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algebra3.cpp
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1609 lines (1332 loc) · 35.9 KB
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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()
---------------------------------------------------------------------
Author: Jean-Francois DOUEg
Revised: Paul Rademacher
Version 3.2 - Feb 1998
Revised: Nigel Stewart (GLUI Code Cleaning)
**************************************************************************/
#include "algebra3.h"
#include "glui_internal.h"
#include <cmath>
#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
/****************************************************************
* *
* vec2 Member functions *
* *
****************************************************************/
/******************** vec2 CONSTRUCTORS ********************/
vec2::vec2()
{
n[VX] = n[VY] = 0.0;
}
vec2::vec2(float x, float y)
{
n[VX] = x;
n[VY] = y;
}
vec2::vec2(const vec2 &v)
{
n[VX] = v.n[VX];
n[VY] = v.n[VY];
}
vec2::vec2(const vec3 &v) // it is up to caller to avoid divide-by-zero
{
n[VX] = v.n[VX]/v.n[VZ];
n[VY] = v.n[VY]/v.n[VZ];
}
vec2::vec2(const vec3 &v, int dropAxis)
{
switch (dropAxis)
{
case VX: n[VX] = v.n[VY]; n[VY] = v.n[VZ]; break;
case VY: n[VX] = v.n[VX]; n[VY] = v.n[VZ]; break;
default: n[VX] = v.n[VX]; n[VY] = v.n[VY]; break;
}
}
/******************** vec2 ASSIGNMENT OPERATORS ******************/
vec2 & vec2::operator=(const vec2 &v)
{
n[VX] = v.n[VX];
n[VY] = v.n[VY];
return *this;
}
vec2 & vec2::operator+=(const vec2 &v)
{
n[VX] += v.n[VX];
n[VY] += v.n[VY];
return *this;
}
vec2 & vec2::operator-=(const vec2 &v)
{
n[VX] -= v.n[VX];
n[VY] -= v.n[VY];
return *this;
}
vec2 &vec2::operator*=(float d)
{
n[VX] *= d;
n[VY] *= d;
return *this;
}
vec2 &vec2::operator/=(float d)
{
float d_inv = 1.0f/d;
n[VX] *= d_inv;
n[VY] *= d_inv;
return *this;
}
float &vec2::operator[](int i)
{
if (i < VX || i > VY)
//VEC_ERROR("vec2 [] operator: illegal access; index = " << i << '\n')
VEC_ERROR("vec2 [] operator: illegal access" );
return n[i];
}
const float &vec2::operator[](int i) const
{
if (i < VX || i > VY)
//VEC_ERROR("vec2 [] operator: illegal access; index = " << i << '\n')
VEC_ERROR("vec2 [] operator: illegal access" );
return n[i];
}
/******************** vec2 SPECIAL FUNCTIONS ********************/
float vec2::length() const
{
return (float) sqrt(length2());
}
float vec2::length2() const
{
return n[VX]*n[VX] + n[VY]*n[VY];
}
vec2 &vec2::normalize() // it is up to caller to avoid divide-by-zero
{
*this /= length();
return *this;
}
vec2 &vec2::apply(V_FCT_PTR fct)
{
