Computer Graphics - B.Sc. (Hons.) Computer Science - Delhi University 2024 Question Paper

Dhruv Badaya
May 30, 2024
3 min read

Updated: Mar 11

This is the official question paper of Computer Graphics Paper of B.Sc. (Hons.) Computer Science Course at the University of Delhi.
All parts of question 1 are compulsory.
Attempt any four questions from question 2 to question 7.
Part of a question must be answered together.
Some symbols may not be visible on mobile devices. Hence we recommend that you use a desktop to view the solutions to the questions.
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Question 1 (a): Prove that two scaling transformations are commutative.

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Question 1 (b): How long would it take to load a 640 x 480 frame buffer with 12-bit per pixel if 10⁵ bits can be transferred per second?

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Question 1 (c): Derive 2D transformation that rotates a point by θ degrees about the origin. Write matrix representation for rotation.

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Question 1 (d): State any two differences between parallel and perspective projection.

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Question 1 (e): Describe briefly the steps involved in design of animation sequence.

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Question 1 (f): What is RGB color model?

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Question 1 (g): Scan convert the first three coordinates of a line segment P(1,1) and Q(8,5) using Bresenham's mid-point line algorithm.

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Question 1 (h): State any two properties of Bezier curve.

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Question 1 (i): What is the condition for trivial rejection of a line segment LM with L(0,5) & M(1,5) in Cohen Sutherland Line Clipping algorithm using rectangular window defined by vertices A(0,0), B(1,0), C(1,1) and D(0,1).

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Question 1 (j): Name two techniques to generate color in a CRT.

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Question 1 (k): Magnify the triangle with vertices A(0,0), B(1,1) and C(5,2) to twice its size keeping C(5,2) fixed.

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Question 1 (l): Define resolution and persistence.

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Question 1 (m): What are the three steps to fill a span in Scanline Polygon filling algorithm?

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Question 1 (n): What is morphing?

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Question 2 (a): Scan convert the first octant of a circle using midpoint circle algorithm whose radius = 8 and centre is (0,0)

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Question 2 (b): Obtain the reflection of triangle ABC with vertices A(0,1), B(1,2) and C(2,0) about the line y = -x. Use homogeneous coordinates.

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Question 3 (a): Derive the Basis matrix for parametric cubic bezier curve. Also, obtain its blending functions.

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Question 3 (b): Find the equation of the Bezier curve which passes through points (0,0) and (4,2) and controlled through points (14,10) and (4,0).

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Question 4 (a): What do you mean by hidden surface removal? Explain depth buffer algorithm for visible surface determination.

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Question 4 (b): What is dithering? What are its advantages over halftoning?

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Question 5 (a): Describe Phong interpolation shading method what are the merits and demerits of this method?

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Question 5 (b): Consider any 3D object, Write the transformations matrices to rotate it about y-axis by θ = -30 degrees, about x-axis by α = 45 degrees ' and projected onto z = 0 plane from center of projection at z꜀=2.5. What will be the value of the vanishing point?

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Question 6 (a): Specify the rules to equalize the set of edges in key frames "k" and "k+1" in an animation scene using these rules, transform a triangle into a pentagon.

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Question 6 (b): Draw the four stages of the Sutherland Hodgeman clipping algorithm as the polygon shown below is clipped by the right, top, left, and bottom clip rectangle edge.

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Question 7 (a): List and explain the data structures used in Scan line Polygon filling algorithm.

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Question 7 (b): Discuss the architecture of raster display system with integrated display processor.

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Question 7 (c): Compute a 4 x 4 3D transformation matrix to rotate the triangle ABC having coordinates A(0,0,0), B(1,1,2) and C(1,1,3) by 90 degrees about X-axis keeping B fixed.

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END OF PAPER

Question 1 (a): Prove that two scaling transformations are commutative.

Question 1 (b): How long would it take to load a 640 x 480 frame buffer with 12-bit per pixel if 10⁵ bits can be transferred per second?

Question 1 (c): Derive 2D transformation that rotates a point by θ degrees about the origin. Write matrix representation for rotation.

Question 1 (d): State any two differences between parallel and perspective projection.

Question 1 (e): Describe briefly the steps involved in design of animation sequence.

Question 1 (f): What is RGB color model?

Question 1 (g): Scan convert the first three coordinates of a line segment P(1,1) and Q(8,5) using Bresenham's mid-point line algorithm.

Question 1 (h): State any two properties of Bezier curve.

Question 1 (i): What is the condition for trivial rejection of a line segment LM with L(0,5) & M(1,5) in Cohen Sutherland Line Clipping algorithm using rectangular window defined by vertices A(0,0), B(1,0), C(1,1) and D(0,1).

Question 1 (j): Name two techniques to generate color in a CRT.

Question 1 (k): Magnify the triangle with vertices A(0,0), B(1,1) and C(5,2) to twice its size keeping C(5,2) fixed.

Question 1 (l): Define resolution and persistence.

Question 1 (m): What are the three steps to fill a span in Scanline Polygon filling algorithm?

Question 1 (n): What is morphing?

Question 2 (a): Scan convert the first octant of a circle using midpoint circle algorithm whose radius = 8 and centre is (0,0)

Question 2 (b): Obtain the reflection of triangle ABC with vertices A(0,1), B(1,2) and C(2,0) about the line y = -x. Use homogeneous coordinates.

Question 3 (a): Derive the Basis matrix for parametric cubic bezier curve. Also, obtain its blending functions.

Question 3 (b): Find the equation of the Bezier curve which passes through points (0,0) and (4,2) and controlled through points (14,10) and (4,0).

Question 4 (a): What do you mean by hidden surface removal? Explain depth buffer algorithm for visible surface determination.

Question 4 (b): What is dithering? What are its advantages over halftoning?

Question 5 (a): Describe Phong interpolation shading method what are the merits and demerits of this method?

Question 5 (b): Consider any 3D object, Write the transformations matrices to rotate it about y-axis by θ = -30 degrees, about x-axis by α = 45 degrees ' and projected onto z = 0 plane from center of projection at z꜀=2.5. What will be the value of the vanishing point?

Question 6 (a): Specify the rules to equalize the set of edges in key frames "k" and "k+1" in an animation scene using these rules, transform a triangle into a pentagon.

Question 6 (b): Draw the four stages of the Sutherland Hodgeman clipping algorithm as the polygon shown below is clipped by the right, top, left, and bottom clip rectangle edge.

Question 7 (a): List and explain the data structures used in Scan line Polygon filling algorithm.

Question 7 (b): Discuss the architecture of raster display system with integrated display processor.

Question 7 (c): Compute a 4 x 4 3D transformation matrix to rotate the triangle ABC having coordinates A(0,0,0), B(1,1,2) and C(1,1,3) by 90 degrees about X-axis keeping B fixed.

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