Programmers Lounge - Graphics Basics

Mid-point Ellipse Algorithm

2007-08-17T01:43:00.002+05:30


/* Midpoint ellipse algorithm - Subhranath Chunder */

#include<stdio.h>
#include<conio.h>
#include<graphics.h>
#include<math.h>

void ellipseMidPoint(int,int,int,int);
void setOthers(int,int,int,int);
void setPixel(int,int);
int equ(float,float,int,int);

void main()
{
  int x,y,rx,ry,driver=DETECT,mode;
  clrscr();

  printf("Enter the co-ordinate of the center of the elipse: ");
  scanf("%d %d",&x,&y);
  printf("Enter the radius along x-axis: ");
  scanf("%d",&rx);
  printf("Enter the radius along y-axis: ");
  scanf("%d",&ry);
  printf("<Press any key to continue>");

  initgraph(&driver,&mode,"f:\\tc\\bgi");
  ellipseMidPoint(x,y,rx,ry);
  getch();
}

void ellipseMidPoint(int xCenter,int yCenter,int rx,int ry)
{
  int x=0,y=ry,a,b;
  setOthers(x,y,xCenter,yCenter);
  while(pow(ry,2)*x<pow(rx,2)*y)
  {
     ++x;
     if( equ(x,y-(float)1/2,rx,ry)>=0)
        --y;
     setOthers(x,y,xCenter,yCenter);
  }
  while(y!=0)
  {
     --y;
     if( equ(x+(float)1/2,y,rx,ry)<=0)
        ++x;
     setOthers(x,y,xCenter,yCenter);
  }
}

void setOthers(int x,int y,int xCenter,int yCenter)
{
  setPixel(xCenter + x,yCenter + y);
  setPixel(xCenter - x,yCenter + y);
  setPixel(xCenter + x,yCenter - y);
  setPixel(xCenter - x,yCenter - y);
}

int equ(float x,float y,int rx,int ry)
{
  int res;
  if( pow(ry,2)*pow(x,2)+pow(rx,2)*pow(y,2)-pow(rx,2)*pow(ry,2) == 0 )
     res=0;
  if( pow(ry,2)*pow(x,2)+pow(rx,2)*pow(y,2)-pow(rx,2)*pow(ry,2) < 0 )
     res=-1;
  if( pow(ry,2)*pow(x,2)+pow(rx,2)*pow(y,2)-pow(rx,2)*pow(ry,2) > 0 )
     res=1;
  return res;
}

void setPixel(int x,int y)
{
  putpixel(x,y,2);
}

Mid-point Circle Scaling

2007-08-17T01:41:00.001+05:30


/* WAP to generate a circle.
    Write a function to scale the circle by sx amount in x-direction and sy amount in y-direction, where sx and sy are integers provided by the user.
    Use matrix method. - Subhranath Chunder */

#include<stdio.h>
#include<conio.h>
#include<graphics.h>
#include<math.h>

void circleMidPoint(int,int,int,int,int);
int equ(float,float,int);
void setOthers(int,int,int,int,int,int);
void scalePoint(int,int,int,int,int*,int*);
void setPixel(int,int);

void main()
{
  int x,y,radius,driver=DETECT,mode,sx,sy;
  clrscr();

  /* Mid-point and radius of the circle are accepted */
  printf("Enter the co-ordinate of the centre: ");
  scanf("%d %d",&x,&y);
  printf("Enter the radius of the circle: ");
  scanf("%d",&radius);
  printf("<Press any key to continue>");

  /* Graphics mode initialized */
  initgraph(&driver,&mode,"F:\\tc\\bgi");

  /* Circle drawn with no scaling */
  circleMidPoint(x,y,radius,1,1);

  /* Amount of scaling */
  printf("Enter the amount of scaling in x-direction: ");
  scanf("%d",&sx);
  printf("Enter the amount of scaling in y-direction: ");
  scanf("%d",&sy);