n[VX] = (*fct)(n[VX]);
n[VY] = (*fct)(n[VY]);
return *this;
}
void vec2::set( float x, float y )
{
n[VX] = x; n[VY] = y;
}
/******************** vec2 FRIENDS *****************************/
vec2 operator-(const vec2 &a)
{
return vec2(-a.n[VX],-a.n[VY]);
}
vec2 operator+(const vec2 &a, const vec2& b)
{
return vec2(a.n[VX]+b.n[VX], a.n[VY]+b.n[VY]);
}
vec2 operator-(const vec2 &a, const vec2& b)
{
return vec2(a.n[VX]-b.n[VX], a.n[VY]-b.n[VY]);
}
vec2 operator*(const vec2 &a, float d)
{
return vec2(d*a.n[VX], d*a.n[VY]);
}
vec2 operator*(float d, const vec2 &a)
{
return a*d;
}
vec2 operator*(const mat3 &a, const vec2 &v)
{
vec3 av;
av.n[VX] = a.v[0].n[VX]*v.n[VX] + a.v[0].n[VY]*v.n[VY] + a.v[0].n[VZ];
av.n[VY] = a.v[1].n[VX]*v.n[VX] + a.v[1].n[VY]*v.n[VY] + a.v[1].n[VZ];
av.n[VZ] = a.v[2].n[VX]*v.n[VX] + a.v[2].n[VY]*v.n[VY] + a.v[2].n[VZ];
return av;
}
vec2 operator*(const vec2 &v, const mat3 &a)
{
return a.transpose() * v;
}
vec3 operator*(const mat3 &a, const vec3 &v)
{
vec3 av;
av.n[VX] = a.v[0].n[VX]*v.n[VX] + a.v[0].n[VY]*v.n[VY] + a.v[0].n[VZ]*v.n[VZ];
av.n[VY] = a.v[1].n[VX]*v.n[VX] + a.v[1].n[VY]*v.n[VY] + a.v[1].n[VZ]*v.n[VZ];
av.n[VZ] = a.v[2].n[VX]*v.n[VX] + a.v[2].n[VY]*v.n[VY] + a.v[2].n[VZ]*v.n[VZ];
return av;
}
vec3 operator*(const vec3 &v, const mat3 &a)
{
return a.transpose() * v;
}
float operator*(const vec2 &a, const vec2 &b)
{
return a.n[VX]*b.n[VX] + a.n[VY]*b.n[VY];
}
vec2 operator/(const vec2 &a, float d)
{
float d_inv = 1.0f/d;
return vec2(a.n[VX]*d_inv, a.n[VY]*d_inv);
}
vec3 operator^(const vec2 &a, const vec2 &b)
{
return vec3(0.0, 0.0, a.n[VX] * b.n[VY] - b.n[VX] * a.n[VY]);
}
int operator==(const vec2 &a, const vec2 &b)
{
return (a.n[VX] == b.n[VX]) && (a.n[VY] == b.n[VY]);
}
int operator!=(const vec2 &a, const vec2 &b)
{
return !(a == b);
}
/*ostream& operator << (ostream& s, vec2& v)
{ return s << "| " << v.n[VX] << ' ' << v.n[VY] << " |"; }
*/
/*istream& operator >> (istream& s, vec2& v) {
vec2 v_tmp;
char c = ' ';
while (isspace(c))
s >> c;
// The vectors can be formatted either as x y or | x y |
if (c == '|') {
s >> v_tmp[VX] >> v_tmp[VY];
while (s >> c && isspace(c)) ;
if (c != '|')
;//s.set(_bad);
}
else {
s.putback(c);
s >> v_tmp[VX] >> v_tmp[VY];
}
if (s)
v = v_tmp;
return s;
}
*/
void swap(vec2 &a, vec2 &b)
{
vec2 tmp(a);
a = b;
b = tmp;
}
vec2 min_vec(const vec2 &a, const vec2 &b)
{
return vec2(MIN(a.n[VX], b.n[VX]), MIN(a.n[VY], b.n[VY]));
}
vec2 max_vec(const vec2 &a, const vec2 &b)
{
return vec2(MAX(a.n[VX], b.n[VX]), MAX(a.n[VY], b.n[VY]));
}
vec2 prod(const vec2 &a, const vec2 &b)
{
return vec2(a.n[VX] * b.n[VX], a.n[VY] * b.n[VY]);
}
