475 lines
96 KiB
Text
475 lines
96 KiB
Text
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/**************************************************************************
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algebra3.cpp, algebra3.h - C++ Vector and Matrix Algebra routines
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There are three vector classes and two matrix classes: vec2, vec3,
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vec4, mat3, and mat4.
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All the standard arithmetic operations are defined, with '*'
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for dot product of two vectors and multiplication of two matrices,
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and '^' for cross product of two vectors.
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Additional functions include length(), normalize(), homogenize for
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vectors, and print(), set(), apply() for all classes.
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There is a function transpose() for matrices, but note that it
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does not actually change the matrix,
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When multiplied with a matrix, a vector is treated as a row vector
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if it precedes the matrix (v*M), and as a column vector if it
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follows the matrix (M*v).
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Matrices are stored in row-major form.
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A vector of one dimension (2d, 3d, or 4d) can be cast to a vector
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of a higher or lower dimension. If casting to a higher dimension,
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the new component is set by default to 1.0, unless a value is
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specified:
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vec3 a(1.0, 2.0, 3.0 );
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vec4 b( a, 4.0 ); // now b == {1.0, 2.0, 3.0, 4.0};
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When casting to a lower dimension, the vector is homogenized in
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the lower dimension. E.g., if a 4d {X,Y,Z,W} is cast to 3d, the
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resulting vector is {X/W, Y/W, Z/W}. It is up to the user to
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insure the fourth component is not zero before casting.
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There are also the following function for building matrices:
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identity2D(), translation2D(), rotation2D(),
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scaling2D(), identity3D(), translation3D(),
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rotation3D(), rotation3Drad(), scaling3D(),
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perspective3D()
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NOTE: When compiling for Windows, include this file first, to avoid
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certain name conflicts
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---------------------------------------------------------------------
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Author: Jean-Francois DOUEg
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Revised: Paul Rademacher
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Version 3.2 - Feb 1998
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**************************************************************************/
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#ifndef _ALGEBRA3_H_
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#define _ALGEBRA3_H_
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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// this line defines a new type: pointer to a function which returns a
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// float and takes as argument a float
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typedef float (*V_FCT_PTR)(float);
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// min-max macros
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#ifndef MIN
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#define MIN(A,B) ((A) < (B) ? (A) : (B))
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#define MAX(A,B) ((A) > (B) ? (A) : (B))
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#endif
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//#include <stream.h>
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// error handling macro
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//#define VEC_ERROR(E) { cerr << E; exit(1); }
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/*#define <<
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#define >>*/
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#ifdef VEC_ERROR_FATAL
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#ifndef VEC_ERROR
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#define VEC_ERROR(E) { printf( "VERROR %s\n", E ); exit(1); }
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#endif
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#else
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#ifndef VEC_ERROR
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#define VEC_ERROR(E) { printf( "VERROR %s\n", E ); }
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#endif
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#endif
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class vec2;
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class vec3;
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class vec4;
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class mat3;
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class mat4;
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/*#ifndef X
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enum {X,Y,Z,W};
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#endif
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*/
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/*#ifndef R
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enum {R,G,B,ALPHA};
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#endif
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*/
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#ifndef M_PI
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#define M_PI 3.141592654
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#endif
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enum {VX, VY, VZ, VW}; // axes
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enum {PA, PB, PC, PD}; // planes
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enum {RED, GREEN, BLUE, ALPHA}; // colors
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enum {KA, KD, KS, ES}; // phong coefficients
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/****************************************************************
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* *
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* 2D Vector *
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* *
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****************************************************************/
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class vec2
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{
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protected:
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float n[2];
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public:
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// Constructors
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vec2(void);
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vec2(const float x, const float y);
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vec2(const float d);
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vec2(const vec2& v); // copy constructor
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vec2(const vec3& v); // cast v3 to v2
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vec2(const vec3& v, int dropAxis); // cast v3 to v2
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// Assignment operators
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vec2& operator = ( const vec2& v ); // assignment of a vec2
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vec2& operator += ( const vec2& v ); // incrementation by a vec2
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vec2& operator -= ( const vec2& v ); // decrementation by a vec2
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vec2& operator *= ( const float d ); // multiplication by a constant
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vec2& operator /= ( const float d ); // division by a constant
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float& operator [] ( int i); // indexing
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// special functions
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float length(void); // length of a vec2
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float length2(void); // squared length of a vec2
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vec2& normalize(void); // normalize a vec2
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vec2& apply(V_FCT_PTR fct); // apply a func. to each component
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void set( float x, float y ); // set vector
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// friends
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friend vec2 operator - (const vec2& v); // -v1
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friend vec2 operator + (const vec2& a, const vec2& b); // v1 + v2
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friend vec2 operator - (const vec2& a, const vec2& b); // v1 - v2
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friend vec2 operator * (const vec2& a, const float d); // v1 * 3.0
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friend vec2 operator * (const float d, const vec2& a); // 3.0 * v1
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friend vec2 operator * (const mat3& a, const vec2& v); // M . v
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friend vec2 operator * (const vec2& v, mat3& a); // v . M
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friend float operator * (const vec2& a, const vec2& b); // dot product
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friend vec2 operator / (const vec2& a, const float d); // v1 / 3.0
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friend vec3 operator ^ (const vec2& a, const vec2& b); // cross product
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friend int operator == (const vec2& a, const vec2& b); // v1 == v2 ?
