| [0b990d] | 1 | /****************************************************************
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| 2 | * *
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| 3 | * C++ Vector and Matrix Algebra routines *
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| 4 | * Author: Jean-Francois DOUE *
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| 5 | * Version 3.1 --- October 1993 *
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| 6 | * *
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| 7 | ****************************************************************/
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| 8 |
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| 9 | #ifndef _util_misc_algebra_h
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| 10 | #define _util_misc_algebra_h
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| 11 |
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| 12 | #include <iostream>
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| 13 | #include <stdlib.h>
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| 14 |
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| 15 | namespace sc {
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| 16 |
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| 17 | // this line defines a new type: pointer to a function which returns a
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| 18 | // double and takes as argument a double
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| 19 | typedef double (*V_FCT_PTR)(double);
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| 20 |
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| 21 | class vec2;
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| 22 | class vec3;
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| 23 | class vec4;
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| 24 | class mat3;
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| 25 | class mat4;
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| 26 |
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| 27 | enum {VX, VY, VZ, VW}; // axes
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| 28 | enum {PA, PB, PC, PD}; // planes
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| 29 | enum {RED, GREEN, BLUE}; // colors
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| 30 |
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| 31 | /****************************************************************
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| 32 | * *
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| 33 | * 2D Vector *
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| 34 | * *
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| 35 | ****************************************************************/
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| 36 |
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| 37 | class vec2
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| 38 | {
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| 39 | protected:
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| 40 |
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| 41 | double n[2];
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| 42 |
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| 43 | public:
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| 44 |
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| 45 | // Constructors
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| 46 |
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| 47 | vec2();
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| 48 | vec2(const double x, const double y);
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| 49 | vec2(const double d);
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| 50 | vec2(const vec2& v); // copy constructor
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| 51 | vec2(const vec3& v); // cast v3 to v2
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| 52 | vec2(const vec3& v, int dropAxis); // cast v3 to v2
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| 53 |
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| 54 | // Assignment operators
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| 55 |
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| 56 | vec2& operator = ( const vec2& v ); // assignment of a vec2
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| 57 | vec2& operator += ( const vec2& v ); // incrementation by a vec2
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| 58 | vec2& operator -= ( const vec2& v ); // decrementation by a vec2
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| 59 | vec2& operator *= ( const double d ); // multiplication by a constant
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| 60 | vec2& operator /= ( const double d ); // division by a constant
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| 61 | double& operator [] ( int i); // indexing
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| 62 | const double& operator[](int i) const; // indexing
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| 63 |
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| 64 | // special functions
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| 65 |
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| 66 | double length(); // length of a vec2
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| 67 | double length2(); // squared length of a vec2
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| 68 | vec2& normalize(); // normalize a vec2
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| 69 | vec2& apply(V_FCT_PTR fct); // apply a func. to each component
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| 70 |
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| 71 | // friends
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| 72 |
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| 73 | friend vec2 operator - (const vec2& v); // -v1
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| 74 | friend vec2 operator + (const vec2& a, const vec2& b); // v1 + v2
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| 75 | friend vec2 operator - (const vec2& a, const vec2& b); // v1 - v2
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| 76 | friend vec2 operator * (const vec2& a, const double d); // v1 * 3.0
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| 77 | friend vec2 operator * (const double d, const vec2& a); // 3.0 * v1
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| 78 | friend vec2 operator * (const mat3& a, const vec2& v); // M . v
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| 79 | friend vec2 operator * (const vec2& v, mat3& a); // v . M
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| 80 | friend double operator * (const vec2& a, const vec2& b); // dot product
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| 81 | friend vec2 operator / (const vec2& a, const double d); // v1 / 3.0
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| 82 | friend vec3 operator ^ (const vec2& a, const vec2& b); // cross product
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| 83 | friend int operator == (const vec2& a, const vec2& b); // v1 == v2 ?
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| 84 | friend int operator != (const vec2& a, const vec2& b); // v1 != v2 ?
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| 85 | friend std::ostream& operator << (std::ostream& s, vec2& v);// output to stream
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| 86 | friend std::istream& operator >> (std::istream& s, vec2& v);// input from strm.