/****************************************************************
* *
* vec3 Member functions *
* *
****************************************************************/
// CONSTRUCTORS
vec3::vec3()
{
n[VX] = n[VY] = n[VZ] = 0.0;
}
vec3::vec3(float x, float y, float z)
{
n[VX] = x;
n[VY] = y;
n[VZ] = z;
}
vec3::vec3(const vec3 &v)
{
n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VZ];
}
vec3::vec3(const vec2 &v)
{
n[VX] = v.n[VX];
n[VY] = v.n[VY];
n[VZ] = 1.0;
}
vec3::vec3(const vec2 &v, float d)
{
n[VX] = v.n[VX];
n[VY] = v.n[VY];
n[VZ] = d;
}
vec3::vec3(const vec4 &v) // it is up to caller to avoid divide-by-zero
{
n[VX] = v.n[VX] / v.n[VW];
n[VY] = v.n[VY] / v.n[VW];
n[VZ] = v.n[VZ] / v.n[VW];
}
vec3::vec3(const vec4 &v, int dropAxis)
{
switch (dropAxis)
{
case VX: n[VX] = v.n[VY]; n[VY] = v.n[VZ]; n[VZ] = v.n[VW]; break;
case VY: n[VX] = v.n[VX]; n[VY] = v.n[VZ]; n[VZ] = v.n[VW]; break;
case VZ: n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VW]; break;
default: n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VZ]; break;
}
}
// ASSIGNMENT OPERATORS
vec3 &vec3::operator=(const vec3 &v)
{
n[VX] = v.n[VX];
n[VY] = v.n[VY];
n[VZ] = v.n[VZ];
return *this;
}
vec3 &vec3::operator+=(const vec3 &v)
{
n[VX] += v.n[VX];
n[VY] += v.n[VY];
n[VZ] += v.n[VZ];
return *this;
}
vec3 &vec3::operator-=(const vec3& v)
{
n[VX] -= v.n[VX];
n[VY] -= v.n[VY];
n[VZ] -= v.n[VZ];
return *this;
}
vec3 &vec3::operator*=(float d)
{
n[VX] *= d;
n[VY] *= d;
n[VZ] *= d;
return *this;
}
vec3 &vec3::operator/=(float d)
{
float d_inv = 1.0f/d;
n[VX] *= d_inv;
n[VY] *= d_inv;
n[VZ] *= d_inv;
return *this;
}
float &vec3::operator[](int i)
{
if (i < VX || i > VZ)
//VEC_ERROR("vec3 [] operator: illegal access; index = " << i << '\n')
VEC_ERROR("vec3 [] operator: illegal access" );
return n[i];
}
const float &vec3::operator[](int i) const
{
if (i < VX || i > VZ)
//VEC_ERROR("vec3 [] operator: illegal access; index = " << i << '\n')
VEC_ERROR("vec3 [] operator: illegal access" );
return n[i];
}
// SPECIAL FUNCTIONS
float vec3::length() const
{
return (float) sqrt(length2());
}
float vec3::length2() const
{
return n[VX]*n[VX] + n[VY]*n[VY] + n[VZ]*n[VZ];
}
vec3 &vec3::normalize() // it is up to caller to avoid divide-by-zero
{
*this /= length();
return *this;
}
vec3 &vec3::homogenize(void) // it is up to caller to avoid divide-by-zero
{
n[VX] /= n[VZ];
n[VY] /= n[VZ];
n[VZ] = 1.0;
return *this;
}
vec3 &vec3::apply(V_FCT_PTR fct)
{
n[VX] = (*fct)(n[VX]);
n[VY] = (*fct)(n[VY]);
n[VZ] = (*fct)(n[VZ]);
return *this;
}
void vec3::set(float x, float y, float z) // set vector
{
n[VX] = x;
n[VY] = y;
n[VZ] = z;
}