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friend int operator != (const vec2& a, const vec2& b); // v1 != v2 ?
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//friend ostream& operator << (ostream& s, vec2& v); // output to stream
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//friend istream& operator >> (istream& s, vec2& v); // input from strm.
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friend void swap(vec2& a, vec2& b); // swap v1 & v2
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friend vec2 min_vec(const vec2& a, const vec2& b); // min(v1, v2)
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friend vec2 max_vec(const vec2& a, const vec2& b); // max(v1, v2)
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friend vec2 prod(const vec2& a, const vec2& b); // term by term *
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// necessary friend declarations
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friend class vec3;
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};
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/****************************************************************
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* *
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* 3D Vector *
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* *
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****************************************************************/
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class vec3
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{
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protected:
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float n[3];
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public:
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// Constructors
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vec3(void);
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vec3(const float x, const float y, const float z);
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vec3(const float d);
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vec3(const vec3& v); // copy constructor
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vec3(const vec2& v); // cast v2 to v3
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vec3(const vec2& v, float d); // cast v2 to v3
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vec3(const vec4& v); // cast v4 to v3
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vec3(const vec4& v, int dropAxis); // cast v4 to v3
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// Assignment operators
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vec3& operator = ( const vec3& v ); // assignment of a vec3
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vec3& operator += ( const vec3& v ); // incrementation by a vec3
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vec3& operator -= ( const vec3& v ); // decrementation by a vec3
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vec3& operator *= ( const float d ); // multiplication by a constant
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vec3& operator /= ( const float d ); // division by a constant
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float& operator [] ( int i); // indexing
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// special functions
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float length(void); // length of a vec3
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float length2(void); // squared length of a vec3
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vec3& normalize(void); // normalize a vec3
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vec3& homogenize(void); // homogenize (div by Z)
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vec3& apply(V_FCT_PTR fct); // apply a func. to each component
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void set( float x, float y, float z ); // set vector
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void print( FILE *file, char *name ); // print vector to a file
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// friends
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friend vec3 operator - (const vec3& v); // -v1
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friend vec3 operator + (const vec3& a, const vec3& b); // v1 + v2
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friend vec3 operator - (const vec3& a, const vec3& b); // v1 - v2
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friend vec3 operator * (const vec3& a, const float d); // v1 * 3.0
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friend vec3 operator * (const float d, const vec3& a); // 3.0 * v1
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friend vec3 operator * (const mat4& a, const vec3& v); // M . v
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friend vec3 operator * (const vec3& v, mat4& a); // v . M
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friend float operator * (const vec3& a, const vec3& b); // dot product
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friend vec3 operator / (const vec3& a, const float d); // v1 / 3.0
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friend vec3 operator ^ (const vec3& a, const vec3& b); // cross product
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friend int operator == (const vec3& a, const vec3& b); // v1 == v2 ?
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friend int operator != (const vec3& a, const vec3& b); // v1 != v2 ?
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//friend ostream& operator << (ostream& s, vec3& v); // output to stream
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//friend istream& operator >> (istream& s, vec3& v); // input from strm.
