Line Algorithm

Introduction#

Line drawing is accomplished by calculating intermediate positions along the line path between two specified endpoint positions. An output device is then directed to fill in these positions between the endpoints.

Bresenham Line Drawing Algorithm

Background Theory: Bresenham’s Line Drawing Algorithm is an efficient and accurate raster line generating algorithm developed by Bresenham. It involves only integer calculation so it is accurate and fast. It can also be extended to display circles another curves.

In Bresenham line drawing algorithm:

For Slope |m|<1:
Either value of x is increased
OR both x and y is increased using decision parameter.

For Slope |m|>1:
Either value of y is increased
OR both x and y is increased using decision parameter.

Algorithm for slope |m|<1:

1. Input two end points (x1,y1) and (x2,y2) of the line.
2. Plot the first point (x1,y1).
3. Calculate
   Delx =| x2 – x1 |

Dely = | y2 – y1 |

4. Obtain the initial decision parameter as
   

P = 2 * dely – delx

5. For I = 0 to delx in step of 1
   
   If p < 0 then
   X1 = x1 + 1
   Pot(x1,y1)
   P = p+ 2dely
   
   Else
   X1 = x1 + 1
   Y1 = y1 + 1
   Plot(x1,y1)
   P = p + 2dely – 2 * delx
   
   End if
   
   

End for
6. END

Source Code:

/* A C program to implement Bresenham line drawing algorithm for |m|<1 */
#include<stdio.h>
#include<conio.h>
#include<graphics.h>
#include<math.h>

int main()
{    
 int gdriver=DETECT,gmode;
 int x1,y1,x2,y2,delx,dely,p,i;
 initgraph(&gdriver,&gmode,"c:\\TC\\BGI");

printf("Enter the intial points: ");
scanf("%d",&x1);
scanf("%d",&y1);
printf("Enter the end points: ");
scanf("%d",&x2);
scanf("%d",&y2);

putpixel(x1,y1,RED);

delx=fabs(x2-x1);
dely=fabs(y2-y1);
p=(2*dely)-delx;
for(i=0;i<delx;i++){
if(p<0)
{
 x1=x1+1;
 putpixel(x1,y1,RED);
 p=p+(2*dely);
}
else
{
 x1=x1+1;
 y1=y1+1;
 putpixel(x1,y1,RED);
 p=p+(2*dely)-(2*delx);
}
}
 getch();
 closegraph();
 return 0;
}

Algorithm for slope |m|>1:

1. Input two end points (x1,y1) and (x2,y2) of the line.
2. Plot the first point (x1,y1).
3. Calculate
   Delx =| x2 – x1 |
   Dely = | y2 – y1 |
4. Obtain the initial decision parameter as

P = 2 * delx – dely 5) For I = 0 to dely in step of 1

If p < 0 then
y1 = y1 + 1
Pot(x1,y1)
P = p+ 2delx

Else
X1 = x1 + 1
Y1 = y1 + 1
Plot(x1,y1)
P = p + 2delx – 2 * dely

End if

End for

6) END

Source Code:

/* A C program to implement Bresenham line drawing algorithm for |m|>1 */
#include<stdio.h>
#include<conio.h>
#include<graphics.h>
#include<math.h>
int main()
{
int gdriver=DETECT,gmode;
int x1,y1,x2,y2,delx,dely,p,i;
initgraph(&gdriver,&gmode,"c:\\TC\\BGI");
printf("Enter the intial points: ");
scanf("%d",&x1);
scanf("%d",&y1);
printf("Enter the end points: ");
scanf("%d",&x2);
scanf("%d",&y2);
putpixel(x1,y1,RED);
delx=fabs(x2-x1);
dely=fabs(y2-y1);
p=(2*delx)-dely;
for(i=0;i<delx;i++){
if(p<0)
{
y1=y1+1;
putpixel(x1,y1,RED);
p=p+(2*delx);
}
else
{
x1=x1+1;
y1=y1+1;
putpixel(x1,y1,RED);
p=p+(2*delx)-(2*dely);
}
}
getch();
closegraph();
 return 0;
}