IGNOU MMTE 4 SOLVED ASSIGNMENT

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MMTE 4 2025 - English

Assignment

Course Code: MMTE-004

Assignment Code: MMTE-004/TMA/2025

Maximum Marks: 100

1. a) Have you used or seen used computer graphics in day-to-day life? How? Explain.

b) Explain the difference between the random scan and raster scan display devices.

c) Consider a non-interlaced raster system with resolution 1024 x1248 , and retrace rate of 40 frames per second. While displaying a frame, an electron beam spends 2 micro seconds in horizontal retrace, and 100 micro seconds in vertical retrace. Compute the fraction of the total refresh time per frame in retracing of the electron beam.

2. a) Modify the program given in Listing 1 of Unit 2 at page 25 of your SLM to draw the following shape

b) Compute the pixel positions along the line path of the line joining the points A(-1, 1) and B(7, 9) using the DDA Algorithm.

c) Write a C program to plot the cosine function from 0 to 2π, taking symmetry into consideration.

3. a) Write the formula for the cubic Bezier curve with control points P₀ (0, 1), P₁ (4, 8), P₂ (5, -1) and P₄ (7, 3).

b) Describe the Odd-Even rule and winding number rule with the help of an example. (

c) Implement the Boundary Fill Algorithm for an 8 -connected region.

d) Explain how will you generate a character using outline font method.

4. a) What will be the new coordinates of the quadrilateral with vertices (0, 2), (3, 2), (-1, 0) and (2, 0), when it is reflected about the y -axis, and then sheared in the x -direction by a factor of -2?

b) Find the normalisation transformation that maps a window with opposite corners at (2, 1) and (6, 8) to a viewport that is the entire normalized device screen.

c) Given the clipping window with corners at (0, 2) and (10, 8), trace the CohenSutherland line clipping algorithm for the triangle with vertices (4, -1), (8, 4) and (6, 10).

5. a) Find the uniform cubic B-spline curve generated by the control points (4, 2), (5, -2), (10, 5), (15, -1).

b) Do 3D translation and scaling commute with each other? Justify.

c) Suppose your camera is located at (8, 2, 0) and you are looking at (4, 1, 0). If the viewup vector is (1, 4, -1), then how will you transform the scene from the world coordinate system to viewing coordinate system?

6. a) Find the coordinates of all the corners of a cube whose two opposite corners have coordinates (1, 1, 1) and (5, 5, 5). What will be the image of this cube under an oblique parallel projection with α = φ = 45^o ? Justify.

b) Write a C program to draw a wireframe model of an octahedron

c) Explain the difference between the OpenGL functions glFrustum ( ) and gluPerspective ( ).

d) Using Liang-Barsky line clipping algorithm, clip the rectangle PQRS with coordinates P(2 3), Q(6, 3), R(6, 4), S(2, 4) against the clip window with opposite corners at (1, 0) and (4, 6).

MMTE 004 (January 2026 - July 2026) - ENGLISH

Assignment

Course Code: MMTE-004

Assignment Code: MMTE-004/TMA/2026

Maximum Marks: 100

1) a) Have you used or seen computer graphics in day-to-day life? Explain it.

b) What do you understand by the following terms? Colour CRT Monitors, Beam Penetration Method, and Shadow Mask Method. 

c) Compute the following

i) Resolution (per square inch) of 3×2 inch image that has 768×512 pixels.

ii) Width of an image having height of 6 inches and an aspect ratio 1.5 .

d) Suppose we have a video monitor with a display area of measurement 12 inches across and 9.6 inches high. If the resolution is 1280×1024 pixels. What is the diameter of each pixel (in cm)?

b) Using the DDA line drawing algorithm, determine the raster points for the line segment joining P(12,4) and Q(4,10). 

c) Write a C code for generating concentric circles. 

d) Using the Midpoint method and taking symmetry into account develop an efficient method for scan converting the curve y = x³/12 in [-10, 10]. 

3) a) Compare Boundary fill algorithm and Flood fill algorithm. Mention at least two advantages and limitations of both algorithms. Why does boundary fill algorithm fail when boundary is not completely closed? Explain with an example. 

b) Find the normalisation transformation matrix that maps the window with corners at (-2,1) and (6,9) onto a normalised viewport [0, 1] × [0, 1]. 

c) A quadrilateral with vertices (-3,2), (1,2), (-2,0), and (2,0) is reflected about the y-axis followed by shearing in the x-direction with the shear factor -2. Find the final coordinates. 

4) a) Let W be a window having two diagonally opposite corners at (1,1) and (5,4). Trace Cohen-Sutherland Line Clipping Algorithm for the line segment having two end points (0,0) and (4,5). 

b) Obtain the Cubic Bezier Curve equation for the control points P₀ = (0,0), P₁ = (2,5), P₂ = (5,1), P₃ = (7,3). 

c) Let W be a window with corners (0,0), (6,0), (6,5), and (0,5). Clip a triangle with vertices (2,1), (8,3) and (4,7) against the window W using the Liang-Barsky line clipping algorithm. 

5) a) Transform the scene from the world coordinate system to the viewing coordinate system with viewpoint at (2,-1,3). The view plane normal vector is (3,-2,4) and the view-up vector is (0,1,2). 

b) An object is rotated about the z-axis with an angle of 30° and then it is uniformly scaled up by a factor of 4. Find the resultant transformation matrix. 

c) Write the syntax of glFrustum() and gluPerspective(). Explain any two parameters of each function. 

d) Design a program that displays the top, front, and right views of a pyramid using orthographic projection. Explain the difference between single-view and multi-view representations of 3D objects. Why are multi-view projections important? 

6) a) Design a program that performs continuous rotation of a hexagon about an arbitrary point (x₀, y₀). 

b) Show that reflection about the line y = mx can be achieved by a sequence of rotation, reflection, and inverse rotation operations. 

c) The centre of projection coincides with the origin. The projection plane passes through the point P(1,5,6) and has a normal vector (3,2,-1). Obtain the perspective projection transformation. 

d) A square has opposite vertices at (0,1) and (2,3). Shear the square 

i) by 1 unit along the x-axis with respect to y = 1.

ii) by 3 units along the y-axis with respect to x = 1.

7) a) A cube has two diagonally opposite vertices at (2, 2, 2) and (6, 6, 6). Find the coordinates of all its corners and obtain its projection using an oblique parallel projection with α = 45°, ϕ = 30°. 

b) Find the uniform cubic B-spline curve generated by the control points (2,1), (6,-3), (9,4), (14,0). 

 

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