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 + 2
    dely – 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 + 2
    delx – 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;
}


2016-10-24
2017-01-20
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