Question 1.

a) Consider two different raster systems with resolutions 10640x480 and 1280x1024. What size of frame buffer (in bytes) is needed for each of these systems to store 12 bits per pixel?

b) State the reason why we prefer unit x interval or unit y interval while scan converting various geometric forms.

c) Write the procedure of boundary fill method along with its disadvantage.

d) What are the major side effects of scan conversion? Describe any two of them.

e) What is the need of using homogeneous coordinate representation? Describe briefly.

f) Given a clipping window A(20, 20), B(60, 20), C(60, 40), D(20, 40). Use Cohen-Sutherland algorithm to find the visible portion of a line segment joining the points P (40, 80) and Q (120, 30).

g) Implement DDA algorithm to compute pixels along the line AB from A(0, 0) to B(-5, -5).

h) Write the transformation matrices for reflection in the following cases:

(i) Axis of reflection is on the xy-plane about the line x = 0.

(ii) Axis of reflection on the xy-plane about the line y =x.

i) What is spline curve? Differentiate between interpolation spline and approximation spline.

j) What is (or are) the importance(s) of vanishing point in perspective projection?

Question 2. a) What is the working principle of color CRT monitors? Explain the different techniques used for producing color displays.

b) Find the pixel positions for the octant from x = 0 to x = y of a circle centered at (2, 0) with radius 15 using the midpoint circle algorithm.

Question 3. a) Show that a 2-D reflection about x-axis followed by a 2-D reflection about the line y = -x is equivalent to rotation about the origin by an angle 0. Find the value of e.

b) Generate the transformation matrix for transformation from Fig. 1 to Fig. 2:

Question 4. a) Given input ellipse parameters r. = 8, ry = 6. Demonstrate the midpoint algorithm determining pixel positions along the ellipse for Region 1 in the first quadrant starting from the position (xo, yo) = (0, 6).

b) Develop the Bresenham's line drawing algorithm for lines having slope less than 1. [4

Question  5. a) Suppose there is a rectangle ABCD whose coordinates are A(1, 1), B(4, 1), C(4, 4), D(1, 4) and the window coordinates are (2, 2), (5, 2), (5, 5), (2, 5). The given viewport location is (0.5, 0), (1, 0), (1, 0.5), (0.5, 0.5). Calculate the viewing transformation matrix.

b) What do you mean by oblique parallel projection? Derive the transformation matrix for oblique parallel projection.

Question 6. a) What is the requirement of visible surface detection algorithms? Explain the scan line algorithm for visible surface detection.

b) What do you mean by window-to-viewport mapping? Given the coordinates of window W(xwmin, xwmax, ywn.) in world coordinates and viewport V(xvith, xvmax, yv.) in normalized device coordinates. Convert the world coordinates of a point Pw(xw, yw) in the window into its corresponding normalized device coordinates 13,(xv, yv) in the viewport.

Question 7. a) How does Z-buffer algorithm determine which surfaces are hidden?

b) Determine 3-D transformation matrix to scale a line AB in z-direction by 3.5 by keeping point A fixed. Then rotate the line by 45° anticlockwise about x-axis. Given A(10, 15, 20) and B(45, 60, 30).

Question 8. Write shorts note on any two.

a) Bezier curve
b) Liquid Crystal Displays
c) Painter's Algorithm
d) Animation