# How To Draw a 3D Bezier Curve of nth Degree in C++

Hi,A Bézier curve is a type of curve that is easy to use, and can describe many shapes. Bézier curves are famously used for representing characters in fonts, and shapes in vehicle design.Bézier curves are also used in vector art packages for curve drawing, and in 3D animation tools to represent animation paths.

Developer : ijaz Rs khAn & Bilal tahir

Email : [email protected]

Compiler : Microsoft Visual Studio 2012

Comp. Date: 1-11-2015

Draw a 3D Bezier Curve of nth Degree in C++ Source Code # include <iostream.h> // for input oupt standerd# include <graphics.h> //for textcolor & textbackground# include <conio.h> // for clrscr# include <math.h> // for math# define f 0.3# define projection_angle 45void show_screen( ); // void screenvoid Bezier_curve(constint,constint [10][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( ) // main function{int driver=VGA;int mode=VGAHI;int n;do{show_screen( ); // screen showgotoxy(8,10);cout<<"Degree of Bezier Curve :::: n :";gotoxy(8,11);cout<<"!!!!!!!!!!!!!!!!!!!!!!!!";gotoxy(12,13);cout<<"Insert 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++) // if condition{gotoxy(8,18);cout<<"Coordinates of Point-"<<count<<" (x"<<count<<",y"<<count<<",z"<<count<<") :";gotoxy(8,19);cout<<"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!";gotoxy(12,21);cout<<"Insert the value of x"<<count<<" = ";cin>>control_points[count][0];gotoxy(12,23);cout<<"Insert the value of y"<<count<<" = ";cin>>control_points[count][1];gotoxy(12,25);cout<<"Isert 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 to continue or any other key to exit.");int key=int(getch( ));if(key!=13)break;}while(1);return 0;}{int color=getcolor( ); // colorsetcolor(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 valuedouble y; // double valuedouble z; // double valuefor(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);}}{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=1; // factorial numberif(number==0 || number==1); // if numberelse{for(int count=1;count<=number;count++)factorial=factorial*count;}return factorial;}{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];}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]);}}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) // while loop{x++;if(p<0)p+=two_dy;else{y+=inc_dec;p+=two_dy_dx;}if((count%2)!=0 && line_type==0) // if conditionputpixel(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) //while loop{y+=inc_dec;if(p<0)p+=two_dx;else{x++;p+=two_dx_dy;}if((count%2)!=0 && line_type==0) // if conditionputpixel(x,y,color);elseif((count%5)!=4 && line_type==1) // else if conditionputpixel(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++;}}}{restorecrtmode( );clrscr( );textmode(C4350);cprintf("/n****************"); // for printcprintf("**********- -*********-*"); // for printcprintf("*---------- ");textbackground(1); // text backgroundcprintf(" Curve ");textbackground(8);cprintf(" ----------------*");cprintf("*-***************- -*************-*");cprintf("*-***************************-*");for(int count=0;count<42;count++) // for loopcprintf("*-* *-*");gotoxy(1,46);cprintf("*-***********************-*");cprintf("*-------------------------*");cprintf("*************************");gotoxy(1,2);}

Copy and paste the following C++ program in test.cpp file and compile and run this program.if you Face any problem Freely contact us.Give your Feed Back.Thank you.

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