Probability Engine · CSC209

Computer Graphics (BSc CSIT, CSC209): the questions likely to come

32 analyzed questions from 8 past papers (2074-2082), grouped by syllabus unit — each with its probability, how often it's been asked, and where to study the answer.

8
Papers analyzed
2074-2082
32
Analyzed questions
across 6 syllabus units
5
Very likely units
high-probability topics
5
Units = 80% of marks
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Model answers for this subject are being written. Every question links to its original paper so you can study from the source meanwhile.
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U5 · Q1/10 · 208110 marks
Three-Dimensional Object Representations, Geometric Transformations and Viewing

Explain parallel and perspective projections in 3D graphics. Derive the transformation matrix for perspective projection.

46%
Possible to appearAppeared in 4 of the last 4 board papers
Seen in
How well do you know this?rating moves you on
MODEL ANSWERU5 · 10 marks

Parallel and Perspective Projections in 3D Graphics

Projection maps 3D points onto a 2D view (projection) plane along projectors (projection lines).

Parallel Projection

The projectors are parallel to one another; the centre of projection is at infinity.

  • Preserves relative proportions and parallelism of lines; no foreshortening with distance.
  • Good for engineering / CAD drawings where true dimensions matter.
  • Sub-types: Orthographic (projectors perpendicular to the plane) and Oblique (projectors at an oblique angle).

Perspective Projection

All projectors converge to a single point called the centre of projection (COP).

  • Objects farther from the viewer appear smaller (perspective foreshortening).
  • Parallel lines (not parallel to the view plane) converge at vanishing points.
  • Produces realistic images, as in photographs and the human eye.
  • Classified by number of vanishing points: one-point, two-point, three-point.

Derivation of the Perspective Projection Matrix

Let the centre of projection be at the origin and the projection plane at z=dz = d (distance dd from the eye), with a point P=(x,y,z)P = (x, y, z) to be projected onto P′=(xp,yp,d)P' = (x_p, y_p, d).

Using similar triangles along the line from the COP through PP to the plane:

xpd=xz⇒xp=xz/d,yp=yz/d\frac{x_p}{d} = \frac{x}{z} \quad\Rightarrow\quad x_p = \frac{x}{z/d}, \qquad y_p = \frac{y}{z/d}

In homogeneous coordinates (x,y,z,1)(x, y, z, 1), this division by z/dz/d is captured by placing 1/d1/d in the matrix so that the homogeneous ww-coordinate becomes z/dz/d:

P′=[x′y′z′w]=[100001000010001/d0][xyz1]=[xyzz/d]P' = \begin{bmatrix} x' \\ y' \\ z' \\ w \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 1/d & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \\ 1 \end{bmatrix} = \begin{bmatrix} x \\ y \\ z \\ z/d \end{bmatrix}

Dividing through by the homogeneous coordinate w=z/dw = z/d gives the projected point:

xp=xz/d,yp=yz/d,zp=dx_p = \frac{x}{z/d}, \qquad y_p = \frac{y}{z/d}, \qquad z_p = d

which is exactly the perspective relation derived above. As d→∞d \to \infty the term 1/d→01/d \to 0 and the matrix reduces to the orthographic (parallel) projection, showing parallel projection is the limiting case of perspective projection.

AI-generated answer · unverifiedView in 2081 paper →
U5 · Question 1 of 10
Question Priority · U5ranked by appearance likelihood — study top-down

Three-Dimensional Object Representations, Geometric Transformations and Viewing

Analyzed next60%
1
★ TOP PICK

Explain parallel and perspective projections in 3D graphics. Derive the transformation matrix for perspective projection.

10 marksSEEN IN
46%
2

Differentiate between parallel projection and perspective projection.

5 marksSEEN IN
60%
3

What is a spline? Differentiate between interpolation and approximation splines.

5 marksSEEN IN
54%
4

What is a polygon mesh? Describe its types. Construct a polygon table and edge table for a cube of side 2 units placed with one vertex at origin.