  /* Translated circle is redrawn */
  circleMidPoint(x,y,radius,sx,sy);
  getch();
  closegraph();
}

void circleMidPoint(int xCenter,int yCenter,int radius,int sx,int sy)
{
  int x=0,y=radius;

  /* Sets the points for all octants */
  setOthers(x,y,xCenter,yCenter,sx,sy);

  /* First octant is drawn */
  while(x<y)
  {
     ++x;

     /* Checking whether y or y-1 is closer to the circle, by taking their mid-point */
     if( equ(x,y-(float)1/2,radius) >=0 )
        --y;

     setOthers(x,y,xCenter,yCenter,sx,sy);
  }

}

/* A function to find whether a given point is inside, outside, or on the circle */
int equ(float x,float y,int r)
{
  int res;
  if( pow(x,2)+pow(y,2)-pow(r,2) == 0)
     res=0;
  else if( pow(x,2)+pow(y,2)-pow(r,2) < 0)
     res=-1;
  else if( pow(x,2)+pow(y,2)-pow(r,2) > 0)
     res=1;
  return res;
}

/* A function to set all other points symmetric to the point (x,y) in all the octants */
void setOthers(int x,int y,int xCenter,int yCenter,int sx,int sy)
{
  int xd,yd;

  /* If sx==1 and sy==1 then no scaling is required. Otherwise, scale each point. */
  if(sx==1 && sy==1)
  {
     setPixel(xCenter+x,yCenter+y);
     setPixel(xCenter-x,yCenter+y);
     setPixel(xCenter+x,yCenter-y);
     setPixel(xCenter-x,yCenter-y);
     setPixel(xCenter+y,yCenter+x);
     setPixel(xCenter-y,yCenter+x);
     setPixel(xCenter+y,yCenter-x);
     setPixel(xCenter-y,yCenter-x);
  }
  else
  {
     scalePoint(xCenter+x,yCenter+y,sx,sy,&xd,&yd);
     setPixel(xd,yd);
     scalePoint(xCenter-x,yCenter+y,sx,sy,&xd,&yd);
     setPixel(xd,yd);
     scalePoint(xCenter+x,yCenter-y,sx,sy,&xd,&yd);
     setPixel(xd,yd);
     scalePoint(xCenter-x,yCenter-y,sx,sy,&xd,&yd);
     setPixel(xd,yd);
     scalePoint(xCenter+y,yCenter+x,sx,sy,&xd,&yd);
     setPixel(xd,yd);
     scalePoint(xCenter-y,yCenter+x,sx,sy,&xd,&yd);
     setPixel(xd,yd);
     scalePoint(xCenter+y,yCenter-x,sx,sy,&xd,&yd);
     setPixel(xd,yd);
     scalePoint(xCenter-y,yCenter-x,sx,sy,&xd,&yd);
     setPixel(xd,yd);
  }
}

/* Scales the point (x,y) by sx and sy amount, and stores the new point in (xd,yd) */
void scalePoint(int x,int y,int sx,int sy,int *xd,int *yd)
{
  int i,j,a[3][3],b[3],c[3];

  a[0][0]=sx; a[0][1]=0; a[0][2]=0;
  a[1][0]=0; a[1][1]=sy; a[1][2]=0;
  a[2][0]=0; a[2][1]=0; a[2][2]=1;

  b[0]=x;
  b[1]=y;
  b[2]=1;

  for(i=0;i<3;++i)
  {
     c[i]=0;
     for(j=0;j<3;++j)
     {
        c[i]+=a[i][j]*b[j];
     }
  }

  /* Scaled point */
  *xd=c[0]/c[2];
  *yd=c[1]/c[2];
}

void setPixel(int x,int y)
{
  putpixel(x,y,2);
}

Mid-point Circle Translation

2007-08-17T01:39:00.002+05:30


/* Midpoint circle translation in homogeneous coordinate form - Subhranath Chunder */

#include<stdio.h>
#include<conio.h>
#include<graphics.h>
#include<math.h>

void circleMidPoint(int,int,int,int,int);
int equ(float,float,int);
void setOthers(int,int,int,int,int,int);
void translatePoint(int,int,int,int,int*,int*);
void setPixel(int,int);

void main()
{
  int x,y,radius,driver=DETECT,mode,xt,yt;
  clrscr();