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friend void swap(vec3& a, vec3& b); // swap v1 & v2
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friend vec3 min_vec(const vec3& a, const vec3& b); // min(v1, v2)
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friend vec3 max_vec(const vec3& a, const vec3& b); // max(v1, v2)
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friend vec3 prod(const vec3& a, const vec3& b); // term by term *
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// necessary friend declarations
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friend class vec2;
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friend class vec4;
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friend class mat3;
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friend vec2 operator * (const mat3& a, const vec2& v); // linear transform
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friend vec3 operator * (const mat3& a, const vec3& v); // linear transform
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friend mat3 operator * (mat3& a, mat3& b); // matrix 3 product
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};
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/****************************************************************
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* *
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* 4D Vector *
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* *
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****************************************************************/
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class vec4
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{
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protected:
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float n[4];
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public:
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// Constructors
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vec4(void);
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vec4(const float x, const float y, const float z, const float w);
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vec4(const float d);
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vec4(const vec4& v); // copy constructor
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vec4(const vec3& v); // cast vec3 to vec4
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vec4(const vec3& v, const float d); // cast vec3 to vec4
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// Assignment operators
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vec4& operator = ( const vec4& v ); // assignment of a vec4
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vec4& operator += ( const vec4& v ); // incrementation by a vec4
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vec4& operator -= ( const vec4& v ); // decrementation by a vec4
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vec4& operator *= ( const float d ); // multiplication by a constant
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vec4& operator /= ( const float d ); // division by a constant
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float& operator [] ( int i); // indexing
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// special functions
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float length(void); // length of a vec4
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float length2(void); // squared length of a vec4
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vec4& normalize(void); // normalize a vec4
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vec4& apply(V_FCT_PTR fct); // apply a func. to each component
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vec4& homogenize(void);
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void print( FILE *file, char *name ); // print vector to a file
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void set( float x, float y, float z, float a );
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// friends
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friend vec4 operator - (const vec4& v); // -v1
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friend vec4 operator + (const vec4& a, const vec4& b); // v1 + v2
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friend vec4 operator - (const vec4& a, const vec4& b); // v1 - v2
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friend vec4 operator * (const vec4& a, const float d); // v1 * 3.0
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friend vec4 operator * (const float d, const vec4& a); // 3.0 * v1
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friend vec4 operator * (const mat4& a, const vec4& v); // M . v
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friend vec4 operator * (const vec4& v, mat4& a); // v . M
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friend float operator * (const vec4& a, const vec4& b); // dot product
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friend vec4 operator / (const vec4& a, const float d); // v1 / 3.0
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friend int operator == (const vec4& a, const vec4& b); // v1 == v2 ?
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friend int operator != (const vec4& a, const vec4& b); // v1 != v2 ?
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//friend ostream& operator << (ostream& s, vec4& v); // output to stream
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//friend istream& operator >> (istream& s, vec4& v); // input from strm.
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friend void swap(vec4& a, vec4& b); // swap v1 & v2
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friend vec4 min_vec(const vec4& a, const vec4& b); // min(v1, v2)
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friend vec4 max_vec(const vec4& a, const vec4& b); // max(v1, v2)
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friend vec4 prod(const vec4& a, const vec4& b); // term by term *
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// necessary friend declarations
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friend class vec3;
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friend class mat4;
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friend vec3 operator * (const mat4& a, const vec3& v); // linear transform
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friend mat4 operator * (mat4& a, mat4& b); // matrix 4 product
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};
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/****************************************************************
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* *
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* 3x3 Matrix *
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* *
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****************************************************************/
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class mat3
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{
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protected:
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vec3 v[3];
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public:
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// Constructors
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mat3(void);
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mat3(const vec3& v0, const vec3& v1, const vec3& v2);
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mat3(const float d);
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mat3(const mat3& m);
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// Assignment operators
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mat3& operator = ( const mat3& m ); // assignment of a mat3
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mat3& operator += ( const mat3& m ); // incrementation by a mat3
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mat3& operator -= ( const mat3& m ); // decrementation by a mat3
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mat3& operator *= ( const float d ); // multiplication by a constant
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mat3& operator /= ( const float d ); // division by a constant
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vec3& operator [] ( int i); // indexing
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// special functions
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mat3 transpose(void); // transpose
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mat3 inverse(void); // inverse
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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
|