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* *
* C++ Vector and Matrix Algebra routines *
* Author: Jean-Francois DOUE *
* Version 3.1 --- October 1993 *
* *
****************************************************************/
//
// From "Graphics Gems IV / Edited by Paul S. Heckbert
// Academic Press, 1994, ISBN 0-12-336156-9
// "You are free to use and modify this code in any way
// you like." (p. xv)
//
// Modified by J. Nagle, March 1997
// - All functions are inline.
// - All functions are const-correct.
// - All checking is via the standard "assert" macro.
// - Stream I/O is disabled for portability, but can be
// re-enabled by defining ALGEBRA3IOSTREAMS.
//
// Modified by J. Gautier April 1997 to compile with GCC in a
// Linux/InterViews environment, also removed warnings by adding
// inline declarations to some member functions.
//
#ifndef ALGEBRA3H
#define ALGEBRA3H
#include <stdlib.h>
#include <assert.h>
//#include <yvals.h>
#include <math.h>
#include <ctype.h>
// this line defines a new type: pointer to a function which returns a
// double and takes as argument a double
typedef double (*V_FCT_PTR)(double);
// min-max macros
#define MIN(A,B) ((A) < (B) ? (A) : (B))
#define MAX(A,B) ((A) > (B) ? (A) : (B))
// InterViews already defines these, so change the function names
#if 0
#undef min // allow as function names
#undef max
#endif
// error handling macro
#define ALGEBRA_ERROR(E) { assert(false); }
class vec2;
class vec3;
class vec4;
class mat3;
class mat4;
enum {VX, VY, VZ, VW}; // axes
enum {PA, PB, PC, PD}; // planes
enum {RED, GREEN, BLUE}; // colors
enum {KA, KD, KS, ES}; // phong coefficients
//
// PI
//
#ifndef M_PI
const double M_PI = 3.14159265358979323846; // per CRC handbook, 14th. ed.
#endif
#ifndef M_PI_2
const double M_PI_2 = (M_PI/2.0); // PI/2
#endif
#ifndef M2_PI
const double M2_PI = (M_PI*2.0); // PI*2
#endif
/****************************************************************
* *
* 2D Vector *
* *
****************************************************************/
class vec2
{
protected:
double n[2];
public:
// Constructors
vec2();
vec2(const double x, const double y);
vec2(const double 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 double d ); // multiplication by a constant
vec2& operator /= ( const double d ); // division by a constant
double& operator [] ( int i); // indexing
double vec2::operator [] ( int i) const;// read-only indexing
// special functions
double length() const; // length of a vec2
inline double length2() const; // squared length of a vec2
vec2& normalize() ; // normalize a vec2 in place
vec2& apply(V_FCT_PTR fct); // apply a func. to each component
// 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 double d); // v1 * 3.0
friend vec2 operator * (const double d, const vec2& a); // 3.0 * v1
friend vec2 operator * (const mat3& a, const vec2& v); // M . v
friend vec2 operator * (const vec2& v, const mat3& a); // v . M
friend double operator * (const vec2& a, const vec2& b); // dot product
friend vec2 operator / (const vec2& a, const double 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 ?
#ifdef ALGEBRA3IOSTREAMS
friend ostream& operator << (ostream& s, const vec2& v); // output to stream
friend istream& operator >> (istream& s, vec2& v); // input from strm.
#endif ALGEBRA3IOSTREAMS
friend void swap(vec2& a, vec2& b); // swap v1 & v2
friend vec2 vec2min(const vec2& a, const vec2& b); // min(v1, v2)
friend vec2 vec2max(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:
double n[3];
public:
// Constructors
inline vec3();
inline vec3(const double x, const double y, const double z);
vec3(const double d);
vec3(const vec3& v); // copy constructor
vec3(const vec2& v); // cast v2 to v3
vec3(const vec2& v, double 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 double d ); // multiplication by a constant
vec3& operator /= ( const double d ); // division by a constant
double& operator [] ( int i); // indexing
double operator[] (int i) const; // read-only indexing
// special functions
double length() const; // length of a vec3
inline double length2() const; // squared length of a vec3
vec3& normalize(); // normalize a vec3 in place
vec3& apply(V_FCT_PTR fct); // apply a func. to each component
// 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 double d); // v1 * 3.0
friend vec3 operator * (const double d, const vec3& a); // 3.0 * v1
friend vec3 operator * (const mat4& a, const vec3& v); // M . v
friend vec3 operator * (const vec3& v, const mat4& a); // v . M
friend double operator * (const vec3& a, const vec3& b); // dot product
friend vec3 operator / (const vec3& a, const double 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 ?