void vec3::print(FILE *file, const char *name) const // print vector to a file
{
fprintf( file, "%s: <%f, %f, %f>\n", name, n[VX], n[VY], n[VZ] );
}
// FRIENDS
vec3 operator-(const vec3 &a)
{
return vec3(-a.n[VX],-a.n[VY],-a.n[VZ]);
}
vec3 operator+(const vec3 &a, const vec3 &b)
{
return vec3(a.n[VX]+ b.n[VX], a.n[VY] + b.n[VY], a.n[VZ] + b.n[VZ]);
}
vec3 operator-(const vec3 &a, const vec3 &b)
{
return vec3(a.n[VX]-b.n[VX], a.n[VY]-b.n[VY], a.n[VZ]-b.n[VZ]);
}
vec3 operator*(const vec3 &a, float d)
{
return vec3(d*a.n[VX], d*a.n[VY], d*a.n[VZ]);
}
vec3 operator*(float d, const vec3 &a)
{
return a*d;
}
vec3 operator*(const mat4 &a, const vec3 &v)
{
return a*vec4(v);
}
vec3 operator*(const vec3 &v, mat4 &a)
{
return a.transpose()*v;
}
float operator*(const vec3 &a, const vec3 &b)
{
return a.n[VX]*b.n[VX] + a.n[VY]*b.n[VY] + a.n[VZ]*b.n[VZ];
}
vec3 operator/(const vec3 &a, float d)
{
float d_inv = 1.0f/d;
return vec3(a.n[VX]*d_inv, a.n[VY]*d_inv, a.n[VZ]*d_inv);
}
vec3 operator^(const vec3 &a, const vec3 &b)
{
return
vec3(a.n[VY]*b.n[VZ] - a.n[VZ]*b.n[VY],
a.n[VZ]*b.n[VX] - a.n[VX]*b.n[VZ],
a.n[VX]*b.n[VY] - a.n[VY]*b.n[VX]);
}
int operator==(const vec3 &a, const vec3 &b)
{
return (a.n[VX] == b.n[VX]) && (a.n[VY] == b.n[VY]) && (a.n[VZ] == b.n[VZ]);
}
int operator!=(const vec3 &a, const vec3 &b)
{
return !(a == b);
}
/*ostream& operator << (ostream& s, vec3& v)
{ return s << "| " << v.n[VX] << ' ' << v.n[VY] << ' ' << v.n[VZ] << " |"; }
istream& operator >> (istream& s, vec3& v) {
vec3 v_tmp;
char c = ' ';
while (isspace(c))
s >> c;
// The vectors can be formatted either as x y z or | x y z |
if (c == '|') {
s >> v_tmp[VX] >> v_tmp[VY] >> v_tmp[VZ];
while (s >> c && isspace(c)) ;
if (c != '|')
;//s.set(_bad);
}
else {
s.putback(c);
s >> v_tmp[VX] >> v_tmp[VY] >> v_tmp[VZ];
}
if (s)
v = v_tmp;
return s;
}
*/
void swap(vec3 &a, vec3 &b)
{
vec3 tmp(a);
a = b;
b = tmp;
}
vec3 min_vec(const vec3 &a, const vec3 &b)
{
return vec3(
MIN(a.n[VX], b.n[VX]),
MIN(a.n[VY], b.n[VY]),
MIN(a.n[VZ], b.n[VZ]));
}
vec3 max_vec(const vec3 &a, const vec3 &b)
{
return vec3(
MAX(a.n[VX], b.n[VX]),
MAX(a.n[VY], b.n[VY]),
MAX(a.n[VZ], b.n[VZ]));
}
vec3 prod(const vec3 &a, const vec3 &b)
{
return vec3(a.n[VX]*b.n[VX], a.n[VY]*b.n[VY], a.n[VZ]*b.n[VZ]);
}
/****************************************************************
* *
* vec4 Member functions *
* *
****************************************************************/
// CONSTRUCTORS
vec4::vec4()
{
n[VX] = n[VY] = n[VZ] = 0.0;
n[VW] = 1.0;
}
vec4::vec4(float x, float y, float z, float w)
{
n[VX] = x;
n[VY] = y;
n[VZ] = z;
n[VW] = w;
}
vec4::vec4(const vec4 &v)
{
n[VX] = v.n[VX];
