# 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); }