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# 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_surface(const int,const int,const int [10][10][3]);
double blending_function(const int,const int,const float);
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;
int m;
do
{
show_screen( );
gotoxy(8,10);
cout<<\"Number of Bezier Curves : m :\";
gotoxy(8,11);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(12,13);
cout<<\"Enter the value of n (1<m<10) = \";
cin>>m;
gotoxy(8,18);
cout<<\"Number of Control Points : n :\";
gotoxy(8,19);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(12,21);
cout<<\"Enter the value of n (1<n<10) = \";
cin>>n;
if(m>=10)
m=10;
if(n>=10)
n=10;
show_screen( );
int control_points[10][10][3]={0};
for(int count_1=0;count_1<m;count_1++)
{
gotoxy(8,10);
cout<<\"Bezier Curves Number : m = \"<<(count_1+1);
gotoxy(8,11);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
for(int count_2=0;count_2<n;count_2++)
{
gotoxy(8,15);
cout<<\"Coordinates of Point-\"<<count_2<<\" (x\"<<count_2<<\",y\"<<count_2<<\",z\"<<count_2<<\") :\";
gotoxy(8,16);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(12,18);
cout<<\"Enter the value of x\"<<count_2<<\" = \";
cin>>control_points[count_1][count_2][0];
gotoxy(12,20);
cout<<\"Enter the value of y\"<<count_2<<\" = \";
cin>>control_points[count_1][count_2][1];
gotoxy(12,22);
cout<<\"Enter the value of z\"<<count_2<<\" = \";
cin>>control_points[count_1][count_2][2];
gotoxy(8,15);
cout<<\" \";
gotoxy(12,18);
cout<<\" \";
gotoxy(12,20);
cout<<\" \";
gotoxy(12,22);
cout<<\" \";
}
}
initgraph(&driver,&mode,\"..\\\\Bgi\");
setcolor(15);
Bezier_surface((m-1),(n-1),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_surface( ) --------------------------//
void Bezier_surface(const int m,const int n,const int cp[10][10][3])
{
double x_1;
double y_1;
double z_1;
double x_2;
double y_2;
double z_2;
setcolor(7);
for(int count_1=0;count_1<=m;count_1++)
{
for(int count_2=0;count_2<n;count_2++)
{
x_1=cp[count_1][count_2][0];
y_1=cp[count_1][count_2][1];
z_1=cp[count_1][count_2][2];
x_2=cp[count_1][(count_2+1)][0];
y_2=cp[count_1][(count_2+1)][1];
z_2=cp[count_1][(count_2+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));
}
}
for(int count_3=0;count_3<=n;count_3++)
{
for(int count_4=0;count_4<m;count_4++)
{
x_1=cp[count_4][count_3][0];
y_1=cp[count_4][count_3][1];
z_1=cp[count_4][count_3][2];
x_2=cp[(count_4+1)][count_3][0];
y_2=cp[(count_4+1)][count_3][1];
z_2=cp[(count_4+1)][count_3][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 v=0.001;v<1.002;v+=0.05)
{
for(float u=0.0005;u<1;u+=0.0005)
{
x=0;
y=0;
z=0;
for(int j=0;j<=m;j++)
{
for(int k=0;k<=n;k++)
{
x+=(cp[j][k][0]*nCr(m,j)*pow(v,j)*powl((1-v),(m-j))*nCr(n,k)*pow(u,k)*powl((1-u),(n-k)));
y+=(cp[j][k][1]*nCr(m,j)*pow(v,j)*powl((1-v),(m-j))*nCr(n,k)*pow(u,k)*powl((1-u),(n-k)));
z+=(cp[j][k][2]*nCr(m,j)*pow(v,j)*powl((1-v),(m-j))*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),15);
}
}
for(float u=0.001;u<1.002;u+=0.05)
{
for(float v=0.0005;v<=1;v+=0.0005)
{
x=0;
y=0;
z=0;
for(int j=0;j<=m;j++)
{
for(int k=0;k<=n;k++)
{
x+=(cp[j][k][0]*blending_function(j,m,v)*
blending_function(k,n,u));
y+=(cp[j][k][1]*blending_function(j,m,v)*
blending_function(k,n,u));
z+=(cp[j][k][2]*blending_function(j,m,v)*
blending_function(k,n,u));
}
}
get_projected_point(x,y,z);
putpixel((int)(x+0.5),(int)(y+0.5),15);
}
}
}
//----------------------- blending_function( ) ------------------------//
double blending_function(const int k,const int n,const float u)
{
double blend;
blend=(nCr(n,k)*pow(u,k)*powl((1-u),(n-k)));
return blend;
}
//------------------------------ 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 Surface \");
textbackground(8);
cprintf(\" ------------------------------*\");
cprintf(\"*-****************************- -****************************-*\");
cprintf(\"*-****************************************************************************-*\");
for(int count=0;count<42;count++)
cprintf(\"*-* *-*\");
gotoxy(1,46);
cprintf(\"*-****************************************************************************-*\");
cprintf(\"*------------------------------------------------------------------------------*\");
cprintf(\"********************************************************************************\");
gotoxy(1,2);
}