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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 #include #include // 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