  /* Mid-point and radius of the circle are accepted */
  printf("Enter the co-ordinate of the centre: ");
  scanf("%d %d",&x,&y);
  printf("Enter the radius of the circle: ");
  scanf("%d",&radius);
  printf("<Press any key to continue>");

  /* Graphics mode initialized */
  initgraph(&driver,&mode,"F:\\tc\\bgi");

  /* Circle drawn with zero translation */
  circleMidPoint(x,y,radius,0,0);

  /* Amount of translation */
  printf("Enter the amount of translation in x-direction: ");
  scanf("%d",&xt);
  printf("Enter the amount of translation in y-direction: ");
  scanf("%d",&yt);

  /* Translated circle is redrawn */
  circleMidPoint(x,y,radius,xt,yt);
  getch();
  closegraph();
}

void circleMidPoint(int xCenter,int yCenter,int radius,int xt,int yt)
{
  int x=0,y=radius;

  /* Sets the points for all octants */
  setOthers(x,y,xCenter,yCenter,xt,yt);

  /* First octant is drawn */
  while(x<y)
  {
     ++x;

     /* Checking whether y or y-1 is closer to the circle, by taking their mid-point */
     if( equ(x,y-(float)1/2,radius) >=0 )
        --y;

     setOthers(x,y,xCenter,yCenter,xt,yt);
  }

}

/* A function to find whether a given point is inside, outside, or on the circle */
int equ(float x,float y,int r)
{
  int res;
  if( pow(x,2)+pow(y,2)-pow(r,2) == 0)
     res=0;
  else if( pow(x,2)+pow(y,2)-pow(r,2) < 0)
     res=-1;
  else if( pow(x,2)+pow(y,2)-pow(r,2) > 0)
     res=1;
  return res;
}

/* A function to set all other points symmetric to the point (x,y) in all the octants */
void setOthers(int x,int y,int xCenter,int yCenter,int xt,int yt)
{
  int xd,yd;

  /* If xt==0 and yt==0 then no translation is required. Otherwise, translate each point. */
  if(xt==0 && yt==0)
  {
     setPixel(xCenter+x,yCenter+y);
     setPixel(xCenter-x,yCenter+y);
     setPixel(xCenter+x,yCenter-y);
     setPixel(xCenter-x,yCenter-y);
     setPixel(xCenter+y,yCenter+x);
     setPixel(xCenter-y,yCenter+x);
     setPixel(xCenter+y,yCenter-x);
     setPixel(xCenter-y,yCenter-x);
  }
  else
  {
     translatePoint(xCenter+x,yCenter+y,xt,yt,&xd,&yd);
     setPixel(xd,yd);
     translatePoint(xCenter-x,yCenter+y,xt,yt,&xd,&yd);
     setPixel(xd,yd);
     translatePoint(xCenter+x,yCenter-y,xt,yt,&xd,&yd);
     setPixel(xd,yd);
     translatePoint(xCenter-x,yCenter-y,xt,yt,&xd,&yd);
     setPixel(xd,yd);
     translatePoint(xCenter+y,yCenter+x,xt,yt,&xd,&yd);
     setPixel(xd,yd);
     translatePoint(xCenter-y,yCenter+x,xt,yt,&xd,&yd);
     setPixel(xd,yd);
     translatePoint(xCenter+y,yCenter-x,xt,yt,&xd,&yd);
     setPixel(xd,yd);
     translatePoint(xCenter-y,yCenter-x,xt,yt,&xd,&yd);
     setPixel(xd,yd);
  }
}

