Computer Graphics · Unit 2 · 6 hrs
Scan Conversion Algorithm
Exam-focused notes for Scan Conversion Algorithm (Computer Graphics, CSC214): what the TU syllabus asks and how it has actually been tested, with 11 solved past questions from this unit.
What this unit covers
- Scan Converting a Point and a straight Line: DDA Line Algorithm, Bresenham's Line Algorithm
- Scan Converting Circle and Ellipse: Mid Point Circle and Ellipse Algorithm
- Area Filling: Scan Line Polygon fill Algorithm, Inside-outside Test, Scan line fill of Curved Boundary area, Boundary-fill and Flood-fill algorithm
Scan Converting a Point and a straight Line
Derive the expression for Bresenham's Line Drawing algorithm. Trace the points in the line path with starting point (6, 12) and end point (10, 5) using Bresenham’s line drawing algorithm.[10]
Bresenham's algorithm draws a line using only integer arithmetic (addition, subtraction, and multiplication by 2). It selects, at each step, the pixel nearest to the true line path. Assume we have plotted pixel $(xk, yk)$. The next pixel is either: - E: $(x...
Full solved answer →What is a Digital Differential Analyzer (DDA)? How can you draw the line using this algorithm? Trace the points on the line path between A (1,3) and B (6,7) using Bresenham's line drawing algorithm.[10]
A Digital Differential Analyzer (DDA) is an incremental scan-conversion line drawing algorithm. It computes points along a line by sampling the line at unit intervals in one coordinate and calculating the corresponding value of the other coordinate using th...
Full solved answer →Explain the working details of Mid-point circle algorithm? Trace the points along the line path having two end points (6,9) and (2,3) using Bresenham's line drawing algorithm.[10]
--- The Mid-Point Circle Algorithm draws a circle using only integer arithmetic (additions/subtractions). At each step it uses a decision parameter to choose between two candidate pixels. A circle centered at origin has 8-fold symmetry. If $(x, y)$ lies on ...
Full solved answer →List the major differences between DDA and Bradenham’s Line drawing algorithm. Illustrate the DDA algorithm to the line width end points (2, 2) and (9, 2).[10]
--- - Algorithm comparison: DDA vs Bresenham's (question spells it "Bradenham's" and "width" is a typo for "with") - Line end points: - Start: $(x1, y1) = (2, 2)$ - End: $(x2, y2) = (9, 2)$ All data present. Proceeding. --- Basis DDA Algorithm Bresenham's A...
Full solved answer →Trace the Bresenham’s Line drawing algorithm for the end points(1, 1) and (8, 5). [5]
- Start point: $(x1, y1) = (1, 1)$ - End point: $(x2, y2) = (8, 5)$ $$\Delta x = x2 - x1 = 8 - 1 = 7$$ $$\Delta y = y2 - y1 = 5 - 1 = 4$$ Since $\Delta x \Delta y$, we step along the x-axis (increment x by 1 each step). Initial decision parameter: $$p0 = 2\...
Full solved answer →Scan Converting Circle and Ellipse
Plot the first octant of a circle centered at (-2, -2), having a radius of 5 units using the mid-point circle algorithm. [5]
- Center: $(xc, yc) = (-2, -2)$ - Radius: $r = 5$ Compute points relative to origin starting at $(0, r)$, then translate by adding $(xc, yc)$. First octant runs while $x \le y$. Initial decision parameter: $$p0 = 1 - r = 1 - 5 = -4$$ Update rules: - If $p <...
Full solved answer →Write down algorithm steps of mid-point ellipse drawing algorithm. [5]
The mid-point ellipse drawing algorithm is an efficient raster scan method that uses integer arithmetic to determine the closest pixel positions along an ellipse path. The algorithm divides the ellipse into two regions based on the slope of the curve. - Reg...
Full solved answer →Plot the 1st octant of a circle centered at origin, having the radius 10 units. [5]
- Center: origin $(0, 0)$ - Radius: $r = 10$ units - Required: 1st octant only (arc from $(0, 10)$ to the $x = y$ line, i.e. 90° to 45°) Starting point: $(x0, y0) = (0, r) = (0, 10)$ Initial decision parameter: $$p0 = 1 - r = 1 - 10 = -9$$ Update rules (for...
Full solved answer →Plot the ellipse centered at (0, 0) with radius rx = 8 and ry = 6, using mid point ellipse drawing algorithm. [5]
--- - Center $(xc, yc) = (0, 0)$ - $rx = 8$ - $ry = 6$ Precomputed: - $rx^2 = 64$ - $ry^2 = 36$ - Starting point: $(x0, y0) = (0, ry) = (0, 6)$ --- Continue while $2 ry^2 x < 2 rx^2 y$. Initial decision parameter: $$p10 = ry^2 - rx^2 ry + \tfrac{1}{4} rx^2 ...
Full solved answer →Area Filling
Explain the importance of filling algorithms in graphics applications. Differentiate between boundary and flood fill algorithm with algorithm. [5]
Filling algorithms are fundamental in computer graphics for the following reasons: - Region coloring: They allow filling closed regions with a desired color, which is essential for rendering 2D shapes, polygons, and objects realistically. - Paint applicatio...
Full solved answer →Describe the requirement for line clipping. Explain the scan line polygon filling algorithm. [5]
--- Line clipping is the process of removing (clipping) portions of a line that lie outside a defined clipping window, retaining only the visible portion inside the window. 1. Clipping Window Definition: A rectangular clipping window must be defined by its ...
Full solved answer →Make Unit 2 stick
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