#ifdef ALGEBRA3IOSTREAMS
friend ostream& operator << (ostream& s, const vec3& v); // output to stream
friend istream& operator >> (istream& s, vec3& v); // input from strm.
#endif // ALGEBRA3IOSTREAMS
friend void swap(vec3& a, vec3& b); // swap v1 & v2
friend vec3 vec3min(const vec3& a, const vec3& b); // min(v1, v2)
friend vec3 vec3max(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 mat3 operator * (const mat3& a, const mat3& b); // matrix 3 product
};
/****************************************************************
* *
* 4D Vector *
* *
****************************************************************/
class vec4
{
protected:
double n[4];
public:
// Constructors
vec4();
vec4(const double x, const double y, const double z, const double w);
vec4(const double d);
vec4(const vec4& v); // copy constructor
inline vec4(const vec3& v); // cast vec3 to vec4
vec4(const vec3& v, const double 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 double d ); // multiplication by a constant
vec4& operator /= ( const double d ); // division by a constant
double& operator [] ( int i); // indexing
double operator[] (int i) const; // read-only indexing
// special functions
double length() const; // length of a vec4
inline double length2() const; // squared length of a vec4
vec4& normalize(); // normalize a vec4 in place
vec4& apply(V_FCT_PTR fct); // apply a func. to each component
// 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 double d); // v1 * 3.0
friend vec4 operator * (const double d, const vec4& a); // 3.0 * v1
friend vec4 operator * (const mat4& a, const vec4& v); // M . v
friend vec4 operator * (const vec4& v, const mat4& a); // v . M
friend double operator * (const vec4& a, const vec4& b); // dot product
friend vec4 operator / (const vec4& a, const double 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 ?
#ifdef ALGEBRA3IOSTREAMS
friend ostream& operator << (ostream& s, const vec4& v); // output to stream
friend istream& operator >> (istream& s, vec4& v); // input from strm.
#endif // ALGEBRA3IOSTREAMS
friend void swap(vec4& a, vec4& b); // swap v1 & v2
friend vec4 vec4min(const vec4& a, const vec4& b); // min(v1, v2)
friend vec4 vec4max(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 * (const mat4& a, const mat4& b); // matrix 4 product
};
/****************************************************************
* *
* 3x3 Matrix *
* *
****************************************************************/
class mat3
{
protected:
vec3 v[3];
public:
// Constructors
mat3();
mat3(const vec3& v0, const vec3& v1, const vec3& v2);
mat3(const double 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 double d ); // multiplication by a constant
mat3& operator /= ( const double d ); // division by a constant
vec3& operator [] ( int i); // indexing
const vec3& operator [] ( int i) const; // read-only indexing
// special functions
inline mat3 transpose() const; // transpose
mat3 inverse() const; // inverse
mat3& apply(V_FCT_PTR fct); // apply a func. to each element
// friends
friend mat3 operator - (const mat3& a); // -m1
friend mat3 operator + (const mat3& a, const mat3& b); // m1 + m2
friend mat3 operator - (const mat3& a, const mat3& b); // m1 - m2
friend mat3 operator * (const mat3& a, const mat3& b); // m1 * m2
friend mat3 operator * (const mat3& a, const double d); // m1 * 3.0
friend mat3 operator * (const double d, const mat3& a); // 3.0 * m1
friend mat3 operator / (const mat3& a, const double 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 ?
#ifdef ALGEBRA3IOSTREAMS
friend ostream& operator << (ostream& s, const mat3& m); // output to stream
friend istream& operator >> (istream& s, mat3& m); // input from strm.
#endif // ALGEBRA3IOSTREAMS
friend void swap(mat3& a, mat3& b); // swap m1 & m2
// necessary friend declarations
friend vec3 operator * (const mat3& a, const vec3& v); // linear transform
friend vec2 operator * (const mat3& a, const vec2& v); // linear transform
};
/****************************************************************
* *
* 4x4 Matrix *
* *
****************************************************************/
class mat4
{
protected:
vec4 v[4];
public:
// Constructors
mat4();
mat4(const vec4& v0, const vec4& v1, const vec4& v2, const vec4& v3);
mat4(const double d);
mat4(const mat4& m);
// 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 double d ); // multiplication by a constant
mat4& operator /= ( const double d ); // division by a constant
vec4& operator [] ( int i); // indexing
const vec4& operator [] ( int i) const; // read-only indexing
// special functions
inline mat4 transpose() const; // transpose
mat4 inverse() const; // inverse
mat4& apply(V_FCT_PTR fct); // apply a func. to each element
// friends
friend mat4 operator - (const mat4& a); // -m1
friend mat4 operator + (const mat4& a, const mat4& b); // m1 + m2
friend mat4 operator - (const mat4& a, const mat4& b); // m1 - m2
friend mat4 operator * (const mat4& a, const mat4& b); // m1 * m2
friend mat4 operator * (const mat4& a, const double d); // m1 * 4.0
friend mat4 operator * (const double d, const mat4& a); // 4.0 * m1
friend mat4 operator / (const mat4& a, const double 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 ?
