if ( i != j ) {
t = x [i][j];
x [i][j] = x [j][i];
x [j][i] = t;
}
}
Matrix& Matrix :: operator += ( const Matrix& A )
{
int j;
for ( int i = 0; i < 4; i++ )
for ( j = 0; j < 4; j++ )
x [i][j] += A.x [i][j];
return *this;
}
Matrix& Matrix :: operator -= ( const Matrix& A )
{
int j;
for ( int i = 0; i < 4; i++ )
for ( j = 0; j < 4; j++ )
x [i][j] -= A.x [i][j];
return *this;
}
Matrix& Matrix :: operator *= ( double v )
{
int j;
for ( int i = 0; i < 4; i++ )
for ( j = 0; j < 4; j++ )
x [i][j] *= v;
return *this;
}
Matrix& Matrix :: operator *= ( const Matrix& A )
{
Matrix res = *this;
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 += res.x [i][k] * A.x [k][j];
x [i][j] = sum;
}
return *this;
}
Matrix operator + ( const Matrix& A, const Matrix& B )
{
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] + B.x [i][j];
return res;
}
Matrix operator - ( const Matrix& A, const Matrix& B )
{
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] - B.x [i][j];
return res;
}
Matrix operator * ( const Matrix& A, const Matrix& B )
{
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 methodsPolygon :: 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 ()
{
Matrix m = MirrorY();
for ( int i = 0; i < PointNumber; i++ )
Point[i] = m * Point[i];
Center = m * Center;
Normal = m * Normal;
}
void Polygon :: PolyMirrorZ ()
{
Matrix m = MirrorZ();
for ( int i = 0; i < PointNumber; i++ )
Point[i] = m * Point[i];
Center = m * Center;
Normal = m * Normal;
}
void Polygon :: Draw ( const Vector& PrCenter )
{
int VisPoint[MaxPoints * 2], k = 0;
for ( int i = 0; i < PointNumber; i++ ) {
double Coeff = 1 / ( 1 - Point[i].z / PrCenter.z );
VisPoint[k++] = ( int ) Point[i].x * Coeff + 320;
VisPoint[k++] = ( int ) -Point[i].y * Coeff + 175;
}
setcolor ( Color );
setfillstyle ( 1, Color );
fillpoly ( PointNumber, VisPoint );
}
// GrObject's methods
GrObject :: GrObject ( Polygon * FacetArr, int FacetNum, const Vector& Crds )
{
if ( FacetNum <= MaxFacets )
{
FacetNumber = FacetNum;
Facet = FacetArr;
Coords = Crds;
}
}
void GrObject :: Move ( const Vector& v )
{
for ( int i = 0; i < FacetNumber; i++ )
Facet[i].Move ( v );
Coords = Translate ( v ) * Coords;
}
void GrObject :: Rotate ( double Alfa, double Beta, double Gamma )
{
for ( int i = 0; i < FacetNumber; i++ )
Facet[i].Rotate ( Alfa, Beta, Gamma );
Coords = RotateX ( Alfa ) * RotateY ( Beta ) * RotateZ ( Gamma ) * Coords;
}
void GrObject :: ObjScale ( const Vector& v )
{
for ( int i = 0; i < FacetNumber; i++ )
Facet[i].PolyScale ( v );
Coords = Scale ( v ) * Coords;
}
void GrObject :: ObjMirrorX ()
{
Matrix m = MirrorX();
for ( int i = 0; i < FacetNumber; i++ )
Facet[i].PolyMirrorX ();
Coords = m * Coords;
}
void GrObject :: ObjMirrorY ()
{
Matrix m = MirrorY();
for ( int i = 0; i < FacetNumber; i++ )
Facet[i].PolyMirrorY ();
Coords = m * Coords;
}
void GrObject :: ObjMirrorZ ()
{
Matrix m = MirrorZ();
for ( int i = 0; i < FacetNumber; i++ )
Facet[i].PolyMirrorZ ();
Coords = m * Coords;
}
// Space's methods
Space :: Space ( GrObject * Obj, int ObjectNum )
{
if ( ObjectNum <= MaxObjects )
{
ObjectNumber = ObjectNum;
for ( int i = 0; i < ObjectNumber; i++ )
Object[i] = &Obj[i];
};
}
void Space :: Add ( GrObject * Obj )
{
if ( ObjectNumber < MaxObjects ) Object [ObjectNumber++] = Obj;
}
void Space :: Draw ( const Vector& PrCenter )
{
}
// Other functions
int IsVisible ( const Polygon& Poly, const Vector& PrCenter )
{
return ( Poly.Normal & ( PrCenter - Poly.Point[0] )) < 0 || Poly.TwoSides;
}
void DrawBSPTree ( BSPNode * Tree, const Vector& PrCntr )
{
if (( Tree -> Poly -> Normal & PrCntr ) > Tree -> d ) {
if ( Tree -> Right != NULL ) DrawBSPTree ( Tree -> Right, PrCntr );
Tree -> Poly -> Draw ( PrCntr );
if ( Tree -> Left != NULL ) DrawBSPTree ( Tree -> Left, PrCntr );
}
else {
if ( Tree -> Left != NULL ) DrawBSPTree ( Tree -> Left, PrCntr );
Tree -> Poly -> Draw ( PrCntr );
if ( Tree -> Right != NULL ) DrawBSPTree ( Tree -> Right, PrCntr );
}
}
Далее представлена демонстрационная программа, которая выполняет все вышеперечисленные операции с тетраэдром.
