--- title: "Bresenham: line (10,20) to (15,2)" subject: "Computer Graphics" chapter: 2 key: "semester_5/computer_graphics:digitize-line-10-20-15-2" source: https://www.bctengineer.com/q/semester_5/computer_graphics/digitize-line-10-20-15-2 site: BCT Engineering --- # Bresenham: line (10,20) to (15,2) Computer Graphics · Chapter 2: Scan-Conversion - Asked in: 2079 Baisakh, 5 marks - Video: [Bresenham’s Line Drawing Algorithm :Problem Solving](https://www.youtube.com/watch?v=3p7-thBl00E) — Namitha Ramachandran - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/computer_graphics/digitize-line-10-20-15-2 - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-2 ## Question Digitize a line with end points (10,20) and (15,2) using Bresenham's algorithm. ## Short answer Use Bresenham with |m|>1 negative. p0 = 2*5 – 18 = –8. y decrements each step; when p<0, x stays, p+=10; when p≥0, x+=1, p–=26. Resulting pixels: (10,20), (10,19), (11,18), (11,17), (11,16), (11,15), (12,14), (12,13), (12,12), (13,11), (13,10), (13,9), (13,8), (14,7), (14,6), (14,5), (14,4), (15,3), (15,2). ## Answer **Given:** (10,20) to (15,2). Δx = 5, |Δy| = 18, the slope is negative with |m| = 3.6 > 1. So y is decremented by 1 at each step and the decision parameter decides whether x stays or increases. ```text p0 = 2Δx − |Δy| = 10 − 18 = −8 If p < 0: x same, p = p + 2Δx = p + 10 If p ≥ 0: x + 1, p = p + 2Δx − 2|Δy| = p − 26 ``` | k | p_k | (x_k, y_k) | |---|---|---| | 0 | -8 | (10,20) | | 1 | 2 | (10,19) | | 2 | -24 | (11,18) | | 3 | -14 | (11,17) | | 4 | -4 | (11,16) | | 5 | 6 | (11,15) | | 6 | -20 | (12,14) | | 7 | -10 | (12,13) | | 8 | 0 | (12,12) | | 9 | -26 | (13,11) | | 10 | -16 | (13,10) | | 11 | -6 | (13,9) | | 12 | 4 | (13,8) | | 13 | -22 | (14,7) | | 14 | -12 | (14,6) | | 15 | -2 | (14,5) | | 16 | 8 | (14,4) | | 17 | -18 | (15,3) | | 18 | -8 | (15,2) | Pixels: ```text (10,20) (10,19) (11,18) (11,17) (11,16) (11,15) (12,14) (12,13) (12,12) (13,11) (13,10) (13,9) (13,8) (14,7) (14,6) (14,5) (14,4) (15,3) (15,2) ``` **Answer: 19 pixels from (10,20) to (15,2) as listed.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For the line (10,20) to (15,2), which axis is stepped by 1 each time? A. y (decreasing), since |Δy| = 18 > Δx = 5 B. x (increasing), since Δx is the smaller change C. x (decreasing) D. y (increasing) Answer: A. The slope magnitude is 3.6 > 1, so y is the unit-step axis and goes down. (Key point: Driving axis) 2. The initial decision parameter p0 is: A. 8 B. −8 C. −13 D. 28 Answer: B. p0 = 2Δx − |Δy| = 10 − 18 = −8. (Key point: Initial parameter) 3. At a step where p = 2 (≥ 0), what happens? A. x stays and the new p = 12 B. x increases by 1 and the new p = 2 + 10 = 12 C. x increases by 1 and the new p = 2 − 26 = −24 D. x stays and the new p = −24 Answer: C. For p ≥ 0: x+1 and p += 2Δx − 2|Δy| = 10 − 36 = −26. (Key point: Update rule) 4. How many pixels are plotted from (10,20) to (15,2)? A. 18 B. 5 C. 20 D. 19 Answer: D. y goes from 20 to 2 in steps of 1, giving 18 steps plus the start point = 19 pixels. (Key point: Number of pixels) ## Close variants set in other exams - [Bresenham: line (20,10) to (30,18)](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adigitize-line-20-10-30-18) — Computer Graphics, chapter 2, asked 4× ## Related in Computer Graphics - [Bresenham: line (25,20) to (15,10)](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adigitize-line-25-20-15-10) — Computer Graphics, chapter 2 - [Bresenham: endpoints (10,18),(15,8)](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adigitize-point-10-18-15-8) — Computer Graphics, chapter 2 - [DDA versus Bresenham line algorithm](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adda-vs-bresenham-line) — Computer Graphics, chapter 2, asked 6× - [Write Bresenham's line algorithm](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Abresenham-line-algorithm) — Computer Graphics, chapter 2, asked 3× - [Bezier points at u=0.25,0.5,0.75: (10,15)...](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Abezier-points-control-10-15) — Computer Graphics, chapter 5, asked 4× - [Bresenham's algorithm for all slopes](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Abresenham-all-slopes) — Computer Graphics, chapter 2 ## Related in other subjects - [Laplace: 2x2 grid 10/15/20](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Alaplace-2x2-10-15-20-25) — Numerical Method, chapter 7, asked 6× - [Fault at far end of 33 kV line](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Afault-far-end-33kv-line) — Power System Analysis II, chapter 3 - [Fault at load end of overhead line](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Afault-load-end-33kv-line) — Power System Analysis II, chapter 3 - [Reactance diagram: 20 MVA generator, 15 kV/25 MVA base](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Areactance-diagram-20mva-15kv-25mva) — Power System Analysis I, chapter 3