#ifdef ALGEBRA3IOSTREAMS
friend ostream& operator << (ostream& s, const mat4& m); // output to stream
friend istream& operator >> (istream& s, mat4& m); // input from strm.
#endif // ALGEBRA3IOSTREAMS
friend void swap(mat4& a, mat4& b); // swap m1 & m2
// necessary friend declarations
inline friend vec4 operator * (const mat4& a, const vec4& v); // linear transform
friend vec3 operator * (const mat4& a, const vec3& v); // linear transform
};
/****************************************************************
* *
* 2D functions and 3D functions *
* *
****************************************************************/
inline mat3 identity2D(); // identity 2D
mat3 translation2D(const vec2& v); // translation 2D
mat3 rotation2D(const vec2& Center, const double angleDeg); // rotation 2D
mat3 scaling2D(const vec2& scaleVector); // scaling 2D
inline mat4 identity3D(); // identity 3D
mat4 translation3D(const vec3& v); // translation 3D
mat4 rotation3D(vec3 Axis, const double angleDeg);// rotation 3D
mat4 scaling3D(const vec3& scaleVector); // scaling 3D
mat4 perspective3D(const double d); // perspective 3D
//
// Implementation
//
/****************************************************************
* *
* vec2 Member functions *
* *
****************************************************************/
// CONSTRUCTORS
inline vec2::vec2() {}
inline vec2::vec2(const double x, const double y)
{ n[VX] = x; n[VY] = y; }
inline vec2::vec2(const double d)
{ n[VX] = n[VY] = d; }
inline vec2::vec2(const vec2& v)
{ n[VX] = v.n[VX]; n[VY] = v.n[VY]; }
inline 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]; };
inline 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;
}
}
// ASSIGNMENT OPERATORS
inline vec2& vec2::operator = (const vec2& v)
{ n[VX] = v.n[VX]; n[VY] = v.n[VY]; return *this; }
inline vec2& vec2::operator += ( const vec2& v )
{ n[VX] += v.n[VX]; n[VY] += v.n[VY]; return *this; }
inline vec2& vec2::operator -= ( const vec2& v )
{ n[VX] -= v.n[VX]; n[VY] -= v.n[VY]; return *this; }
inline vec2& vec2::operator *= ( const double d )
{ n[VX] *= d; n[VY] *= d; return *this; }
inline vec2& vec2::operator /= ( const double d )
{ double d_inv = 1./d; n[VX] *= d_inv; n[VY] *= d_inv; return *this; }
inline double& vec2::operator [] ( int i) {
assert(!(i < VX || i > VY)); // subscript check
return n[i];
}
inline double vec2::operator [] ( int i) const {
assert(!(i < VX || i > VY));
return n[i];
}
// SPECIAL FUNCTIONS
inline double vec2::length() const
{ return sqrt(length2()); }
inline double vec2::length2() const
{ return n[VX]*n[VX] + n[VY]*n[VY]; }
inline vec2& vec2::normalize() // it is up to caller to avoid divide-by-zero
{ *this /= length(); return *this; }
inline vec2& vec2::apply(V_FCT_PTR fct)
{ n[VX] = (*fct)(n[VX]); n[VY] = (*fct)(n[VY]); return *this; }
// FRIENDS
inline vec2 operator - (const vec2& a)
{ return vec2(-a.n[VX],-a.n[VY]); }
inline vec2 operator + (const vec2& a, const vec2& b)
{ return vec2(a.n[VX]+ b.n[VX], a.n[VY] + b.n[VY]); }
inline vec2 operator - (const vec2& a, const vec2& b)
{ return vec2(a.n[VX]-b.n[VX], a.n[VY]-b.n[VY]); }
inline vec2 operator * (const vec2& a, const double d)
{ return vec2(d*a.n[VX], d*a.n[VY]); }
inline vec2 operator * (const double d, const vec2& a)
{ return a*d; }
inline 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;
}
inline vec2 operator * (const vec2& v, const mat3& a)
{ return a.transpose() * v; }
inline double operator * (const vec2& a, const vec2& b)
{ return (a.n[VX]*b.n[VX] + a.n[VY]*b.n[VY]); }
inline vec2 operator / (const vec2& a, const double d)
{ double d_inv = 1./d; return vec2(a.n[VX]*d_inv, a.n[VY]*d_inv); }
inline 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]); }
inline int operator == (const vec2& a, const vec2& b)
{ return (a.n[VX] == b.n[VX]) && (a.n[VY] == b.n[VY]); }
inline int operator != (const vec2& a, const vec2& b)
{ return !(a == b); }
#ifdef ALGEBRA3IOSTREAMS
inline ostream& operator << (ostream& s, const vec2& v)
{ return s << "| " << v.n[VX] << ' ' << v.n[VY] << " |"; }
inline 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;
}
#endif // ALGEBRA3IOSTREAMS
inline void swap(vec2& a, vec2& b)
{ vec2 tmp(a); a = b; b = tmp; }
inline vec2 vec2min(const vec2& a, const vec2& b)
