{

Matrix res;

int j;

for ( int i = 0; i < 4; i++ )

for ( j = 0; j < 4; j++ ) {

double sum = 0;

for ( int k = 0; k < 4; k++ )

sum += A.x [i][k] * B.x [k][j];

res.x [i][j] = sum;

}

return res;

}

Matrix operator * ( const Matrix& A, double v )

{

Matrix res;

int j;

for ( int i = 0; i < 4; i++ )

for ( j = 0; j < 4; j++ )

res.x [i][j] = A.x [i][j] * v;

return res;

}

Vector operator * ( const Matrix& M, const Vector& v )

{

Vector res;

res.x = v.x * M.x [0][0] + v.y * M.x [1][0] + v.z * M.x [2][0] + M.x [3][0];

res.y = v.x * M.x [0][1] + v.y * M.x [1][1] + v.z * M.x [2][1] + M.x [3][1];

res.z = v.x * M.x [0][2] + v.y * M.x [1][2] + v.z * M.x [2][2] + M.x [3][2];

double denom = v.x * M.x [0][3] + v.y * M.x [1][3] +

v.z * M.x [2][3] + M.x[3][3];

if ( denom != 1.0 )

res /= denom;

return res;

}

Matrix Translate ( const Vector& Loc )

{

Matrix res ( 1 );

res.x [3][0] = Loc.x;

res.x [3][1] = Loc.y;

res.x [3][2] = Loc.z;

return res;

};

Matrix Scale ( const Vector& v )

{

Matrix res ( 1 );

res.x [0][0] = v.x;

res.x [1][1] = v.y;

res.x [2][2] = v.z;

return res;

};

Matrix RotateX ( double Angle )

{

Matrix res ( 1 );

double Cosine = cos ( Angle );

double Sine = sin ( Angle );

res.x [1][1] = Cosine;

res.x [2][1] = - Sine;

res.x [1][2] = Sine;

res.x [2][2] = Cosine;

return res;

};

Matrix RotateY ( double Angle )

{

Matrix res ( 1 );

double Cosine = cos ( Angle );

double Sine = sin ( Angle );

res.x [0][0] = Cosine;

res.x [2][0] = - Sine;

res.x [0][2] = Sine;

res.x [2][2] = Cosine;

return res;

};

Matrix RotateZ ( double Angle )

{

Matrix res ( 1 );

double Cosine = cos ( Angle );

double Sine = sin ( Angle );

res.x [0][0] = Cosine;

res.x [1][0] = - Sine;

res.x [0][1] = Sine;

res.x [1][1] = Cosine;

return res;

};

Matrix Rotate ( const Vector& axis, double angle )

{

Matrix res ( 1 );

double Cosine = cos ( angle );

double Sine = sin ( angle );

res.x [0][0] = axis.x * axis.x + ( 1 - axis.x * axis.x ) * Cosine;

res.x [0][1] = axis.x * axis.y * ( 1 - Cosine ) + axis.z * Sine;

res.x [0][2] = axis.x * axis.z * ( 1 - Cosine ) - axis.y * Sine;

res.x [0][3] = 0;

res.x [1][0] = axis.x * axis.y * ( 1 - Cosine ) - axis.z * Sine;

res.x [1][1] = axis.y * axis.y + ( 1 - axis.y * axis.y ) * Cosine;

res.x [1][2] = axis.y * axis.z * ( 1 - Cosine ) + axis.x * Sine;

res.x [1][3] = 0;

res.x [2][0] = axis.x * axis.z * ( 1 - Cosine ) + axis.y * Sine;

res.x [2][1] = axis.y * axis.z * ( 1 - Cosine ) - axis.x * Sine;

res.x [2][2] = axis.z * axis.z + ( 1 - axis.z * axis.z ) * Cosine;

res.x [2][3] = 0;

res.x [3][0] = 0;

res.x [3][1] = 0;

res.x [3][2] = 0;

res.x [3][3] = 1;

return res;

};

Matrix MirrorX ()