10 marksSEEN IN
25%
5

Write the transformation matrices for 3D translation, scaling and rotation about the x-axis.

5 marksSEEN IN
48%
6

Explain Bezier curves and their properties. Derive the equation of a cubic Bezier curve with four control points.

10 marksSEEN IN
19%
7

Explain the 3D viewing pipeline in computer graphics. Explain about how a 3D world coordinate system is transformed to a 2D screen.

5 marksSEEN IN
25%
8

For control points P0(0,0), P1(1,2), P2(3,3), and P3(4,0), calculate the Bezier curve point at u = 0.5. Also plot the rough curve shape.

5 marksSEEN IN
25%
9

What is spatial-partitioning representation? Explain how it differs from boundary representation in terms of geometry storage and processing.

5 marksSEEN IN
25%
10

Write short notes on:

a. Lighting in OpenGL

b. Orthographic projection

5 marksSEEN IN
25%
03The mock

Sit a probable paper

A full mock exam built from the most likely questions, mirroring the real paper's structure. Every slot is a real past question.

Most Probable Paper

Mirrors the real structure · 60 marks · based on 8 past papers

Section A: Long Answer QuestionsAttempt any TWO questions.
  1. 1.

    Explain parallel and perspective projections in 3D graphics. Derive the transformation matrix for perspective projection.

    [10 marks]
    Three-Dimensional Object Representations, Geometric Transformations and ViewingVery likelyfrom 2081 paper →

    This question has recurred in 4 of 8 years; so far only in internal assessments, not the board; and its topic (Three-Dimensional Object Representations, Geometric Transformations and Viewing) appears in 100% of years.

  2. 2.

    What is 2D geometric transformation? Explain translation, rotation and scaling with their transformation matrices in homogeneous coordinates.

    [10 marks]
    Two-Dimensional Geometric TransformationsVery likelyfrom 2080 paper →

    This question has recurred in 4 of 8 years; so far only in internal assessments, not the board; and its topic (Two-Dimensional Geometric Transformations) appears in 100% of years.

  3. 3.

    Explain the scan-line polygon fill algorithm and the boundary fill algorithm with examples.

    [10 marks]
    Graphics Output Primitives and AttributesLikelyfrom 2081 paper →

    This question has recurred in 3 of 8 years; so far only in internal assessments, not the board; and its topic recurs in 6 of 8 years.

Section B: Short Answer QuestionsAttempt any EIGHT questions.
  1. 1.

    Differentiate between parallel projection and perspective projection.

    [5 marks]
    Three-Dimensional Object Representations, Geometric Transformations and ViewingVery likelyfrom 2081 paper →

    This question has recurred in 6 of 8 years; so far only in internal assessments, not the board; and its topic (Three-Dimensional Object Representations, Geometric Transformations and Viewing) appears in 100% of years.

  2. 2.

    Explain the working of a CRT (Cathode Ray Tube) with a suitable diagram.

    [5 marks]
    IntroductionVery likelyfrom 2081 paper →

    This question has recurred in 6 of 8 years; so far only in internal assessments, not the board; and its topic (Introduction) appears in 100% of years.

  3. 3.

    Explain the concept of window to viewport transformation.

    [5 marks]
    Two-Dimensional ViewingVery likelyfrom 2081 paper →

    This question has recurred in 6 of 8 years; so far only in internal assessments, not the board; and its topic (Two-Dimensional Viewing) appears in 88% of years.

  4. 4.

    What is a spline? Differentiate between interpolation and approximation splines.

    [5 marks]
    Three-Dimensional Object Representations, Geometric Transformations and ViewingVery likelyfrom 2081 paper →

    This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Three-Dimensional Object Representations, Geometric Transformations and Viewing) appears in 100% of years.

  5. 5.

    Write the transformation matrices for 3D translation, scaling and rotation about the x-axis.

    [5 marks]
    Three-Dimensional Object Representations, Geometric Transformations and ViewingVery likelyfrom 2080 paper →

    This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Three-Dimensional Object Representations, Geometric Transformations and Viewing) appears in 100% of years.