{ return vec2(MIN(a.n[VX], b.n[VX]), MIN(a.n[VY], b.n[VY])); }
inline vec2 vec2max(const vec2& a, const vec2& b)
{ return vec2(MAX(a.n[VX], b.n[VX]), MAX(a.n[VY], b.n[VY])); }
inline 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
inline vec3::vec3() {}
inline vec3::vec3(const double x, const double y, const double z)
{ n[VX] = x; n[VY] = y; n[VZ] = z; }
inline vec3::vec3(const double d)
{ n[VX] = n[VY] = n[VZ] = d; }
inline vec3::vec3(const vec3& v)
{ n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VZ]; }
inline vec3::vec3(const vec2& v)
{ n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = 1.0; }
inline vec3::vec3(const vec2& v, double d)
{ n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = d; }
inline 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]; }
inline 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
inline vec3& vec3::operator = (const vec3& v)
{ n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VZ]; return *this; }
inline vec3& vec3::operator += ( const vec3& v )
{ n[VX] += v.n[VX]; n[VY] += v.n[VY]; n[VZ] += v.n[VZ]; return *this; }
inline vec3& vec3::operator -= ( const vec3& v )
{ n[VX] -= v.n[VX]; n[VY] -= v.n[VY]; n[VZ] -= v.n[VZ]; return *this; }
inline vec3& vec3::operator *= ( const double d )
{ n[VX] *= d; n[VY] *= d; n[VZ] *= d; return *this; }
inline vec3& vec3::operator /= ( const double d )
{ double d_inv = 1./d; n[VX] *= d_inv; n[VY] *= d_inv; n[VZ] *= d_inv;
return *this; }
inline double& vec3::operator [] ( int i) {
assert(! (i < VX || i > VZ));
return n[i];
}
inline double vec3::operator [] ( int i) const {
assert(! (i < VX || i > VZ));
return n[i];
}
// SPECIAL FUNCTIONS
inline double vec3::length() const
{ return sqrt(length2()); }
inline double vec3::length2() const
{ return n[VX]*n[VX] + n[VY]*n[VY] + n[VZ]*n[VZ]; }
inline vec3& vec3::normalize() // it is up to caller to avoid divide-by-zero
{ *this /= length(); return *this; }
inline vec3& vec3::apply(V_FCT_PTR fct)
{ n[VX] = (*fct)(n[VX]); n[VY] = (*fct)(n[VY]); n[VZ] = (*fct)(n[VZ]);
return *this; }
// FRIENDS
inline vec3 operator - (const vec3& a)
{ return vec3(-a.n[VX],-a.n[VY],-a.n[VZ]); }
inline 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]); }
inline 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]); }
inline vec3 operator * (const vec3& a, const double d)
{ return vec3(d*a.n[VX], d*a.n[VY], d*a.n[VZ]); }
inline vec3 operator * (const double d, const vec3& a)
{ return a*d; }
inline vec3 operator * (const mat4& a, const vec3& v)
{ return a * vec4(v); }
inline vec3 operator * (const vec3& v, const mat4& a)
{ return a.transpose() * v; }
inline double 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]); }
inline vec3 operator / (const vec3& a, const double d)
{ double d_inv = 1./d; return vec3(a.n[VX]*d_inv, a.n[VY]*d_inv,
a.n[VZ]*d_inv); }
inline 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]);
}
inline 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]);
}
inline int operator != (const vec3& a, const vec3& b)
{ return !(a == b); }
#ifdef ALGEBRA3IOSTREAMS
inline ostream& operator << (ostream& s, const vec3& v)
{ return s << "| " << v.n[VX] << ' ' << v.n[VY] << ' ' << v.n[VZ] << " |"; }
inline 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;
}
#endif // ALGEBRA3IOSTREAMS
inline void swap(vec3& a, vec3& b)
{ vec3 tmp(a); a = b; b = tmp; }
inline vec3 vec3min(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])); }
inline vec3 vec3max(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])); }
inline 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
inline vec4::vec4() {}
inline vec4::vec4(const double x, const double y, const double z, const double w)
{ n[VX] = x; n[VY] = y; n[VZ] = z; n[VW] = w; }
inline vec4::vec4(const double d)
{ n[VX] = n[VY] = n[VZ] = n[VW] = d; }
inline 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]; }
inline vec4::vec4(const vec3& v)
{ n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VZ]; n[VW] = 1.0; }
inline vec4::vec4(const vec3& v, const double d)
{ n[VX] = v.n[VX]; n[VY] = v.n[VY]; n[VZ] = v.n[VZ]; n[VW] = d; }
// ASSIGNMENT OPERATORS
inline 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; }
inline 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; }