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| 87 | friend void swap(vec2& a, vec2& b); // swap v1 & v2
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| 88 | friend vec2 min(const vec2& a, const vec2& b); // min(v1, v2)
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| 89 | friend vec2 max(const vec2& a, const vec2& b); // max(v1, v2)
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| 90 | friend vec2 prod(const vec2& a, const vec2& b); // term by term *
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| 91 |
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| 92 | // necessary friend declarations
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| 93 |
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| 94 | friend class vec3;
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| 95 | };
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| 96 |
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| 97 | /****************************************************************
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| 98 | * *
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| 99 | * 3D Vector *
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| 100 | * *
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| 101 | ****************************************************************/
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| 102 |
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| 103 | class vec3
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| 104 | {
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| 105 | protected:
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| 106 |
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| 107 | double n[3];
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| 108 |
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| 109 | public:
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| 110 |
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| 111 | // Constructors
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| 112 |
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| 113 | vec3();
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| 114 | vec3(const double x, const double y, const double z);
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| 115 | vec3(const double d);
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| 116 | vec3(const vec3& v); // copy constructor
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| 117 | vec3(const vec2& v); // cast v2 to v3
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| 118 | vec3(const vec2& v, double d); // cast v2 to v3
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| 119 | vec3(const vec4& v); // cast v4 to v3
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| 120 | vec3(const vec4& v, int dropAxis); // cast v4 to v3
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| 121 |
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| 122 | // Assignment operators
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| 123 |
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| 124 | vec3& operator = ( const vec3& v ); // assignment of a vec3
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| 125 | vec3& operator += ( const vec3& v ); // incrementation by a vec3
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| 126 | vec3& operator -= ( const vec3& v ); // decrementation by a vec3
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| 127 | vec3& operator *= ( const double d ); // multiplication by a constant
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| 128 | vec3& operator /= ( const double d ); // division by a constant
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| 129 | double& operator [] ( int i); // indexing
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| 130 | const double& operator[](int i) const; // indexing
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| 131 |
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| 132 | // special functions
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| 133 |
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| 134 | double length(); // length of a vec3
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| 135 | double length2(); // squared length of a vec3
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| 136 | vec3& normalize(); // normalize a vec3
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| 137 | vec3& apply(V_FCT_PTR fct); // apply a func. to each component
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| 138 |
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| 139 | // friends
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| 140 |
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| 141 | friend vec3 operator - (const vec3& v); // -v1
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| 142 | friend vec3 operator + (const vec3& a, const vec3& b); // v1 + v2
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| 143 | friend vec3 operator - (const vec3& a, const vec3& b); // v1 - v2
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| 144 | friend vec3 operator * (const vec3& a, const double d); // v1 * 3.0
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| 145 | friend vec3 operator * (const double d, const vec3& a); // 3.0 * v1
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| 146 | friend vec3 operator * (const mat4& a, const vec3& v); // M . v
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| 147 | friend vec3 operator * (const vec3& v, const mat4& a); // v . M
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| 148 | friend double operator * (const vec3& a, const vec3& b); // dot product
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| 149 | friend vec3 operator / (const vec3& a, const double d); // v1 / 3.0
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| 150 | friend vec3 operator ^ (const vec3& a, const vec3& b); // cross product
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| 151 | friend int operator == (const vec3& a, const vec3& b); // v1 == v2 ?
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| 152 | friend int operator != (const vec3& a, const vec3& b); // v1 != v2 ?
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| 153 | friend std::ostream& operator << (std::ostream& s, vec3& v);// output to stream
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| 154 | friend std::istream& operator >> (std::istream& s, vec3& v);// input from strm.
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| 155 | friend void swap(vec3& a, vec3& b); // swap v1 & v2
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| 156 | friend vec3 min(const vec3& a, const vec3& b); // min(v1, v2)
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| 157 | friend vec3 max(const vec3& a, const vec3& b); // max(v1, v2)
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| 158 | friend vec3 prod(const vec3& a, const vec3& b); // term by term *
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| 159 |
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| 160 | // necessary friend declarations
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| 161 |
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| 162 | friend class vec2;
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| 163 | friend class vec4;
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| 164 | friend class mat3;
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| 165 | friend vec2 operator * (const mat3& a, const vec2& v); // linear transform
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| 166 | friend mat3 operator * (const mat3& a, const mat3& b); // matrix 3 product
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| 167 | };
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| 168 |
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| 169 | /****************************************************************
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| 170 | * *
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| 171 | * 4D Vector *
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| 172 | * *
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| 173 | ****************************************************************/
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| 174 |
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| 175 | class vec4
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| 176 | {
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| 177 | protected:
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| 178 |
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| 179 | double n[4];
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| 180 |
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| 181 | public:
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| 182 |
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| 183 | // Constructors
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| 184 |
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| 185 | vec4();
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| 186 | vec4(const double x, const double y, const double z, const double w);
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| 187 | vec4(const double d);