/* Translates the point (x,y) by xt and yt amount, and stores the new point in (xd,yd) */
void translatePoint(int x,int y,int xt,int yt,int *xd,int *yd)
{
  int i,j,a[3][3],b[3],c[3];

  a[0][0]=1; a[0][1]=0; a[0][2]=xt;
  a[1][0]=0; a[1][1]=1; a[1][2]=yt;
  a[2][0]=0; a[2][1]=0; a[2][2]=1;

  b[0]=x;
  b[1]=y;
  b[2]=1;

  for(i=0;i<3;++i)
  {
     c[i]=0;
     for(j=0;j<3;++j)
     {
        c[i]+=a[i][j]*b[j];
     }
  }

  /* Translated point */
  *xd=c[0]/c[2];
  *yd=c[1]/c[2];
}

void setPixel(int x,int y)
{
  putpixel(x,y,2);
}

Mid-point Circle Algorithm

2007-08-17T01:37:00.001+05:30


/* Midpoint circle algorithm - Subhranath Chunder */

#include<stdio.h>
#include<conio.h>
#include<graphics.h>
#include<math.h>

void circleMidPoint(int,int,int);
int equ(float,float,int);
void setPixel(int,int);
void setOthers(int x,int y,int xCenter,int yCenter);

void main()
{
  int x,y,radius,driver=DETECT,mode;
  clrscr();

  printf("Enter the co-ordinate of the centre: ");
  scanf("%d %d",&x,&y);
  printf("Enter the radius of the circle: ");
  scanf("%d",&radius);
  printf("<Press any key to continue>");

  initgraph(&driver,&mode,"F:\\tc\\bgi");
  circleMidPoint(x,y,radius);
  getch();
  closegraph();
}

void circleMidPoint(int xCenter,int yCenter,int radius)
{
  int x=0,y=radius;
  setOthers(x,y,xCenter,yCenter);
  while(x<y)
  {
     ++x;
     if( equ(x,y-(float)1/2,radius) >=0 )
        --y;
     setOthers(x,y,xCenter,yCenter);
  }
}

int equ(float x,float y,int r)
{
  int res;
  if( pow(x,2)+pow(y,2)-pow(r,2) == 0)
     res=0;
  else if( pow(x,2)+pow(y,2)-pow(r,2) < 0)
     res=-1;
  else if( pow(x,2)+pow(y,2)-pow(r,2) > 0)
     res=1;
  return res;
}

void setOthers(int x,int y,int xCenter,int yCenter)
{
  setPixel(xCenter+x,yCenter+y);
  setPixel(xCenter-x,yCenter+y);
  setPixel(xCenter+x,yCenter-y);
  setPixel(xCenter-x,yCenter-y);
  setPixel(xCenter+y,yCenter+x);
  setPixel(xCenter-y,yCenter+x);
  setPixel(xCenter+y,yCenter-x);
  setPixel(xCenter-y,yCenter-x);
}

void setPixel(int x,int y)
{
  putpixel(x,y,2);
}

Line Translation (DDA used here)

2007-08-17T01:33:00.001+05:30


/* WAP to generate a line using DDA.
    Write a function to translate the line by tx amount in x-direction and ty amount in y-direction, where tx and ty are integers provided by the user.
    Use matrix method. - Subhranath Chunder */

#include<stdio.h>
#include<conio.h>
#include<graphics.h>

void lineDDA(int,int,int,int,int,int);
void translatePoint(float,float,int,int,float*,float*);
void setPixel(int,int);

void main()
{
int x1,y1,x2,y2,xt,yt;
int driver=DETECT,mode;
clrscr();

/* Two end-points of the line are accepted */
printf("Enter the co-ordinates of the first point (a b): ");
scanf("%d %d",&x1,&y1);
printf("Enter the co-ordinates of the second point (a b): ");
scanf("%d %d",&x2,&y2);
printf("<Press any key to continue>");
getch();

/* Initialize graphics mode */
initgraph(&driver,&mode,"F:\\TC\\BGI");

/* Line drawn with zero translation */
lineDDA(x1,y1,x2,y2,0,0);

/* Amount of translation, if any */
printf("Enter the amount of translation in x-direction: ");
scanf("%d",&xt);
printf("Enter the amount of translation in y-direction: ");
scanf("%d",&yt);