inline 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; }
inline vec4& vec4::operator *= ( const double d )
{ n[VX] *= d; n[VY] *= d; n[VZ] *= d; n[VW] *= d; return *this; }
inline vec4& vec4::operator /= ( const double d )
{ double d_inv = 1./d; n[VX] *= d_inv; n[VY] *= d_inv; n[VZ] *= d_inv;
n[VW] *= d_inv; return *this; }
inline double& vec4::operator [] ( int i) {
assert(! (i < VX || i > VW));
return n[i];
}
inline double vec4::operator [] ( int i) const {
assert(! (i < VX || i > VW));
return n[i];
}
// SPECIAL FUNCTIONS
inline double vec4::length() const
{ return sqrt(length2()); }
inline double vec4::length2() const
{ return n[VX]*n[VX] + n[VY]*n[VY] + n[VZ]*n[VZ] + n[VW]*n[VW]; }
inline vec4& vec4::normalize() // it is up to caller to avoid divide-by-zero
{ *this /= length(); return *this; }
inline 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; }
// FRIENDS
inline vec4 operator - (const vec4& a)
{ return vec4(-a.n[VX],-a.n[VY],-a.n[VZ],-a.n[VW]); }
inline 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]); }
inline 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]); }
inline vec4 operator * (const vec4& a, const double d)
{ return vec4(d*a.n[VX], d*a.n[VY], d*a.n[VZ], d*a.n[VW] ); }
inline vec4 operator * (const double d, const vec4& a)
{ return a*d; }
inline 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 // (i)
}
inline vec4 operator * (const vec4& v, const mat4& a)
{ return a.transpose() * v; }
inline double 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]); }
inline vec4 operator / (const vec4& a, const double d)
{ double d_inv = 1./d; return vec4(a.n[VX]*d_inv, a.n[VY]*d_inv, a.n[VZ]*d_inv,
a.n[VW]*d_inv); }
inline 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]); }
inline int operator != (const vec4& a, const vec4& b)
{ return !(a == b); }
#ifdef ALGEBRA3IOSTREAMS
inline ostream& operator << (ostream& s, const vec4& v)
{ return s << "| " << v.n[VX] << ' ' << v.n[VY] << ' ' << v.n[VZ] << ' '
<< v.n[VW] << " |"; }
inline stream& 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;
}
#endif // ALGEBRA3IOSTREAMS
inline void swap(vec4& a, vec4& b)
{ vec4 tmp(a); a = b; b = tmp; }
inline vec4 vec4min(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])); }
inline vec4 vec4max(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])); }
inline 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
inline mat3::mat3() {}
inline mat3::mat3(const vec3& v0, const vec3& v1, const vec3& v2)
{ v[0] = v0; v[1] = v1; v[2] = v2; }
inline mat3::mat3(const double d)
{ v[0] = v[1] = v[2] = vec3(d); }
inline mat3::mat3(const mat3& m)
{ v[0] = m.v[0]; v[1] = m.v[1]; v[2] = m.v[2]; }
// ASSIGNMENT OPERATORS
inline mat3& mat3::operator = ( const mat3& m )
{ v[0] = m.v[0]; v[1] = m.v[1]; v[2] = m.v[2]; return *this; }
inline mat3& mat3::operator += ( const mat3& m )
{ v[0] += m.v[0]; v[1] += m.v[1]; v[2] += m.v[2]; return *this; }
inline mat3& mat3::operator -= ( const mat3& m )
{ v[0] -= m.v[0]; v[1] -= m.v[1]; v[2] -= m.v[2]; return *this; }
inline mat3& mat3::operator *= ( const double d )
{ v[0] *= d; v[1] *= d; v[2] *= d; return *this; }
inline mat3& mat3::operator /= ( const double d )
{ v[0] /= d; v[1] /= d; v[2] /= d; return *this; }
inline vec3& mat3::operator [] ( int i) {
assert(! (i < VX || i > VZ));
return v[i];
}
inline const vec3& mat3::operator [] ( int i) const {
assert(!(i < VX || i > VZ));
return v[i];
}
// SPECIAL FUNCTIONS
inline mat3 mat3::transpose() const {
return mat3(vec3(v[0][0], v[1][0], v[2][0]),
vec3(v[0][1], v[1][1], v[2][1]),
vec3(v[0][2], v[1][2], v[2][2]));
}
inline mat3 mat3::inverse() const // Gauss-Jordan elimination with partial pivoting
{
mat3 a(*this), // As a evolves from original mat into identity
b(identity2D()); // b evolves from identity into inverse(a)
int i, j, i1;
// Loop over cols of a from left to right, eliminating above and below diag
for (j=0; j<3; j++) { // Find largest pivot in column j among rows j..2
i1 = j; // Row with largest pivot candidate
for (i=j+1; i<3; i++)
if (fabs(a.v[i].n[j]) > fabs(a.v[i1].n[j]))
i1 = i;
// Swap rows i1 and j in a and b to put pivot on diagonal
swap(a.v[i1], a.v[j]);
swap(b.v[i1], b.v[j]);
// Scale row j to have a unit diagonal
if (a.v[j].n[j]==0.)