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| 188 | vec4(const vec4& v); // copy constructor
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| 189 | vec4(const vec3& v); // cast vec3 to vec4
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| 190 | vec4(const vec3& v, const double d); // cast vec3 to vec4
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| 191 |
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| 192 | // Assignment operators
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| 193 |
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| 194 | vec4& operator = ( const vec4& v ); // assignment of a vec4
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| 195 | vec4& operator += ( const vec4& v ); // incrementation by a vec4
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| 196 | vec4& operator -= ( const vec4& v ); // decrementation by a vec4
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| 197 | vec4& operator *= ( const double d ); // multiplication by a constant
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| 198 | vec4& operator /= ( const double d ); // division by a constant
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| 199 | double& operator [] ( int i); // indexing
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| 200 | const double& operator [] ( int i) const; // indexing
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| 201 |
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| 202 | // special functions
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| 203 |
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| 204 | double length(); // length of a vec4
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| 205 | double length2(); // squared length of a vec4
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| 206 | vec4& normalize(); // normalize a vec4
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| 207 | vec4& apply(V_FCT_PTR fct); // apply a func. to each component
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| 208 |
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| 209 | // friends
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| 210 |
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| 211 | friend vec4 operator - (const vec4& v); // -v1
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| 212 | friend vec4 operator + (const vec4& a, const vec4& b); // v1 + v2
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| 213 | friend vec4 operator - (const vec4& a, const vec4& b); // v1 - v2
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| 214 | friend vec4 operator * (const vec4& a, const double d); // v1 * 3.0
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| 215 | friend vec4 operator * (const double d, const vec4& a); // 3.0 * v1
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| 216 | friend vec4 operator * (const mat4& a, const vec4& v); // M . v
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| 217 | friend vec4 operator * (const vec4& v, const mat4& a); // v . M
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| 218 | friend double operator * (const vec4& a, const vec4& b); // dot product
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| 219 | friend vec4 operator / (const vec4& a, const double d); // v1 / 3.0
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| 220 | friend int operator == (const vec4& a, const vec4& b); // v1 == v2 ?
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| 221 | friend int operator != (const vec4& a, const vec4& b); // v1 != v2 ?
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| 222 | friend std::ostream& operator << (std::ostream& s, vec4& v);// output to stream
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| 223 | friend std::istream& operator >> (std::istream& s, vec4& v);// input from strm.
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| 224 | friend void swap(vec4& a, vec4& b); // swap v1 & v2
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| 225 | friend vec4 min(const vec4& a, const vec4& b); // min(v1, v2)
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| 226 | friend vec4 max(const vec4& a, const vec4& b); // max(v1, v2)
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| 227 | friend vec4 prod(const vec4& a, const vec4& b); // term by term *
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| 228 |
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| 229 | // necessary friend declarations
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| 230 |
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| 231 | friend class vec3;
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| 232 | friend class mat4;
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| 233 | friend vec3 operator * (const mat4& a, const vec3& v); // linear transform
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| 234 | friend mat4 operator * (const mat4& a, const mat4& b); // matrix 4 product
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| 235 | };
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| 236 |
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| 237 | /****************************************************************
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| 238 | * *
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| 239 | * 3x3 Matrix *
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| 240 | * *
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| 241 | ****************************************************************/
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| 242 |
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| 243 | class mat3
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| 244 | {
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| 245 | protected:
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| 246 |
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| 247 | vec3 v[3];
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| 248 |
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| 249 | public:
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| 250 |
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| 251 | // Constructors
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| 252 |
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| 253 | mat3();
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| 254 | mat3(const vec3& v0, const vec3& v1, const vec3& v2);
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| 255 | mat3(const double d);
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| 256 | mat3(const mat3& m);
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| 257 |
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| 258 | // Assignment operators
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| 259 |
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| 260 | mat3& operator = ( const mat3& m ); // assignment of a mat3
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| 261 | mat3& operator += ( const mat3& m ); // incrementation by a mat3
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| 262 | mat3& operator -= ( const mat3& m ); // decrementation by a mat3
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| 263 | mat3& operator *= ( const double d ); // multiplication by a constant
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| 264 | mat3& operator /= ( const double d ); // division by a constant
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| 265 | vec3& operator [] ( int i); // indexing
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| 266 | const vec3& operator [] ( int i) const; // indexing
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| 267 |
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| 268 | // special functions
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| 269 |
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| 270 | mat3 transpose() const; // transpose
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| 271 | mat3 inverse(); // inverse
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| 272 | mat3& apply(V_FCT_PTR fct); // apply a func. to each element
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| 273 |
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| 274 | // friends
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| 275 |
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| 276 | friend mat3 operator - (const mat3& a); // -m1
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| 277 | friend mat3 operator + (const mat3& a, const mat3& b); // m1 + m2
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| 278 | friend mat3 operator - (const mat3& a, const mat3& b); // m1 - m2
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| 279 | friend mat3 operator * (const mat3& a, const mat3& b); // m1 * m2
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| 280 | friend mat3 operator * (const mat3& a, const double d); // m1 * 3.0
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| 281 | friend mat3 operator * (const double d, const mat3& a); // 3.0 * m1
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| 282 | friend mat3 operator / (const mat3& a, const double d); // m1 / 3.0
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| 283 | friend int operator == (const mat3& a, const mat3& b); // m1 == m2 ?