  6. 6.

    Explain the key frame system in computer animation.

    [5 marks]
    IntroductionVery likelyfrom 2081 paper →

    This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Introduction) appears in 100% of years.

  7. 7.

    Explain the working principle of a Raster scan display and a Random (vector) scan display.

    [5 marks]
    IntroductionVery likelyfrom 2081 paper →

    This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Introduction) appears in 100% of years.

  8. 8.

    Explain the DDA line drawing algorithm with its advantages and disadvantages.

    [5 marks]
    Graphics Output Primitives and AttributesLikelyfrom 2081 paper →

    This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic recurs in 6 of 8 years.

  9. 9.

    Differentiate between object-space and image-space methods of hidden surface removal.

    [5 marks]
    Visible Surface Detection and Illumination ModelsVery likelyfrom 2081 paper →

    This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Visible Surface Detection and Illumination Models) appears in 100% of years.

04The receipts

Behind the numbers

The raw evidence the predictions are computed from: marks per unit per year, syllabus weights, trends, and coverage.

Show the heatmap, topic table and coverage analysis

The receipt: marks per unit, per year

Each row is a syllabus unit, each column an exam year, each cell the marks that unit earned that year. Click any cell to see the actual questions behind it.

Marks:nonefew → many
2074
2075
2077
2078
2079
2080
2081
2082
Total
U5Three-Dimensional Object Representations, Geometric Transformations and Viewing
160
U1Introduction
90
U2Graphics Output Primitives and Attributes
115
U6Visible Surface Detection and Illumination Models
85
U3Two-Dimensional Geometric Transformations
75
U4Two-Dimensional Viewing
75
#Syllabus unitProbabilityAppearedAvg marksSyllabus weightExam vs syllabusTrendQuestions
1U5Three-Dimensional Object Representations, Geometric Transformations and ViewingVery likely100%
20742075207720782079208020812082
2020%9 lecture hrsOver-examinedexam 27% · syllabus 20%Rising4 recurring10 total
2U1IntroductionVery likely100%
20742075207720782079208020812082
11.29%4 lecture hrsOver-examinedexam 15% · syllabus 9%Steady3 recurring5 total
3U2Graphics Output Primitives and AttributesLikely75%
207420772078207920812082
19.220%9 lecture hrsBalancedexam 19% · syllabus 20%Steady4 recurring5 total
4U6Visible Surface Detection and Illumination ModelsVery likely100%
20742075207720782079208020812082
10.616%7 lecture hrsBalancedexam 14% · syllabus 16%Rising3 recurring5 total
5U3Two-Dimensional Geometric TransformationsVery likely100%
20742075207720782079208020812082
9.418%8 lecture hrsUnder-examinedexam 12% · syllabus 18%Steady2 recurring4 total
6U4Two-Dimensional ViewingVery likely88%
2074207520772078207920802081
10.718%8 lecture hrsUnder-examinedexam 12% · syllabus 18%Fading3 recurring3 total

Study smart, not hard

Drag the slider: studying the top 5 units in priority order covers ~88% of all observed marks.

  5. ~80% line

Lecture time vs exam marks

Where the exam pays more than the curriculum spends: ● lectures vs ● exam marks, as a share of the whole course. A long teal-leading bar = high-yield unit.

U5Three-Dimensional Object Representations, Geometric Transformations and Viewing
20% of lectures → 27% of markshigh yield
U1Introduction
9% of lectures → 15% of markshigh yield
U2Graphics Output Primitives and Attributes
20% of lectures → 19% of marks
U6Visible Surface Detection and Illumination Models
16% of lectures → 14% of marks
U3Two-Dimensional Geometric Transformations
18% of lectures → 12% of markslow yield
U4Two-Dimensional Viewing
18% of lectures → 12% of markslow yield

Topics are the official CSC209 syllabus units. Predictions are data-driven probabilities computed from 8 past papers (2074-2082) by mapping each real question to its syllabus unit. They indicate what has historically been likely, not guaranteed questions. Always study the full syllabus.