Computer Graphics · Unit 3
Line and Circle Drawing Algorithms
Exam-focused notes for Line and Circle Drawing Algorithms (Computer Graphics, BIT304): what the TU syllabus asks and how it has actually been tested, with 7 solved past questions from this unit.
What this unit covers
- DDA line drawing algorithm
- Bresenham's line drawing algorithm
- Comparison of line drawing algorithms
- Midpoint circle drawing algorithm
- Bresenham's circle drawing algorithm
- Decision parameters for circle generation
DDA line drawing algorithm
Bresenham's Circle Drawing Algorithm & DDA Line Algorithm Trace [10]
Part B (numeric): - Start point: $(x1, y1) = (2, 2)$ - End point: $(x2, y2) = (6, 6)$ Part A is descriptive (no numeric inputs required). --- Definition: Bresenham's circle drawing algorithm is an efficient scan-conversion technique that plots the pixels cl...
Full solved answer →Midpoint circle drawing algorithm
Digitize circle with center (0, 0) and radius = 6. [5]
- Center: $(xc, yc) = (0, 0)$ - Radius: $r = 6$ - Start point: $(x, y) = (0, r) = (0, 6)$ - Initial decision parameter: $p0 = 1 - r = 1 - 6 = -5$ We compute points in the second octant ($x$ from 0 up to $x = y$), then apply 8-way symmetry. - If $p < 0$: cho...
Full solved answer →Write mid point circle drawing algorithm. [5]
The Midpoint Circle Drawing Algorithm (also called Bresenham's Circle Algorithm) is used to draw circles on a raster display by determining which pixels should be illuminated to form a circle with a given center and radius. The algorithm uses the midpoint b...
Full solved answer →Bresenham's line drawing algorithm
Write the algorithm for Bresenham's line drawing? Digitize a line with end points A(6, 9) and B(10,5) using Bresenham's line drawing algorithm.[10]
- Endpoint A: $(x1, y1) = (6, 9)$ - Endpoint B: $(x2, y2) = (10, 5)$ 1. Input the two endpoints $(x1, y1)$ and $(x2, y2)$. 2. Compute $\Delta x = x2 - x1$ and $\Delta y = y2 - y1$. 3. Plot the first point $(x1, y1)$. 4. Calculate the initial decision parame...
Full solved answer →List the major differences between DDA and Bresenham's algorithm. Illustrate the Bresenham's algorithm to the line with end points(10, 6) and (12, 1).[10]
- Endpoint 1: $(x1, y1) = (10, 6)$ - Endpoint 2: $(x2, y2) = (12, 1)$ Feature DDA Algorithm Bresenham's Algorithm ---------------------------------------------- Computation Uses floating-point arithmetic Uses only integer arithmetic Speed Slower (floating-p...
Full solved answer →Derive the Bresenham's decision parameter to draw a line with negative slope. [5]
For a line with negative slope (m < -1 or -1 < m < 0), we move from point (x₀, y₀) to (xₙ, yₙ) where: - x increases (or stays same) - y decreases We assume the line equation: y = mx + c where m is negative At each step, we are at pixel (xₖ, yₖ). We must cho...
Full solved answer →Decision parameters for circle generation
How decision parameter can be used to draw circle? Calculate the points to draw a circle having radius 5 and center as (10, 5).[10]
- Radius $r = 5$ - Center $(xc, yc) = (10, 5)$ The Midpoint Circle Algorithm uses a decision parameter to choose between two candidate pixels while scanning one octant, avoiding floating-point square roots. For a circle centered at origin: $$f(x, y) = x^2 +...
Full solved answer →Make Unit 3 stick
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