This document describes Bresenham's line algorithm for drawing lines on a pixel-based display. It discusses how Bresenham's algorithm uses integer arithmetic to calculate pixel coordinates along the line between two points, to avoid issues with floating-point values. The algorithm works by incrementing the x coordinate by 1 each time and selectively increasing the y coordinate to stay closest to the true line. It uses a decision parameter and slope error value to determine whether to increment y at each step. Examples are provided to illustrate the output coordinates generated between two points.

1. Bresenham’s Line Generation
Algorithm
Dr. R. B. Chadge
Department of Mechanical Engineering
YCCE, Nagpur

2. Introduction
• Computer graphics use three different types of
algorithms to generate lines namely:
1) DDA Line drawing algorithm
2) Bresenham Line drawing algorithm
3) Mid Point Line drawing algorithm

3. Introduction
• This algorithm is named after Bresenham. Here, the main
task is to find all the intermediate points required for
drawing line AB on the computer screen of pixels.
• In this algorithm, every pixel has integer coordinates.
Apart from that, the Bresenham algorithm works on
addition and subtraction operations.
• It has more precision or accuracy and the complexity of
calculation is simple.

4. Bresenham’s Line Generation Algorithm
• Given the coordinate of two points A(x1, y1) and
B(x2, y2).
• The task is to find all the intermediate points
required for drawing line AB on the computer screen
of pixels.
• Note that every pixel has integer coordinates.

5. Bresenham’s Line Generation Algorithm
• Examples:
1. Input : A(0,0), B(4,4)
Output : (0,0), (1,1), (2,2), (3,3), (4,4)
2. Input : A(0,0), B(4,2)
Output : (0,0), (1,0), (2,1), (3,1), (4,2)

6. Bresenham’s Line Generation Algorithm
• Below are some assumptions to keep the algorithm
simple.
1. We draw lines from left to right.
2. x1 < x2 and y1< y2
3. Slope of the line is between 0 and 1. We draw a line
from lower left to upper right.

7. Bresenham’s Line Generation Algorithm
• The idea of Bresenham’s algorithm is to avoid
floating point multiplication and addition to compute
mx + c, and then compute the round value of (mx +
c) in every step.
• In Bresenham’s algorithm, we move across the x-axis
in unit intervals.

8. Bresenham’s Line Generation Algorithm
• We always increase x by 1, and we choose about
next y, whether we need to go to y+1 or remain on y.
• In other words, from any position (Xk, Yk) we need to
choose between (Xk + 1, Yk) and (Xk + 1, Yk + 1).

9. Bresenham’s Line Generation Algorithm

10. • We would like to pick the y value (among Yk + 1 and
Yk) corresponding to a point that is closer to the
original line.
• We need a decision parameter to decide whether to
pick Yk + 1 or Yk as the next point.
• The idea is to keep track of slope error from the
previous increment to y.
Bresenham’s Line Generation Algorithm

11. • If the slope error becomes greater than 0.5, we know
that the line has moved upwards one pixel and that
we must increment our y coordinate and readjust the
error to represent the distance from the top of the
new pixel – which is done by subtracting one from
the error.
Bresenham’s Line Generation Algorithm