Bresenham Line Drawing Algorithm
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This document explains the Bresenham line drawing algorithm in 5 parts. It describes how the algorithm works to draw a line on a pixel grid by incrementally choosing the next pixel based on the slope. It provides an example of drawing a line from (2,3) to (7,5), showing each step of calculating the error term and choosing the next pixel. The algorithm is useful for raster graphics as it results in the fastest line drawing method for slopes less than 1.
![Computer Graphics
2 of 5
Bresenham Line Drawing Algorithm in Step Form for |m| < 1
Note: Let (x1, y1) is the left endpoint, (x2, y2) is the right endpoint,
and m is the gradient of the line segment.
1) Set k = 0.
2) Fill pixel (x[k], y[k]); i.e., fill pixel (x1, y1).
3) Compute p [k] = 2 * dy – dx where dx = x2 – x1 and dy = y2 – y1.
4) If p [k] < 0, fill pixel (x [k] + 1, y [k]) and p [k + 1] = p [k] + 2 * dy.
Otherwise, fill pixel (x [k] + 1, y [k] + 1) and p [k + 1] = p [k] + 2 *
dy – 2 * dx.
5) Set k = k + 1 and go to step 4 if k < dx.](https://image.slidesharecdn.com/bresenham-200621103800/85/Bresenham-Line-Drawing-Algorithm-2-320.jpg)
![Computer Graphics
3 of 5
Example
Demonstrate drawing a line segment from (2, 3) to (7, 5).
Answer:
5
4
3
2 3 4 5 6 7
k = 0;
SET_PIXEL (2, 3);
5
4
3
2 3 4 5 6 7
dx = 7 – 2 = 5;
dy = 5 – 3 = 2;
p [0] = 2 * 2 – 5 = -1;
p [0] < 0;
SET_PIXEL (3, 3);
5
4
3
2 3 4 5 6 7](https://image.slidesharecdn.com/bresenham-200621103800/85/Bresenham-Line-Drawing-Algorithm-3-320.jpg)
![Computer Graphics
4 of 5
p [1] = -1 + 2 (2) = 3;
k = 1 < 5;
p [1] ≥ 0;
SET_PIXEL (4, 4);
5
4
3
2 3 4 5 6 7
p [2] = 3 + 2 (2) – 2 (5) = -3;
k = 2 < 5;
p [2] < 0;
SET_PIXEL (5, 4);
5
4
3
2 3 4 5 6 7
p [3] = -3 + 2 (2) = 1;
k = 3 < 5;](https://image.slidesharecdn.com/bresenham-200621103800/85/Bresenham-Line-Drawing-Algorithm-4-320.jpg)
![Computer Graphics
5 of 5
p [3] ≥ 0;
SET_PIXEL (6, 5);
5
4
3
2 3 4 5 6 7
p [4] = 1 + 2 (2) – 2 (5) = -5;
k = 4 < 5;
p [4] < 0;
SET_PIXEL (7, 5);
5
4
3
2 3 4 5 6 7
p [5] = -5 + 2 (2) = -1;
k = 5 ≥ 5.](https://image.slidesharecdn.com/bresenham-200621103800/85/Bresenham-Line-Drawing-Algorithm-5-320.jpg)
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Bresenham Line Drawing Algorithm
- 1. Computer Graphics 1 of 5 Lesson 2: Bresenham Line Drawing Algorithm Author: Kasun Ranga Wijeweera Email: [email protected] Date: 2020 June 19 The screen of a computer is a rectangular grid. A cell in the grid is called a “pixel”. An example is given below that has 20 × 20 pixels. 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
- 2. Computer Graphics 2 of 5 Bresenham Line Drawing Algorithm in Step Form for |m| < 1 Note: Let (x1, y1) is the left endpoint, (x2, y2) is the right endpoint, and m is the gradient of the line segment. 1) Set k = 0. 2) Fill pixel (x[k], y[k]); i.e., fill pixel (x1, y1). 3) Compute p [k] = 2 * dy – dx where dx = x2 – x1 and dy = y2 – y1. 4) If p [k] < 0, fill pixel (x [k] + 1, y [k]) and p [k + 1] = p [k] + 2 * dy. Otherwise, fill pixel (x [k] + 1, y [k] + 1) and p [k + 1] = p [k] + 2 * dy – 2 * dx. 5) Set k = k + 1 and go to step 4 if k < dx.
- 3. Computer Graphics 3 of 5 Example Demonstrate drawing a line segment from (2, 3) to (7, 5). Answer: 5 4 3 2 3 4 5 6 7 k = 0; SET_PIXEL (2, 3); 5 4 3 2 3 4 5 6 7 dx = 7 – 2 = 5; dy = 5 – 3 = 2; p [0] = 2 * 2 – 5 = -1; p [0] < 0; SET_PIXEL (3, 3); 5 4 3 2 3 4 5 6 7
- 4. Computer Graphics 4 of 5 p [1] = -1 + 2 (2) = 3; k = 1 < 5; p [1] ≥ 0; SET_PIXEL (4, 4); 5 4 3 2 3 4 5 6 7 p [2] = 3 + 2 (2) – 2 (5) = -3; k = 2 < 5; p [2] < 0; SET_PIXEL (5, 4); 5 4 3 2 3 4 5 6 7 p [3] = -3 + 2 (2) = 1; k = 3 < 5;
- 5. Computer Graphics 5 of 5 p [3] ≥ 0; SET_PIXEL (6, 5); 5 4 3 2 3 4 5 6 7 p [4] = 1 + 2 (2) – 2 (5) = -5; k = 4 < 5; p [4] < 0; SET_PIXEL (7, 5); 5 4 3 2 3 4 5 6 7 p [5] = -5 + 2 (2) = -1; k = 5 ≥ 5.