# Program to draw a 3D Bezier Curve of nth degree

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

# define  f                 0.3
# define  projection_angle   45

void show_screen( );

void Bezier_curve(const int,const int [10][3]);

double nCr(int,int);
double factorial(int);

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

void Dashed_line(const int,const int,const int,const int,const int=0);

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

int n;

do
{
show_screen( );

gotoxy(8,10);
cout<<\"Degree of Bezier Curve : n :\";

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

gotoxy(12,13);
cout<<\"Enter the value of n (1<n<10) = \";
cin>>n;

if(n>=10)
n=10;

int control_points[10][3]={0};

for(int count=0;count<=n;count++)
{
gotoxy(8,18);
cout<<\"Coordinates of Point-\"<<count<<\" (x\"<<count<<\",y\"<<count<<\",z\"<<count<<\") :\";

gotoxy(8,19);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

gotoxy(12,21);
cout<<\"Enter the value of x\"<<count<<\" = \";
cin>>control_points[count][0];

gotoxy(12,23);
cout<<\"Enter the value of y\"<<count<<\" = \";
cin>>control_points[count][1];

gotoxy(12,25);
cout<<\"Enter the value of z\"<<count<<\" = \";
cin>>control_points[count][2];

gotoxy(8,18);
cout<<\"                                            \";

gotoxy(12,21);
cout<<\"                                            \";

gotoxy(12,23);
cout<<\"                                            \";

gotoxy(12,25);
cout<<\"                                            \";
}

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

setcolor(15);
Bezier_curve(n,control_points);

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;
}

//--------------------------  Bezier_curve( )  --------------------------//

void Bezier_curve(const int n,const int cp[10][3])
{
int color=getcolor( );

setcolor(7);

double x_1;
double y_1;
double z_1;
double x_2;
double y_2;
double z_2;

for(int count=0;count<n;count++)
{
x_1=cp[count][0];
y_1=cp[count][1];
z_1=cp[count][2];
x_2=cp[(count+1)][0];
y_2=cp[(count+1)][1];
z_2=cp[(count+1)][2];

get_projected_point(x_1,y_1,z_1);
get_projected_point(x_2,y_2,z_2);

Dashed_line((int)(x_1+0.5),(int)(y_1+0.5),
(int)(x_2+0.5),(int)(y_2+0.5));
}

double x;
double y;
double z;

for(float u=0.0005;u<=1;u+=0.0005)
{
x=0;
y=0;
z=0;

for(int k=0;k<=n;k++)
{
x+=(cp[k][0]*nCr(n,k)*pow(u,k)*powl((1-u),(n-k)));
y+=(cp[k][1]*nCr(n,k)*pow(u,k)*powl((1-u),(n-k)));
z+=(cp[k][2]*nCr(n,k)*pow(u,k)*powl((1-u),(n-k)));
}

get_projected_point(x,y,z);

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

//------------------------------  nCr( )  -------------------------------//

double nCr(int n,int r)
{
double nf;
double rf;
double nrf;
double ncr;

nf=factorial(n);
rf=factorial(r);
nrf=factorial((n-r));

ncr=(nf/(rf*nrf));

return ncr;
}

//---------------------------  factorial( )  ----------------------------//

double factorial(int number)
{
double factorial=1;

if(number==0 || number==1);

else
{
for(int count=1;count<=number;count++)
factorial=factorial*count;
}

return factorial;
}

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

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

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

float xy[4]={x,y,z,1};
float 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 float matrix_1[4],
const float matrix_2[4][4],float 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]);
}
}

//---------------------------  Dashed_line( )  --------------------------//

void Dashed_line(const int x_1,const int y_1,const int x_2,
const int y_2,const int line_type)
{
int count=0;
int color=getcolor( );

int x1=x_1;
int y1=y_1;

int x2=x_2;
int y2=y_2;

if(x_1>x_2)
{
x1=x_2;
y1=y_2;

x2=x_1;
y2=y_1;
}

int dx=abs(x2-x1);
int dy=abs(y2-y1);
int inc_dec=((y2>=y1)?1:-1);

if(dx>dy)
{
int two_dy=(2*dy);
int two_dy_dx=(2*(dy-dx));
int p=((2*dy)-dx);

int x=x1;
int y=y1;

putpixel(x,y,color);

while(x<x2)
{
x++;

if(p<0)
p+=two_dy;

else
{
y+=inc_dec;
p+=two_dy_dx;
}

if((count%2)!=0 && line_type==0)
putpixel(x,y,color);

else if((count%5)!=4 && line_type==1)
putpixel(x,y,color);

else if((count%10)!=8 && (count%10)!=9 && line_type==2)
putpixel(x,y,color);

else if((count%20)!=18 && (count%20)!=19 && line_type==3)
putpixel(x,y,color);

else if((count%12)!=7 && (count%12)!=8 &&
(count%12)!=10 && (count%12)!=11 && line_type==4)
putpixel(x,y,color);

count++;
}
}

else
{
int two_dx=(2*dx);
int two_dx_dy=(2*(dx-dy));
int p=((2*dx)-dy);

int x=x1;
int y=y1;

putpixel(x,y,color);

while(y!=y2)
{
y+=inc_dec;

if(p<0)
p+=two_dx;

else
{
x++;
p+=two_dx_dy;
}

if((count%2)!=0 && line_type==0)
putpixel(x,y,color);

else if((count%5)!=4 && line_type==1)
putpixel(x,y,color);

else if((count%10)!=8 && (count%10)!=9 && line_type==2)
putpixel(x,y,color);

else if((count%20)!=18 && (count%20)!=19 && line_type==3)
putpixel(x,y,color);

else if((count%12)!=7 && (count%12)!=8 &&
(count%12)!=10 && (count%12)!=11 && line_type==4)
putpixel(x,y,color);

count++;
}
}
}

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

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

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

textbackground(1);
cprintf(\" Bezier Curve \");
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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