//Файл 3dgame.cpp
#include <dos.h>#include <graphics.h>#include <math.h>
#include <stdio.h>
#include <conio.h>
#include <stdlib.h>
#include "3dworks.h"
void DrawObject ( GrObject* Obj, const Vector& v )
{
for ( int i = 0; i < Obj->FacetNumber; i++ )
if ( IsVisible ( Obj->Facet[i], v )) Obj->Facet[i].Draw ( v );
}
main ()
{
Vector Poly1[3], Poly2[3], Poly3[3], Poly4[3];
Polygon O[4];
Vector A ( -50, 0, 0 ),
B ( 0, 0, 50 ),
C ( 50, 0, 0 ),
D ( 0, 100, 0 ),
PrCenter ( 0, 0, 1000 );
Poly1[0] = A; Poly2[0] = B;
Poly1[1] = D; Poly2[1] = D;
Poly1[2] = B; Poly2[2] = C;
Poly3[0] = C; Poly4[0] = C;
Poly3[1] = A; Poly4[1] = D;
Poly3[2] = B; Poly4[2] = A;
Polygon * P1 = new Polygon ( Poly1, 3, 11, OneSd );
Polygon * P2 = new Polygon ( Poly2, 3, 12, OneSd );
Polygon * P3 = new Polygon ( Poly3, 3, 13, OneSd );
Polygon * P4 = new Polygon ( Poly4, 3, 14, OneSd );
O[0] = *P1; O[1] = *P2;
O[2] = *P3; O[3] = *P4;
delete P1; delete P2;
delete P3; delete P4;
GrObject * Obj = new GrObject ( O, 4, Vector ( 0 ) );
double fi = 0.1, psi = 0.1, step = 0.1;
int ch = 0, Page = 3;
int driver = DETECT, mode, res;
initgraph ( &driver, &mode, "" );
if ( ( res = graphresult () ) != grOk ) {
printf ( "\nGraphics error: %s\n", grapherrormsg ( res ) );
exit ( 1 );
}
setgraphmode ( 1 );
DrawObject ( Obj, PrCenter );
do {
setactivepage ( Page % 2 );
clearviewport ();
if ( kbhit ())
{
switch ( ch = getch() ) {
case '+': Obj->ObjScale ((1.1,1.1,1.1)); break;
case '-': Obj->ObjScale ((0.9,0.9,0.9)); break;
case 'x': Obj->ObjMirrorX (); break;
case 'y': Obj->ObjMirrorY (); break;
case 'z': Obj->ObjMirrorZ (); break;
};
if ( ch == 0 )
{
switch ( ch = getch () ) {
case 72 : fi -= step; break;
case 80 : fi += step; break;
case 75 : psi += step; break;
case 77 : psi -= step; break;
};
};
};
Obj->Rotate ( fi, psi, 0 );
DrawObject ( Obj, PrCenter );
setvisualpage ( Page++ % 2 );
if ( fi == 0 && psi == 0 ) while ( !kbhit ());
} while ( ch != 27 );
delete Obj;
closegraph ();
}