ALGEBRA_ERROR("mat3::inverse: singular matrix; can't invert\n")
b.v[j] /= a.v[j].n[j];
a.v[j] /= a.v[j].n[j];
// Eliminate off-diagonal elems in col j of a, doing identical ops to b
for (i=0; i<3; i++)
if (i!=j) {
b.v[i] -= a.v[i].n[j]*b.v[j];
a.v[i] -= a.v[i].n[j]*a.v[j];
}
}
return b;
}
inline mat3& mat3::apply(V_FCT_PTR fct) {
v[VX].apply(fct);
v[VY].apply(fct);
v[VZ].apply(fct);
return *this;
}
// FRIENDS
inline mat3 operator - (const mat3& a)
{ return mat3(-a.v[0], -a.v[1], -a.v[2]); }
inline mat3 operator + (const mat3& a, const mat3& b)
{ return mat3(a.v[0] + b.v[0], a.v[1] + b.v[1], a.v[2] + b.v[2]); }
inline mat3 operator - (const mat3& a, const mat3& b)
{ return mat3(a.v[0] - b.v[0], a.v[1] - b.v[1], a.v[2] - b.v[2]); }
inline mat3 operator * (const mat3& a, const mat3& b) {
#define ROWCOL(i, j) \
a.v[i].n[0]*b.v[0][j] + a.v[i].n[1]*b.v[1][j] + a.v[i].n[2]*b.v[2][j]
return mat3(vec3(ROWCOL(0,0), ROWCOL(0,1), ROWCOL(0,2)),
vec3(ROWCOL(1,0), ROWCOL(1,1), ROWCOL(1,2)),
vec3(ROWCOL(2,0), ROWCOL(2,1), ROWCOL(2,2)));
#undef ROWCOL // (i, j)
}
inline mat3 operator * (const mat3& a, const double d)
{ return mat3(a.v[0] * d, a.v[1] * d, a.v[2] * d); }
inline mat3 operator * (const double d, const mat3& a)
{ return a*d; }
inline mat3 operator / (const mat3& a, const double d)
{ return mat3(a.v[0] / d, a.v[1] / d, a.v[2] / d); }
inline int operator == (const mat3& a, const mat3& b)
{ return (a.v[0] == b.v[0]) && (a.v[1] == b.v[1]) && (a.v[2] == b.v[2]); }
inline int operator != (const mat3& a, const mat3& b)
{ return !(a == b); }
#ifdef ALGEBRA3IOSTREAMS
inline ostream& operator << (ostream& s, const mat3& m)
{ return s << m.v[VX] << '\n' << m.v[VY] << '\n' << m.v[VZ]; }
inline stream& operator >> (istream& s, mat3& m) {
mat3 m_tmp;
s >> m_tmp[VX] >> m_tmp[VY] >> m_tmp[VZ];
if (s)
m = m_tmp;
return s;
}
#endif // ALGEBRA3IOSTREAMS
inline void swap(mat3& a, mat3& b)
{ mat3 tmp(a); a = b; b = tmp; }
/****************************************************************
* *
* mat4 member functions *
* *
****************************************************************/
// CONSTRUCTORS
inline mat4::mat4() {}
inline mat4::mat4(const vec4& v0, const vec4& v1, const vec4& v2, const vec4& v3)
{ v[0] = v0; v[1] = v1; v[2] = v2; v[3] = v3; }
inline mat4::mat4(const double d)
{ v[0] = v[1] = v[2] = v[3] = vec4(d); }
inline mat4::mat4(const mat4& m)
{ v[0] = m.v[0]; v[1] = m.v[1]; v[2] = m.v[2]; v[3] = m.v[3]; }
// ASSIGNMENT OPERATORS
inline mat4& mat4::operator = ( const mat4& m )
{ v[0] = m.v[0]; v[1] = m.v[1]; v[2] = m.v[2]; v[3] = m.v[3];
return *this; }
inline mat4& mat4::operator += ( const mat4& m )
{ v[0] += m.v[0]; v[1] += m.v[1]; v[2] += m.v[2]; v[3] += m.v[3];
return *this; }
inline mat4& mat4::operator -= ( const mat4& m )
{ v[0] -= m.v[0]; v[1] -= m.v[1]; v[2] -= m.v[2]; v[3] -= m.v[3];
