C++ Programming Tutorial

 
 
 

Graphics Programming

Quadratic Surfaces

Draw a Sphere using Ellipses Draw a Sphere using Parametric Equations Draw an Ellipsoid using Parametric Equations

Character Generation

Urdu Alphabets using Stroke Method Urdu Alphabets using Matrix Method

Arc

Circular Arc using Trigo. Method Elliptical Arc using Trigo. Method

General Programs

C-Curve of nth order K-Curve of nth order Cubic Bezier Curve Bezier Curve of nth degree Scanfill algorithm Boundary Fill - 8 Connected Point Flood fill algorithm Rotate About Origin Rotate about reference point Scaling about origin Scaling about reference point Polyline translation Reflection in x axis Reflection in y Axis Reflection on any line Midpoint Circle Drawing Bresenhams Line Algorithm (BLA) Generate a pattern Draw a Chess Board Draw a Luddo Board Deterministic Finite Automation for identifier Kurskals algo - Minimum Cost Spanning Tree

Windows Programs

Checkbox like windows Simple windows & buttons Moving message box like windows Text box Graphical Rep. of tower of hanoi Graphical menu - operate it using arrow keys Text animation

Line

Line using Parametric equations Line-Cartesian Slope-Intercept Equation simple imp Line using Cartesian Slope-Intercept Equation Line - BLA - slopes negative and greater than 1 Line - BLA - slopes negative and less than 1 Line - BLA - slopes positive and greater than 1 Line - BLA - slopes positive and less than 1 DDA line drawing algorithm Bresenham line drawing algorithm Cohen sutherland Line clipping algo.

Line Styles

Different kinds of Dashed Lines Different kinds of Thick Lines

Polygons

Draw a Polygon Draw a Triangle Draw a Rectangle Sutherland-Hodgeman Polygon Clipping Algo

Circle

Circle using Trigo. Method Circle using Polynomial Method Circle using Bresenhams Circle algo. Circle using MidPoint Circle algo.

Ellipse

Ellipse using Polynomial Method Ellipse using Trigo. Method Ellipse using MidPoint Ellipse algo.

2D Transformations

Translation Transformation Scaling Transformation Scaling Trans along a Fixed Point Scaling Trans along Arbitrary Direction Rotation Transformation Rotation Trans along a Pivot Point Reflection tran of x-axix, y-axis and w.r.t origin Reflection tran of line y=x and y=-x X-Direction Shear Transformation Y-Direction Shear Transformation

2D Viewing - Clipping

Window-to-Viewport Coordinate Tran Point Clipping Algorithm Cohen-Sutherland Line Clipping Algo Cohen-Sutherland MidPoint Subdivision Line Nicol Lee Nicol algo. for Line Clipping Liang-Barsky Line Clipping Algo Window-to-Viewport Transformaton None-or-All String Clipping Strategy None-or-All Character Clipping Strategy

3D Object Representations

3D object using Polygon-Mesh Rep. 3D object - Translational Sweep Representatiom 3D object - Rotational Sweep Rep.

3D Transformations

3D Rotation Trans along x-axis 3D Rotation Trans along y-axis 3D Rotation Trans along z-axis 3D Reflection Trans along xy-plane 3D Reflection Trans along yz-plane 3D Reflection Trans along zx-plane 3D Shearing Trans along x-axis 3D Shearing Trans along y-axis 3D Shearing Trans along z-axis

Bezier Curves - Surfaces

3D Cubic Bezier Curve 3D Bezier Curve of nth degree 3D Piece-Wise Bezier Curve of nth degree 3D Bezier Surface for MxN control points

Projection

3D objects - Standard Perspective Projection 3D obj - Arbitrary Plane and Center of Projection 3D objects using General Perspective Projection 3D obj-Orthographics Proje Parallel onto xy-plane 3D obj-Cavalier Oblique Parallel prj-xy-plane 3D obj-Cabinet Oblique Parallel prj - xy-plane

Fill Algorithm or Area Filling

Geometric shapes using Boundary Geometric shapes - Boundary - Linked List Geometric shapes using Flood Geometric shapes - Flood - Linked-List Polygon using Scan Line Polygon Rectangle using Scan-Line Rectangle Circle using Scan-Line Circle Circle - Scan-Line Circle - Polar Coordinates
 

Program to draw a 3D Bezier Surface for MxN control points

 
 # 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);
    }

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