n[VY] = v.n[VY];
n[VZ] = v.n[VZ];
n[VW] = v.n[VW];
}
vec4::vec4(const vec3 &v)
{
n[VX] = v.n[VX];
n[VY] = v.n[VY];
n[VZ] = v.n[VZ];
n[VW] = 1.0;
}
vec4::vec4(const vec3 &v, float d)
{
n[VX] = v.n[VX];
n[VY] = v.n[VY];
n[VZ] = v.n[VZ];
n[VW] = d;
}
// ASSIGNMENT OPERATORS
vec4 &vec4::operator=(const vec4 &v)
{
n[VX] = v.n[VX];
n[VY] = v.n[VY];
n[VZ] = v.n[VZ];
n[VW] = v.n[VW];
return *this;
}
vec4 &vec4::operator+=(const vec4 &v)
{
n[VX] += v.n[VX];
n[VY] += v.n[VY];
n[VZ] += v.n[VZ];
n[VW] += v.n[VW];
return *this;
}
vec4 &vec4::operator-=(const vec4 &v)
{
n[VX] -= v.n[VX];
n[VY] -= v.n[VY];
n[VZ] -= v.n[VZ];
n[VW] -= v.n[VW];
return *this;
}
vec4 &vec4::operator*=(float d)
{
n[VX] *= d;
n[VY] *= d;
n[VZ] *= d;
n[VW] *= d;
return *this;
}
vec4 &vec4::operator/=(float d)
{
float d_inv = 1.0f/d;
n[VX] *= d_inv;
n[VY] *= d_inv;
n[VZ] *= d_inv;
n[VW] *= d_inv;
return *this;
}
float &vec4::operator[](int i)
{
if (i < VX || i > VW)
//VEC_ERROR("vec4 [] operator: illegal access; index = " << i << '\n')
VEC_ERROR("vec4 [] operator: illegal access" );
return n[i];
}
const float &vec4::operator[](int i) const
{
if (i < VX || i > VW)
//VEC_ERROR("vec4 [] operator: illegal access; index = " << i << '\n')
VEC_ERROR("vec4 [] operator: illegal access" );
return n[i];
}
// SPECIAL FUNCTIONS
float vec4::length() const
{
return (float) sqrt(length2());
}
float vec4::length2() const
{
return n[VX]*n[VX] + n[VY]*n[VY] + n[VZ]*n[VZ] + n[VW]*n[VW];
}
vec4 &vec4::normalize() // it is up to caller to avoid divide-by-zero
{
*this /= length();
return *this;
}
vec4 &vec4::homogenize() // it is up to caller to avoid divide-by-zero
{
n[VX] /= n[VW];
n[VY] /= n[VW];
n[VZ] /= n[VW];
n[VW] = 1.0;
return *this;
}
vec4 &vec4::apply(V_FCT_PTR fct)
{
n[VX] = (*fct)(n[VX]);
n[VY] = (*fct)(n[VY]);
n[VZ] = (*fct)(n[VZ]);
n[VW] = (*fct)(n[VW]);
return *this;
}
void vec4::print(FILE *file, const char *name) const // print vector to a file
{
fprintf( file, "%s: <%f, %f, %f, %f>\n", name, n[VX], n[VY], n[VZ], n[VW]);
}
void vec4::set(float x, float y, float z, float a)
{
n[0] = x;
n[1] = y;
n[2] = z;
n[3] = a;
}
// FRIENDS
vec4 operator-(const vec4 &a)
{
return vec4(-a.n[VX],-a.n[VY],-a.n[VZ],-a.n[VW]);
}
vec4 operator+(const vec4 &a, const vec4 &b)
{
return vec4(
a.n[VX] + b.n[VX],
a.n[VY] + b.n[VY],
a.n[VZ] + b.n[VZ],
a.n[VW] + b.n[VW]);
}
vec4 operator-(const vec4 &a, const vec4 &b)
{
return vec4(
a.n[VX] - b.n[VX],
a.n[VY] - b.n[VY],
a.n[VZ] - b.n[VZ],
a.n[VW] - b.n[VW]);
}
vec4 operator*(const vec4 &a, float d)
{
return vec4(d*a.n[VX], d*a.n[VY], d*a.n[VZ], d*a.n[VW]);
}
vec4 operator*(float d, const vec4 &a)
{
return a*d;