return *this; }
inline mat4& mat4::operator *= ( const double d )
{ v[0] *= d; v[1] *= d; v[2] *= d; v[3] *= d; return *this; }
inline mat4& mat4::operator /= ( const double d )
{ v[0] /= d; v[1] /= d; v[2] /= d; v[3] /= d; return *this; }
inline vec4& mat4::operator [] ( int i) {
assert(! (i < VX || i > VW));
return v[i];
}
inline const vec4& mat4::operator [] ( int i) const {
assert(! (i < VX || i > VW));
return v[i];
}
// SPECIAL FUNCTIONS;
inline mat4 mat4::transpose() const{
return mat4(vec4(v[0][0], v[1][0], v[2][0], v[3][0]),
vec4(v[0][1], v[1][1], v[2][1], v[3][1]),
vec4(v[0][2], v[1][2], v[2][2], v[3][2]),
vec4(v[0][3], v[1][3], v[2][3], v[3][3]));
}
inline mat4 mat4::inverse() const // Gauss-Jordan elimination with partial pivoting
{
mat4 a(*this), // As a evolves from original mat into identity
b(identity3D()); // b evolves from identity into inverse(a)
int i, j, i1;
// Loop over cols of a from left to right, eliminating above and below diag
for (j=0; j<4; j++) { // Find largest pivot in column j among rows j..3
i1 = j; // Row with largest pivot candidate
for (i=j+1; i<4; i++)
if (fabs(a.v[i].n[j]) > fabs(a.v[i1].n[j]))
i1 = i;
// Swap rows i1 and j in a and b to put pivot on diagonal
swap(a.v[i1], a.v[j]);
swap(b.v[i1], b.v[j]);
// Scale row j to have a unit diagonal
if (a.v[j].n[j]==0.)
ALGEBRA_ERROR("mat4::inverse: singular matrix; can't invert\n");
b.v[j] /= a.v[j].n[j];
a.v[j] /= a.v[j].n[j];
// Eliminate off-diagonal elems in col j of a, doing identical ops to b
for (i=0; i<4; i++)
if (i!=j) {
b.v[i] -= a.v[i].n[j]*b.v[j];
a.v[i] -= a.v[i].n[j]*a.v[j];
}
}
return b;
}
inline mat4& mat4::apply(V_FCT_PTR fct)
{ v[VX].apply(fct); v[VY].apply(fct); v[VZ].apply(fct); v[VW].apply(fct);
return *this; }
// FRIENDS
inline mat4 operator - (const mat4& a)
{ return mat4(-a.v[0], -a.v[1], -a.v[2], -a.v[3]); }
inline mat4 operator + (const mat4& a, const mat4& b)
{ return mat4(a.v[0] + b.v[0], a.v[1] + b.v[1], a.v[2] + b.v[2],
a.v[3] + b.v[3]);
}
inline mat4 operator - (const mat4& a, const mat4& b)
{ return mat4(a.v[0] - b.v[0], a.v[1] - b.v[1], a.v[2] - b.v[2], a.v[3] - b.v[3]); }
inline mat4 operator * (const mat4& a, const mat4& b) {
#define ROWCOL(i, j) a.v[i].n[0]*b.v[0][j] + a.v[i].n[1]*b.v[1][j] + \
a.v[i].n[2]*b.v[2][j] + a.v[i].n[3]*b.v[3][j]
return mat4(
vec4(ROWCOL(0,0), ROWCOL(0,1), ROWCOL(0,2), ROWCOL(0,3)),
vec4(ROWCOL(1,0), ROWCOL(1,1), ROWCOL(1,2), ROWCOL(1,3)),
vec4(ROWCOL(2,0), ROWCOL(2,1), ROWCOL(2,2), ROWCOL(2,3)),
vec4(ROWCOL(3,0), ROWCOL(3,1), ROWCOL(3,2), ROWCOL(3,3))
);
}
inline mat4 operator * (const mat4& a, const double d)
{ return mat4(a.v[0] * d, a.v[1] * d, a.v[2] * d, a.v[3] * d); }
inline mat4 operator * (const double d, const mat4& a)
{ return a*d; }
inline mat4 operator / (const mat4& a, const double d)
{ return mat4(a.v[0] / d, a.v[1] / d, a.v[2] / d, a.v[3] / d); }