{

Matrix res ( 1 );

res.x [0][0] = -1;

return res;

};

Matrix MirrorY ()

{

Matrix res ( 1 );

res.x [1][1] = -1;

return res;

};

Matrix MirrorZ ()

{

Matrix res ( 1 );

res.x [2][2] = -1;

return res;

}

В следующей библиотеке была реализована работа с трехмерными объектами: гранью, графическим объектом и пространством. Реализованы следующие возможности:

- поворот объектов вокруг координатных осей;

- зеркальное отображение объектов по отношению к координатным осям;

- центральное и параллельное проектирование;

- масштабирование объектов;

- удаление невидимых поверхностей;

- перемещение объектов в пространстве.

//Файл 3dworks.h

#ifndef 3DWORKS

#define 3DWORKS

#include <graphics.h>

#include <stdlib.h>

#include "vector.h"

#include "matrix.h"

#define OneSd 0

#define TwoSds 1

#define MaxPoints 10

#define MaxFacets 10

#define MaxObjects 10

class Polygon

{

public:

int PointNumber;

Vector * Point;

Vector Normal;

Vector Center;

int Color;

int TwoSides;

Polygon () {};

Polygon ( Vector *, int, int, int );

void Draw ( const Vector& );

void Move ( const Vector& );

void Rotate ( double, double, double );

void PolyScale ( const Vector& );

void PolyMirrorX ();

void PolyMirrorY ();

void PolyMirrorZ ();

};

class GrObject

{

public:

int FacetNumber;

Polygon * Facet;

Vector Coords;

GrObject () {};

GrObject ( Polygon *, int, const Vector& );

void Move ( const Vector& );

void Rotate ( double, double, double );

void ObjScale ( const Vector& );

void ObjMirrorX ();

void ObjMirrorY ();

void ObjMirrorZ ();

};

struct BSPNode

{

Polygon * Poly;

double d;

BSPNode * Left;

BSPNode * Right;

};

class Space

{

public:

int ObjectNumber;

GrObject * Object [MaxObjects];

Space () { ObjectNumber = 0; };

Space ( GrObject *, int );

void Add ( GrObject * );

void Draw ( const Vector& );

};

int IsVisible ( const Polygon&, const Vector& );

void DrawBSPTree ( BSPNode *, const Vector& );

#endif

//----------------------------------------------------------------------------

//Файл 3dworks.cpp

#include "3dworks.h"

// Polygon's methods

Polygon :: Polygon ( Vector * PointArr, int PointNum, int Col, int TS )

{

if ( PointNum <= MaxPoints )

{

PointNumber = PointNum;

Point = PointArr;

Color = Col;

TwoSides = TS;

Normal = Normalize (

( Point [1] - Point [0] ) ^ ( Point [PointNumber-1] - Point [0] ));

Center = 0;

for ( int i = 0; i < PointNumber; i++ )

Center += Point[i];

Center /= PointNumber;

}

}

void Polygon :: Move ( const Vector& v )

{

Matrix m = Translate ( v );

for ( int i = 0; i < PointNumber; i++ )

Point[i] = m * Point[i];

Center = m * Center;

}

void Polygon :: Rotate ( double Alfa, double Beta, double Gamma )

{

Matrix m = RotateX ( Alfa ) * RotateY ( Beta ) * RotateZ ( Gamma );

for ( int i = 0; i < PointNumber; i++ )

Point[i] = m * Point[i];

Normal = m * Normal;

Center = m * Center;

}

void Polygon :: PolyScale ( const Vector& v )

{

Matrix m = Scale ( v );

for ( int i = 0; i < PointNumber; i++ )

Point[i] = m * Point[i];

Center = m * Center;

}

void Polygon :: PolyMirrorX ()

{

Matrix m = MirrorX();

for ( int i = 0; i < PointNumber; i++ )

Point[i] = m * Point[i];

Center = m * Center;

Normal = m * Normal;

}

void Polygon :: PolyMirrorY ()