}
vec4 operator*(const mat4 &a, const vec4 &v)
{
#define ROWCOL(i) \
a.v[i].n[0]*v.n[VX] + \
a.v[i].n[1]*v.n[VY] + \
a.v[i].n[2]*v.n[VZ] + \
a.v[i].n[3]*v.n[VW]
return vec4(ROWCOL(0), ROWCOL(1), ROWCOL(2), ROWCOL(3));
#undef ROWCOL
}
vec4 operator*(const vec4 &v, const mat4 &a)
{
return a.transpose()*v;
}
float operator*(const vec4 &a, const vec4 &b)
{
return
a.n[VX]*b.n[VX] +
a.n[VY]*b.n[VY] +
a.n[VZ]*b.n[VZ] +
a.n[VW]*b.n[VW];
}
vec4 operator/(const vec4 &a, float d)
{
float d_inv = 1.0f/d;
return vec4(
a.n[VX]*d_inv,
a.n[VY]*d_inv,
a.n[VZ]*d_inv,
a.n[VW]*d_inv);
}
int operator==(const vec4 &a, const vec4 &b)
{
return
(a.n[VX] == b.n[VX]) &&
(a.n[VY] == b.n[VY]) &&
(a.n[VZ] == b.n[VZ]) &&
(a.n[VW] == b.n[VW]);
}
int operator!=(const vec4 &a, const vec4 &b)
{
return !(a == b);
}
/*ostream& operator << (ostream& s, vec4& v)
{ return s << "| " << v.n[VX] << ' ' << v.n[VY] << ' ' << v.n[VZ] << ' '
<< v.n[VW] << " |"; }
istream& operator >> (istream& s, vec4& v) {
vec4 v_tmp;
char c = ' ';
while (isspace(c))
s >> c;
// The vectors can be formatted either as x y z w or | x y z w |
if (c == '|') {
s >> v_tmp[VX] >> v_tmp[VY] >> v_tmp[VZ] >> v_tmp[VW];
while (s >> c && isspace(c)) ;
if (c != '|')
;//s.set(_bad);
}
else {
s.putback(c);
s >> v_tmp[VX] >> v_tmp[VY] >> v_tmp[VZ] >> v_tmp[VW];
}
if (s)
v = v_tmp;
return s;
}
*/
void swap(vec4 &a, vec4 &b)
{
vec4 tmp(a);
a = b;
b = tmp;
}
vec4 min_vec(const vec4 &a, const vec4 &b)
{
return vec4(
MIN(a.n[VX], b.n[VX]),
MIN(a.n[VY], b.n[VY]),
MIN(a.n[VZ], b.n[VZ]),
MIN(a.n[VW], b.n[VW]));
}
vec4 max_vec(const vec4 &a, const vec4 &b)
{
return vec4(
MAX(a.n[VX], b.n[VX]),
MAX(a.n[VY], b.n[VY]),
MAX(a.n[VZ], b.n[VZ]),
MAX(a.n[VW], b.n[VW]));
}
vec4 prod(const vec4 &a, const vec4 &b)
{
return vec4(
a.n[VX] * b.n[VX],
a.n[VY] * b.n[VY],
a.n[VZ] * b.n[VZ],
a.n[VW] * b.n[VW]);
}
/****************************************************************
* *
* mat3 member functions *
* *
****************************************************************/
// CONSTRUCTORS
mat3::mat3()
{
*this = identity2D();
}
mat3::mat3(const vec3 &v0, const vec3 &v1, const vec3 &v2)
{
set(v0, v1, v2);
}
mat3::mat3(const mat3 &m)
{
v[0] = m.v[0];
v[1] = m.v[1];
v[2] = m.v[2];
}
// ASSIGNMENT OPERATORS
mat3 &mat3::operator=(const mat3 &m)
{
v[0] = m.v[0];
v[1] = m.v[1];
v[2] = m.v[2];
return *this;
}
mat3 &mat3::operator+=(const mat3& m)
{
v[0] += m.v[0];
v[1] += m.v[1];
v[2] += m.v[2];
return *this;
}
mat3 &mat3::operator-=(const mat3& m)
{
v[0] -= m.v[0];
v[1] -= m.v[1];
v[2] -= m.v[2];
return *this;
}
mat3 &mat3::operator*=(float d)
{
v[0] *= d;
v[1] *= d;
v[2] *= d;
return *this;
}