inline int operator == (const mat4& a, const mat4& b)
{ return ((a.v[0] == b.v[0]) && (a.v[1] == b.v[1]) && (a.v[2] == b.v[2]) &&
(a.v[3] == b.v[3])); }
inline int operator != (const mat4& a, const mat4& b)
{ return !(a == b); }
#ifdef ALGEBRA3IOSTREAMS
inline ostream& operator << (ostream& s, const mat4& m)
{ return s << m.v[VX] << '\n' << m.v[VY] << '\n' << m.v[VZ] << '\n' << m.v[VW]; }
inline istream& operator >> (istream& s, mat4& m)
{
mat4 m_tmp;
s >> m_tmp[VX] >> m_tmp[VY] >> m_tmp[VZ] >> m_tmp[VW];
if (s)
m = m_tmp;
return s;
}
#endif // ALGEBRA3IOSTREAMS
inline void swap(mat4& a, mat4& b)
{ mat4 tmp(a); a = b; b = tmp; }
/****************************************************************
* *
* 2D functions and 3D functions *
* *
****************************************************************/
inline mat3 identity2D()
{ return mat3(vec3(1.0, 0.0, 0.0),
vec3(0.0, 1.0, 0.0),
vec3(0.0, 0.0, 1.0)); }
inline mat3 translation2D(const vec2& v)
{ return mat3(vec3(1.0, 0.0, v[VX]),
vec3(0.0, 1.0, v[VY]),
vec3(0.0, 0.0, 1.0)); }
inline mat3 rotation2D(const vec2& Center, const double angleDeg) {
double angleRad = radians(angleDeg),
c = cos(angleRad),
s = sin(angleRad);
return mat3(vec3(c, -s, Center[VX] * (1.0-c) + Center[VY] * s),
vec3(s, c, Center[VY] * (1.0-c) - Center[VX] * s),
vec3(0.0, 0.0, 1.0));
}
inline mat3 scaling2D(const vec2& scaleVector)
{ return mat3(vec3(scaleVector[VX], 0.0, 0.0),
vec3(0.0, scaleVector[VY], 0.0),
vec3(0.0, 0.0, 1.0)); }
inline mat4 identity3D()
{ return mat4(vec4(1.0, 0.0, 0.0, 0.0),
vec4(0.0, 1.0, 0.0, 0.0),
vec4(0.0, 0.0, 1.0, 0.0),
vec4(0.0, 0.0, 0.0, 1.0)); }
inline mat4 translation3D(const vec3& v)
{ return mat4(vec4(1.0, 0.0, 0.0, v[VX]),
vec4(0.0, 1.0, 0.0, v[VY]),
vec4(0.0, 0.0, 1.0, v[VZ]),
vec4(0.0, 0.0, 0.0, 1.0)); }
inline mat4 rotation3D(vec3 Axis, const double angleDeg) {
double angleRad = radians(angleDeg),
c = cos(angleRad),
s = sin(angleRad),
t = 1.0 - c;
Axis.normalize();
return mat4(vec4(t * Axis[VX] * Axis[VX] + c,
t * Axis[VX] * Axis[VY] - s * Axis[VZ],
t * Axis[VX] * Axis[VZ] + s * Axis[VY],
0.0),
vec4(t * Axis[VX] * Axis[VY] + s * Axis[VZ],
t * Axis[VY] * Axis[VY] + c,
t * Axis[VY] * Axis[VZ] - s * Axis[VX],
0.0),
vec4(t * Axis[VX] * Axis[VZ] - s * Axis[VY],
t * Axis[VY] * Axis[VZ] + s * Axis[VX],
t * Axis[VZ] * Axis[VZ] + c,
0.0),
vec4(0.0, 0.0, 0.0, 1.0));
}
inline mat4 scaling3D(const vec3& scaleVector)
{ return mat4(vec4(scaleVector[VX], 0.0, 0.0, 0.0),
vec4(0.0, scaleVector[VY], 0.0, 0.0),
vec4(0.0, 0.0, scaleVector[VZ], 0.0),
vec4(0.0, 0.0, 0.0, 1.0)); }
inline mat4 perspective3D(const double d)
{ return mat4(vec4(1.0, 0.0, 0.0, 0.0),
vec4(0.0, 1.0, 0.0, 0.0),
vec4(0.0, 0.0, 1.0, 0.0),
vec4(0.0, 0.0, 1.0/d, 0.0)); }
#endif // ALGEBRA3H
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