Program to draw a Sphere using Parametric Equations

``` # include <iostream.h>
# include <graphics.h>
# include    <conio.h>
# include     <math.h>

# define  f                 0.3
# define  projection_angle   45

void show_screen( );

void Sphere(const int,const int,const int,const int);

void get_projected_point(double&,double&,double&);
void multiply_matrices(const double[4],const double[4][4],double[4]);

int main( )
{
int driver=VGA;
int mode=VGAHI;

int x=0;
int y=0;
int z=0;
int r=0;

do
{
show_screen( );

gotoxy(8,10);
cout<<\"Coordinates of Central Point - (x,y,z) :\";

gotoxy(8,11);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

gotoxy(12,13);
cout<<\"Enter the value of x = \";
cin>>x;

gotoxy(12,15);
cout<<\"Enter the value of y = \";
cin>>y;

gotoxy(12,17);
cout<<\"Enter the value of z = \";
cin>>z;

gotoxy(8,21);
cout<<\"Radius of the Sphere - r :\";

gotoxy(8,22);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

gotoxy(12,24);
cout<<\"Enter the value of r = \";
cin>>r;

initgraph(&driver,&mode,\"..\\\\Bgi\");

setcolor(15);
Sphere(x,y,z,r);

setcolor(15);
outtextxy(110,460,\"Press <Enter> to continue or any other key to exit.\");

int key=int(getch( ));

if(key!=13)
break;
}
while(1);

return 0;
}

//-----------------------------  Sphere( )  -----------------------------//

void Sphere(const int _x,const int _y,const int _z,const int r)
{
double x;
double y;
double z;

for(float u=0;u<=1;u+=0.0005)
{
for(float v=0;v<=1;v+=0.05)
{
x=((r*cosl((u*M_PI))*cosl((v*2*M_PI)))+_x);
y=((r*cosl((u*M_PI))*sinl((v*2*M_PI)))+_y);
z=((r*sinl((u*M_PI)))+_z);

get_projected_point(x,y,z);

putpixel(int(x+0.5),int(y+0.5),15);
}
}

for(float v=0;v<=1;v+=0.0005)
{
for(float u=0;u<=1;u+=0.05)
{
x=((r*cosl((u*M_PI))*cosl((v*2*M_PI)))+_x);
y=((r*cosl((u*M_PI))*sinl((v*2*M_PI)))+_y);
z=((r*sinl((u*M_PI)))+_z);

get_projected_point(x,y,z);

putpixel(int(x+0.5),int(y+0.5),15);
}
}
}

/************************************************************************/
//---------------------  get_projected_point( )  -----------------------//
/************************************************************************/

void get_projected_point(double& x,double& y,double& z)
{
double fcos0=(f*cos(projection_angle*(M_PI/180)));
double fsin0=(f*sin(projection_angle*(M_PI/180)));

double Par_v[4][4]={
{1,0,0,0},
{0,1,0,0},
{fcos0,fsin0,0,0},
{0,0,0,1}
};

double xy[4]={x,y,z,1};
double new_xy[4]={0};

multiply_matrices(xy,Par_v,new_xy);

x=new_xy[0];
y=new_xy[1];
z=new_xy[2];
}

/************************************************************************/
//----------------------  multiply_matrices( )  ------------------------//
/************************************************************************/

void multiply_matrices(const double matrix_1[4],
const double matrix_2[4][4],double matrix_3[4])
{
for(int count_1=0;count_1<4;count_1++)
{
for(int count_2=0;count_2<4;count_2++)
matrix_3[count_1]+=
(matrix_1[count_2]*matrix_2[count_2][count_1]);
}
}

//--------------------------  show_screen( )  ---------------------------//

void show_screen( )
{
restorecrtmode( );
clrscr( );
textmode(C4350);

cprintf(\"\\n********************************************************************************\");
cprintf(\"*-********************************-          -********************************-*\");
cprintf(\"*---------------------------------- \");

textbackground(1);
cprintf(\" Sphere \");
textbackground(8);

cprintf(\" ----------------------------------*\");
cprintf(\"*-********************************-          -********************************-*\");
cprintf(\"*-****************************************************************************-*\");

for(int count=0;count<42;count++)
cprintf(\"*-*                                                                          *-*\");

gotoxy(1,46);
cprintf(\"*-****************************************************************************-*\");
cprintf(\"*------------------------------------------------------------------------------*\");
cprintf(\"********************************************************************************\");

gotoxy(1,2);
}
```

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