const vec3 &a, 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 vec2 operator * (const mat3 &a, const vec2 &v); // linear transform
friend vec3 operator * (const mat3 &a, const vec3 &v); // linear transform
friend mat3 operator * (const mat3 &a, const mat3 &b); // matrix 3 product
};
/****************************************************************
* *
* 4D Vector *
* *
****************************************************************/
class vec4
{
friend class vec3;
friend class mat4;
protected:
float n[4];
public:
// Constructors
vec4();
vec4(float x, float y, float z, float w);
vec4(const vec4 &v); // copy constructor
vec4(const vec3 &v); // cast vec3 to vec4
vec4(const vec3 &v, 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 *= (float d); // multiplication by a constant
vec4 &operator /= (float d); // division by a constant
// special functions
float length() const; // length of a vec4
float length2() const; // squared length of a vec4
vec4 &normalize(); // normalize a vec4
vec4 &apply(V_FCT_PTR fct); // apply a func. to each component
vec4 &homogenize();
void print(FILE *file, const char *name) const; // print vector to a file
void set(float x, float y, float z, float a);
float &operator [] (int i); // indexing
const float &operator [] (int i) const; // indexing
// 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, float d); // v1 * 3.0
friend vec4 operator * (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, const mat4 &a); // v . M
friend float operator * (const vec4 &a, const vec4 &b); // dot product
friend vec4 operator / (const vec4 &a, 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 vec3 operator * (const mat4 &a, const vec3 &v); // linear transform
friend mat4 operator * (const mat4 &a, const mat4 &b); // matrix 4 product
};
/****************************************************************
* *
* 3x3 Matrix *
* *
****************************************************************/
class mat3
{
protected:
vec3 v[3];
public:
// Constructors
mat3();
mat3(const vec3 &v0, const vec3 &v1, const vec3 &v2);
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 *= (float d); // multiplication by a constant
mat3 &operator /= (float d); // division by a constant
// special functions
mat3 transpose() const; // transpose
mat3 inverse() const; // inverse
mat3 &apply(V_FCT_PTR fct); // apply a func. to each element
void print(FILE *file, const char *name ) const; // print matrix to a file
void set(const vec3 &v0, const vec3 &v1, const vec3 &v2);
vec3 &operator [] (int i); // indexing
const vec3 &operator [] (int i) const; // indexing
// 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 * (const mat3 &a, const mat3 &b); // m1 * m2
friend mat3 operator * (const mat3 &a, float d); // m1 * 3.0
friend mat3 operator * (float d, const mat3 &a); // 3.0 * m1
friend mat3 operator / (const mat3 &a, 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:
vec4 v[4];
public:
// Constructors
mat4();
mat4(const vec4 &v0, const vec4 &v1, const vec4 &v2, const vec4 &v3);
mat4(const mat4 &m);
mat4(float a00, float a01, float a02, float a03,
float a10, float a11, float a12, float a13,
float a20, float a21, float a22, float a23,
float a30, float a31, float a32, 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 *= (float d); // multiplication by a constant
mat4 &operator /= (float d); // division by a constant
// special functions
mat4 transpose() const; // transpose
mat4 inverse() const; // inverse
mat4 &apply(V_FCT_PTR fct); // apply a func. to each element
void print(FILE *file, const char *name) const; // print matrix to a file
vec4 &operator [] (int i); // indexing
const vec4 &operator [] (int i) const; // indexing
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 * (const mat4 &a, const mat4 &b); // m1 * m2
friend mat4 operator * (const mat4 &a, float d); // m1 * 4.0
friend mat4 operator * (float d, const mat4 &a); // 4.0 * m1
friend mat4 operator / (const mat4 &a, 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 (); // identity 2D
mat3 translation2D(const vec2 &v); // translation 2D
mat3 rotation2D (const vec2 &Center, float angleDeg); // rotation 2D
mat3 scaling2D (const vec2 &scaleVector); // scaling 2D
mat4 identity3D (); // identity 3D
mat4 translation3D(const vec3 &v); // translation 3D
mat4 rotation3D (const vec3 &Axis, float angleDeg); // rotation 3D
mat4 rotation3Drad(const vec3 &Axis, float angleRad); // rotation 3D
mat4 scaling3D (const vec3 &scaleVector); // scaling 3D
mat4 perspective3D(float d); // perspective 3D
vec3 operator * (const vec3 &v, const mat3 &a);
vec2 operator * (const vec2 &v, const mat3 &a);
vec3 operator * (const vec3 &v, const mat4 &a);
vec4 operator * (const vec4 &v, const mat4 &a);
#endif