Bresenham's line drawing algorithm

A line segment is defined by an infinite set of points which lie between two points; these points have no area. A problem occurs, however, when drawing lines on a computer screen, namely that we have to approximate the line with pixels which are not infinitely small, and which are limited to fixed positions based on the
screen resolution.

A simple line drawing algorithm can be implemented as,
filename dda.py


from Tkinter import *
import math

#defining main function
def main():
#reading end points of line x0 = int(raw_input("ENTER THE Xo : "))
y0 = int(raw_input("ENTER THE Yo : "))
x1 = int(raw_input("ENTER THE Xn : "))
y1 = int(raw_input("ENTER THE Yn : "))
root = Tk()
pic = PhotoImage(width=800,height=800)
lb = Label(root,image=pic)
lb.pack()
color = "blue"
dx = x2 – x1;
dy = y2 – y1;
m = dy/dx
for x in range(x1,x2)
y = m*x + y1 + 0.5;
pic.put(color(x, y));
#for loop end here

root.mainloop()
#main end

main()

This is the basic incremental algorithm,often referred as a digital differential analyser(DDA) algorithm.
This algorithm, of course, relies on some assumptions such as:
• Non-infinite slope
• x1 < x2
• y1 < y2


The problem about this is it is slow and can be solved by using mid-point algorithm.

The Bresenham / Midpoint Algorithm is a solution that not only correctly picks
these same points, it does it with integer math only, which results in a big speed
improvement.

Here is an implementation of Bresenham's/mid-point algorithm.The program is coded in python, using the Tkinter module.


filename:midpoint.py

from Tkinter import *
import math

#defining main function
def main():

#main starts
#reading end points of line
x0 = int(raw_input("ENTER THE Xo : "))
y0 = int(raw_input("ENTER THE Yo : "))
x1 = int(raw_input("ENTER THE Xn : "))
y1 = int(raw_input("ENTER THE Yn : "))
root = Tk()
pic = PhotoImage(width=800,height=800)
lb = Label(root,image=pic)
lb.pack()
color = "blue"

#Now Drawing Line

steep = abs(y1 - y0) > abs(x1 - x0)
if steep:
x0, y0 = y0, x0
x1, y1 = y1, x1 #if ends
if x0 > x1:
x0, x1 = x1, x0
y0, y1 = y1, y0
if y0 < y1:
ystep = 1
else:
ystep = -1

deltax = x1 - x0
deltay = abs(y1 - y0)
error = -deltax / 2
y = y0
for x in range(x0, x1 + 1):
if steep:
pic.put(color,(y,x)) #if end
else:
pic.put(color,(x,y)) #else end

error = error + deltay
if error > 0:
y = y + ystep
error = error - deltax #if end
root.mainloop() #main ends

main()


#the indentation of program is changed after posting,edit it while implementing.(python works based on indentation)