/* Translated line */
lineDDA(x1,y1,x2,y2,xt,yt);
getch();
closegraph();
}

void lineDDA(int x1,int y1,int x2,int y2,int xt,int yt)
{
float m,x,y,xd,yd;
x=x1;
y=y1;

/* If xt=0 and yt=0, then no translation. */
if(xt==0 && yt==0)
  setPixel(x,y);
/* Otherwise translate each point */
else
{
  translatePoint(x,y,xt,yt,&xd,&yd);
  setPixel(xd,yd);
}

/* For vertical lines */
if(x1==x2)
{
  while(y!=y2)
  {
     if(y2-y1>0)
        ++y;
     else
        --y;
     if(xt==0 && yt==0)
        setPixel(x,y);
     else
     {
        translatePoint(x,y,xt,yt,&xd,&yd);
        setPixel(xd,yd);
     }
  }
}

/* Non-vertical lines */
else
{
  m=(float)(y2-y1)/(x2-x1);

  /* When -1<=m<=1 we calculate the corresponding y's for unit intervals of x */
  if(m<=1 && m>=-1)
  {
     while(x!=x2)
     {
        /* To check whether the line is drawn from left to right, or the reverse */
        if(x2-x1>0)
        {
           y=y+m;
           ++x;
        }
        else
        {
           y=y-m;
           --x;
        }

        /* x and y is plotted, with or without translation */
        if(xt==0 && yt==0)
           setPixel(x,y);
        else
        {
           translatePoint(x,y,xt,yt,&xd,&yd);
           setPixel(xd,yd);
        }

     }

  }

  /* When m<-1 or m>1 we calculate the corresponding x's for unit intervals of y */
  else
  {
     while(y!=y2)
     {
        /* To check whether the line is drawn from bottom to top, or it's reverse */
        if((y2-y1)>0)
        {
           x=x+(1/m);
           ++y;
        }
        else
        {
           x=x-(1/m);
           --y;
        }

        /* x and y is plotted, with or without translation */
        if(xt==0 && yt==0)
           setPixel(x,y);
        else
        {
           translatePoint(x,y,xt,yt,&xd,&yd);
           setPixel(xd,yd);
        }

     }

  }
}
}

/* Translates the point (x,y) by xt and yt amount, and stores the new point in (xd,yd) */
void translatePoint(float x,float y,int xt,int yt,float *xd,float *yd)
{
int i,j;
float a[3][3],b[3],c[3];

a[0][0]=1; a[0][1]=0; a[0][2]=xt;
a[1][0]=0; a[1][1]=1; a[1][2]=yt;
a[2][0]=0; a[2][1]=0; a[2][2]=1;

b[0]=x;
b[1]=y;
b[2]=1;

for(i=0;i<3;++i)
{
  c[i]=0;
  for(j=0;j<3;++j)
  {
     c[i]+=a[i][j]*b[j];
  }
}

/* Translated point */
*xd=c[0]/c[2];
*yd=c[1]/c[2];
}

void setPixel(int x,int y)
{
putpixel(x,y,2);
}

Rectangle using Bresenham's line

2007-08-17T01:28:00.001+05:30


/* WAP to draw a rectangle whose lower left corner, length and breadth are provided by the user.
    Use Bresenham’s algorithm to draw the sides of the rectangle - Subhranath Chunder */

#include<stdio.h>
#include<conio.h>
#include<graphics.h>

void lineBres(int,int,int,int);
void setPixel(int,int);

void main()
{
int x,y,length,breadth;
int driver=DETECT,mode;

clrscr();
printf("Enter the co-ordinates of the lower left corner (a b): ");
scanf("%d %d",&x,&y);
printf("Enter the length of the rectangle: ");
scanf("%d",&length);
printf("Enter the breadth of the rectangle: ");
scanf("%d",&breadth);
printf("<Press any key to continue>");
getch();

