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