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| 284 | friend int operator != (const mat3& a, const mat3& b); // m1 != m2 ?
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| 285 | friend std::ostream& operator << (std::ostream& s, mat3& m);// output to stream
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| 286 | friend std::istream& operator >> (std::istream& s, mat3& m);// input from strm.
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| 287 | friend void swap(mat3& a, mat3& b); // swap m1 & m2
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| 288 |
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| 289 | // necessary friend declarations
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| 290 |
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| 291 | friend vec3 operator * (const mat3& a, const vec3& v); // linear transform
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| 292 | friend vec2 operator * (const mat3& a, const vec2& v); // linear transform
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| 293 | };
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| 294 |
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| 295 | /****************************************************************
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| 296 | * *
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| 297 | * 4x4 Matrix *
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| 298 | * *
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| 299 | ****************************************************************/
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| 300 |
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| 301 | class mat4
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| 302 | {
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| 303 | protected:
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| 304 |
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| 305 | vec4 v[4];
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| 306 |
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| 307 | public:
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| 308 |
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| 309 | // Constructors
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| 310 |
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| 311 | mat4();
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| 312 | mat4(const vec4& v0, const vec4& v1, const vec4& v2, const vec4& v3);
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| 313 | mat4(const double d);
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| 314 | mat4(const mat4& m);
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| 315 |
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| 316 | // Assignment operators
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| 317 |
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| 318 | mat4& operator = ( const mat4& m ); // assignment of a mat4
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| 319 | mat4& operator += ( const mat4& m ); // incrementation by a mat4
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| 320 | mat4& operator -= ( const mat4& m ); // decrementation by a mat4
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| 321 | mat4& operator *= ( const double d ); // multiplication by a constant
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| 322 | mat4& operator /= ( const double d ); // division by a constant
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| 323 | vec4& operator [] ( int i); // indexing
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| 324 | const vec4& operator [] ( int i) const; // indexing
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| 325 |
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| 326 | // special functions
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| 327 |
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| 328 | mat4 transpose() const; // transpose
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| 329 | mat4 inverse(); // inverse
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| 330 | mat4& apply(V_FCT_PTR fct); // apply a func. to each element
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| 331 |
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| 332 | // friends
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| 333 |
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| 334 | friend mat4 operator - (const mat4& a); // -m1
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| 335 | friend mat4 operator + (const mat4& a, const mat4& b); // m1 + m2
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| 336 | friend mat4 operator - (const mat4& a, const mat4& b); // m1 - m2
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| 337 | friend mat4 operator * (const mat4& a, const mat4& b); // m1 * m2
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| 338 | friend mat4 operator * (const mat4& a, const double d); // m1 * 4.0
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| 339 | friend mat4 operator * (const double d, const mat4& a); // 4.0 * m1
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| 340 | friend mat4 operator / (const mat4& a, const double d); // m1 / 3.0
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| 341 | friend int operator == (const mat4& a, const mat4& b); // m1 == m2 ?
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| 342 | friend int operator != (const mat4& a, const mat4& b); // m1 != m2 ?
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| 343 | friend std::ostream& operator << (std::ostream& s, mat4& m);// output to stream
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| 344 | friend std::istream& operator >> (std::istream& s, mat4& m);// input from strm.
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| 345 | friend void swap(mat4& a, mat4& b); // swap m1 & m2
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| 346 |
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| 347 | // necessary friend declarations
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| 348 |
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| 349 | friend vec4 operator * (const mat4& a, const vec4& v); // linear transform
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| 350 | friend vec3 operator * (const mat4& a, const vec3& v); // linear transform
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| 351 | };
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| 352 |
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| 353 | /****************************************************************
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| 354 | * *
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| 355 | * 2D functions and 3D functions *
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| 356 | * *
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| 357 | ****************************************************************/
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| 358 |
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| 359 | mat3 identity2D(); // identity 2D
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| 360 | mat3 translation2D(const vec2& v); // translation 2D
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| 361 | mat3 rotation2D(const vec2& Center, const double angleDeg); // rotation 2D
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| 362 | mat3 scaling2D(const vec2& scaleVector); // scaling 2D
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| 363 | mat4 identity3D(); // identity 3D
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| 364 | mat4 translation3D(const vec3& v); // translation 3D
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| 365 | mat4 rotation3D(const vec3& Axis, const double angleDeg); // rotation 3D
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| 366 | mat4 scaling3D(const vec3& scaleVector); // scaling 3D
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| 367 | mat4 perspective3D(const double d); // perspective 3D
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| 368 |
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| 369 | }
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| 370 |
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| 371 | #endif
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