Coding Fever: Program to draw a 3D Piece-Wise Bezier Curve of nth degree with Zeroth Order Continuity

# 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(constint,constint [4][3]);
void Piece_wise_bezier_curve(constint,constint [25][3]);

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

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

void Dashed_line(constint,constint,constint,constint,constint=0);

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

int n;

do
{
show_screen( );

gotoxy(8,10);
cout<<"Number of Control Points : n :";

gotoxy(8,11);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(12,13);
cout<<"Enter the value of n (1<n<=25) = ";
cin>>n;

if(n>=10)
n=10;

int control_points[25][3]={0};

for(int count=0;count<n;count++)
{
gotoxy(8,16);
cout<<"Coordinates of Point-"<<count<<" (x"<<count<<",y"<<count<<",z"<<count<<") :";

gotoxy(8,17);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(12,19);
cout<<"Enter the value of x"<<count<<" = ";
cin>>control_points[count][0];

gotoxy(12,21);
cout<<"Enter the value of y"<<count<<" = ";
cin>>control_points[count][1];

gotoxy(12,23);
cout<<"Enter the value of z"<<count<<" = ";
cin>>control_points[count][2];

gotoxy(8,16);
cout<<" ";

gotoxy(12,19);
cout<<" ";

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

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

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

setcolor(15);
Piece_wise_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;
}

void Piece_wise_bezier_curve(constint n,constint cpts[25][3])
{
int pieces=(n/4);
int extra_points=(n%4);

int point=1;

int cp[4][3]={0};

for(int count_1=0;count_1<pieces;count_1++)
{
point--;

for(int count_2=0;count_2<4;count_2++)
{
cp[count_2][0]=cpts[point][0];
cp[count_2][1]=cpts[point][1];
cp[count_2][2]=cpts[point][2];

point++;
}

Bezier_curve(3,cp);
}

if(extra_points)
{
for(int count_3=(point-1),count_4=0;count_3<n;
count_3++,count_4++)
{
cp[count_4][0]=cpts[count_3][0];
cp[count_4][1]=cpts[count_3][1];
cp[count_4][2]=cpts[count_3][2];
}

Bezier_curve(extra_points,cp);
}
}

void Bezier_curve(constint n,constint cp[4][3])
{
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),15);
}
}

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;
}

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;
}

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];
}

void multiply_matrices(constfloat matrix_1[4],
constfloat 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]);
}
}

void Dashed_line(constint x_1,constint y_1,constint x_2,
constint y_2,constint 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);

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

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

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

elseif((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);

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

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

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

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

count++;
}
}
}

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

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

textbackground(1);
cprintf(" Piece-Wise Bezier Curve ");
textbackground(8);

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

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

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

gotoxy(1,2);
}

Coding Fever

Program to draw a 3D Piece-Wise Bezier Curve of nth degree with Zeroth Order Continuity

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