initgraph(&driver,&mode,"F:\\TC\\BGI");
lineBres(x,y,x+length,y);
lineBres(x+length,y,x+length,y-breadth);
lineBres(x+length,y-breadth,x,y-breadth);
lineBres(x,y-breadth,x,y);
getch();
closegraph();
}

void lineBres(int x1,int y1,int x2,int y2)
{
float error,m;
int x,y;
x=x1;
y=y1;
if(x1==x2)
{
   while(y!=y2)
   {
      if(y2-y1>0)
         ++y;
      else
         --y;
      setPixel(x,y);
   }
}
else
{
   m=(float)(y2-y1)/(x2-x1);
   error=0;
   setPixel(x,y);
   while(x!=x2)
   {
      error+=m;
      if(error>.5)
      {
         if(x2-x1>0)
            y+=1;
         else
            y-=1;
         --error;
      }
      if(x2-x1>0)
         ++x;
      else
         --x;
      setPixel(x,y);
   }
}
}

void setPixel(int x,int y)
{
putpixel(x,y,2);
}

Bresenham's Line (for slope 0 to 1)

2007-08-17T01:25:00.001+05:30

/* Bresenham's Line Implementation for 0<=m<=1 and drawing from left to right. - Subhranath Chunder */


#include<stdio.h>
#include<conio.h>
#include<graphics.h>

void lineBres(int,int,int,int);
void setPixel(int,int);

void main()
{
 int x1,y1,x2,y2;
 int driver=DETECT,mode;

 clrscr();
 printf("Enter the co-ordinates of the first point (a b): ");
 scanf("%d %d",&x1,&y1);
 printf("Enter the co-ordinates of the second point (a b): ");
 scanf("%d %d",&x2,&y2);
 printf("<Press any key to continue>");
 getch();

 initgraph(&driver,&mode,"F:\\TC\\BGI");
 lineBres(x1,y1,x2,y2);
 getch();
 closegraph();
}

void lineBres(int x1,int y1,int x2,int y2)
{
 float error,m;
 int x,y;
 m=(float)(y2-y1)/(x2-x1);
 error=0;
 y=y1;
 x=x1;
 setPixel(x,y);
 while(x<=x2)
 {
    error+=m;
    if(error>.5)
    {
       y+=1;
       --error;
    }
    ++x;
    setPixel(x,y);
 }
}

void setPixel(int x,int y)
{
 putpixel(x,y,2);
}

DDA Line Implementation

2007-08-17T01:19:00.001+05:30

/* DDA Line Implementation - Subhranath Chunder */

#include<stdio.h>
#include<conio.h>
#include<graphics.h>

void lineDDA(int,int,int,int);
void setPixel(int,int);

void main()
{
int x1,y1,x2,y2;
int driver=DETECT,mode;

clrscr();
printf("Enter the co-ordinates of the first point (a b): ");
scanf("%d %d",&x1,&y1);
printf("Enter the co-ordinates of the second point (a b): ");
scanf("%d %d",&x2,&y2);
printf("<Press any key to continue>");
getch();

initgraph(&driver,&mode,"F:\\TC\\BGI");
lineDDA(x1,y1,x2,y2);
getch();
closegraph();
}

void lineDDA(int x1,int y1,int x2,int y2)
{
float m,x,y;
x=x1;
y=y1;
setPixel(x,y);
if(x1==x2)
{
   while(y!=y2)
   {
      if(y2-y1>0)
         ++y;
      else
         --y;
      setPixel(x,y);
   }
}
else
{
   m=(float)(y2-y1)/(x2-x1);
   if(m<=1 && m>=-1)
   {
      while(x!=x2)
      {
         if(x2-x1>0)
         {
            y=y+m;
            ++x;
         }
         else
         {
            y=y-m;
            --x;
         }
         setPixel(x,y);
      }
   }
   else
   {
      while(y!=y2)
      {
         if((y2-y1)>0)
         {
            x=x+(1/m);
            ++y;
         }
         else
         {
            x=x-(1/m);
            --y;
         }
         setPixel(x,y);
      }
   }
}
}

void setPixel(int x,int y)
{
putpixel(x,y,2);
}