**IGNOU MCA MCS-053 5th semester term-end examination (**

**COMPUTER GRAPHICS AND**

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**Notes-1**

(b) Obtain the matrix that represents two dimensional xy shearing by factors a and b along x & y axis, respectively about the origin.

(c) Differentiate between window and viewport in clipping.

(d) Explain flood-fill method of polygon filling.

(e) Differentiate between the following :

(i) Zero Vs. Non- zero accelerations for simulating motion

(ii) GIF Vs. JPEG

(f) What is a homogenous coordinate system for 3D- transformation ? What are the advantages of using homogenous coordinate system ?

(g) Derive an expression to show the combined effect of ambient and diffused reflection in the context of illumination model.

(h) What is Hypermedia ? How is it different from hypertext ?

2. (a) Write DDA line drawing algorithm; use this algorithm draw a to line between (0,0) and

(6,6).

(b) Explain Prong Illumination model with the help of diagram.

(c) What is orthographic projection ? Write a matrix for an orthographic projection for Z = 0 plane.

3. (a) Explain Cohen Sutherland line clipping algorithm. State the merits and demerits of Cohen Sutherland algorithm over Cyrus-Beck line clipping algorithm.

(b) Derive a general 2D-transformation matrix of rotation of a point P(x,y) though an angle in counterclockwise direction with respect to origin.

(c) Differentiate between Ray Tracing & Ray Casting.

4. (a) What is Bezier curve ? Prove the following for Bezier curve :

(b) What is digital video ? Define Frame rate,and Frame dimensions in the context of digital video.

(c) Explain the scan line method for identifying visible surfaces.

(d) Explain the following in the context of multimedia :

(i) Morphing

(ii) Authoring tools

(iii) Vector graphics

5. (a) The unit cube (Fig.1) is projected onto the xy plane. Note the position of the x, y and z axes. Draw the projected image using perspective projection on the z = 0 plane with the Centre Of Projection (COP) is E(0,0, -10)

(b) Explain the following terms :

(i) Z Buffer

(ii) Types of Animation

(iii) Aspect Ratio

(iv) Video Conferencing

(v) Parallel Projection

(vi) Specular Reflection

(vii) Ambient light.

**Notes-2**

(b) Write 3D transformation matrices for rotation using homogeneous coordinate system with respect to X, Y and Z axes respectively.

(c) Draw the tree structure to describe the taxonomy of projection.

(d) How is frame buffer used to control the color and intensity of the computer screen ?

(e) Determine the general expression for a cubic Bezier curve, with vertices (control points) P0(0, 40); P1(40, 40); P2(60, 20); P3(60, -10).

(f) How many key frames are required to produce a five-minute animation film sequence with no duplicates ?

(g) Explain Window-to-Viewport transformation with the help of a diagram.

(h) Explain how ray tracing differs from raycasting with the help of a diagram.

2. (a) Derive the conditions for generating the line segment, by using DDA line generation algorithm for both cases (i.e. when slope < 1 and slope > 1). Write the pseudo code of DDA line generation algorithm, and use it to produce a line segment between points (2, 4) and (9, 9).

(b) Explain the Area-subdivision method of visible surface detection.

(c) Explain the mathematical expression for the combined effect of Ambient, Diffused and Specular reflection for Phong's Specular Reflection Model.

3. (a) Determine the point of intersection of the projection of edges AB and CD of a unit cube, on z = 0 plane, where the centre of projection , is at (0, 0, - d).

(b) Verify that two successive rotations are additive in nature i.e.

R(Q1) . R(Q2) = R(Q1 + Q2) where R(Q1), R(Q2) and R(Q1 + Q2) are 2D-rotational transformations,respectively.

(c) Compare and contrast the Cohen-Sutherland line clipping algorithm with the Cyrus-Beck line clipping algorithm with the help of a diagram.

4. (a) How does simulation of zero acceleration differ from non-zero acceleration, in an animation ? Briefly discuss the formulation of a mathematical function, that regulates the frame spacing in an animation with positive acceleration.

(b) Explain any two of the following :

(i) Keyframe Systems

(ii) Scripting Systems

(iii) Morphing

(c) Explain the differences between parametric and geometric continuities in Bezier curve.

5. (a) Differentiate between any two of the following :

(i) Graphics and Animation

(ii) Printer and Plotter

(iii) Hypertext and Hypermedia

(b) Briefly describe any two of the following file formats :

(i) jpeg

(ii) tiff

(iii) bmp

(iv) gif

(c) Explain any two of the following :

(i) Authoring tools

(ii) Z-buffer algorithm

(iii) Video file formats

(d) What is Video Conferencing ? Discuss the challenges related to such facilities.

**Notes-3**

1. (a) What is staircase effect ? Do you agree with the statement "Staircase effect facilitates smooth line generation" ? Justify your answer with suitable arguments.

(b) Compare and contrast the 2D Euclidean coordinate system with the 2D Homogeneous coordinate system with the help of an example.

(c) Determine the perspective projection of point P(x, y, z) on z = 0 plane, where the centre of projection is at E(0, 0, -10).

(d) How does frame buffer differ from the display buffer ? How does frame buffer overcome the limitation of display buffer ?

(e) Prove the following properties of a Bezier curve :

(i) P(u = 0) = P0

(ii) P(u = 1) = Pn

where u is the parameter and p 0 and Pn are the zeroth and nth control points,respectively.

(f) How does frame spacing influence the simulation of acceleration in an animation ? Justify your answer with suitable illustrations.

(g) Differentiate between window and viewport region ? Explain how window to viewport mapping is performed.

(h) What is Aliasing ? Explain how Antialiasing overcomes the problem of Aliasing.

2. (a) Write the pseudocode for Bresenham circle generation algorithm, and use it to produce an arc of radius r = 4 units, in the first quadrant from x = 0 to x = y.

(b) Differentiate between scan line polygon fill algorithm and flood fill algorithm.

(c) Differentiate between Parallel projection and Perspective projection.

3. (a) Determine the final coordinates of the perspective projection of an object, when the object is first rotated w.r.t. y-axis by 30° in clockwise direction and then w.r.t. x-axis by 45° in clockwise direction and finally it is projected on to z = 0 plane with the centre of projection at (0, 0, - 5).

(b) Show that 2D rotational transformations are commutative in nature i.e. R1 . R2 = R2 . R1 .

(c) Explain all the four cases of Sutherland-Hodgman polygon clipping algorithm, with suitable examples.

4. (a) Formulate the mathematical function, to regulate the frame spacing, for simulating

(i) Zero acceleration motion,

(ii) Negative acceleration motion.

(b) Explain any two of the following :

(i) Cel Animation

(ii) Frame Animation

(iii) Sprite Animation

(c) Briefly discuss the different polygon representation methods.

5. (a) Expand the following abbreviations of file formats :

(i) GIF

(ii ) JPEG

(iii) MPEG

(iv) TIFF

(v) BMP

(b) Explain any two of the following :

(i) Compression in digital video

(ii) Authoring tools

(iii) Morphing

(c) Write the pseudocode for Z-buffer algorithm for visible surface detection.What is the maximum number of objects that can be handled by Z-buffer algorithm ? Give two advantages and two disadvantages of Z-buffer algorithm.

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