AMIETE –CS (OLD SCHEME)

Code: AC15 Subject: COMPUTER GRAPHICS

Time: 3 Hours Max. Marks: 100

NOTE: There are 9 Questions in all.

· Question 1 is compulsory and carries 20 marks. Answer to Q. 1 must be written in the space provided for it in the answer book supplied and nowhere else.

· Out of the remaining EIGHT Questions, answer any FIVE Questions. Each question carries 16 marks.

· Any required data not explicitly given, may be suitably assumed and stated.

Q.1 Choose the correct or the best alternative in the following: (210)

a. This projection technique has the direction of projection perpendicular to the viewing plane, and the viewing direction is perpendicular to one of the principle faces.

(A) Orthographic Parallel Projection

(B) Axonometric Parallel Projection

(C) Oblique Parallel Projection

(D) None of these

b. Which of the following is not true for Bezier curves?

(A) It passes through all control points.

(B) The initial slope is given by first two points.

(C) Changing any control point alters the shape of the curve.

(D) The curve lies within the convex Hull of the control points.

c. Interlacing the horizontal refresh____________

(A) Fools the human eye into thinking the horizontal refresh rate is faster.

(B) Is distracting and can cause eye fatigue.

(C) Is necessary because of the shape of the rods in the human eye.

(D) Is no longer used in any system.

d. If the refresh rate of a picture is 10 frames/sec and size of frame buffer is then time required to access a pixel is

(A) 100 ns (B) 100 microsec

(C) 200 ns (D) 1200 ns

e. Which of the following curves is symmetric about the line x=y?

(A) y=|x| (B) 1+x+y =0

(C) y=x³ (D) none of these

f. The refresh rate below which a picture flickers is______.

(A) 35 (B) 25

(C) 60 (D) 40

g. Given a rectangular window and what is the outcode of an end point of a line? The out code format is L, R, B, T.

(A) 1000 (B) 0001

(C) 1001 (D) 0000

h. Intensities are interpolated for rendering in

(A) Bezier shading. (B) Phong shading.

(C) Gaurand shading. (D) B-spline shading.

i. The Graphics pipeline has several stages. Which of the following is not a responsibility of the geometry portion of the pipeline?

(A) clipping objects external to the viewing window

(B) applying all affine transforms

(C) converting the geometry into fragments

(D) applying the projective transform

j. Which of the following projection techniques does not have the direction of projection perpendicular to the viewing plane?

(A) Orthographic Parallel Projection

(B) Axonometric Parallel Projection

(C) Oblique Parallel Projection

(D) None of these

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2 a. Explain the architecture of a simple random scan system. Compare and contrast random scan systems and raster scan systems based on the principles of operation. (8)

b. Explain the Bresenham line algorithm for drawing a line with a slope less than 1 and greater than 0. (8)

Q.3 a. Digitze the line segment with endpoint (25, 15) and (30, 19) using Bresenham line drawing algorithm. (8)

b. Convert these homogeneous points to Cartesian coordinate system: (0,1,3,2), (2,1,3,4), (2,4,3,5) (3)

c. Give the 44 homogeneous matrix for a translation by (2, 1, 3). (2)

d. Consider a perspective projection with the center of projection at (0, 0, 0), and the projection plane at Y=1. Where do the following points project to: (0,1,2), (1,2,3), (2,3,4)? (3)

Q.4 a. Draw a rough sketch of Bezier curve with following control points P1 (60, 30), P2 (0, 30), P3 (80, 25), P4 (80, 0). (8)

b. Briefly describe the scan line z-Buffer algorithm. (8)

Q.5 a. Give the 2D transformation matrices for the following transformations (include the order applied) (6)

(i) A unit square is translated x=2, y=3 followed by a uniform scale of 3

(ii) A unit square is translated x=8, y=2, then rotated an angle, θ =45 degrees

b. Derive the 3D transformation equations for rotations about the three

coordinate axes (6)

c. What is a vanishing point in graphics? (4)

Q.6 a. Explain Cohen-Sutherland line clipping algorithm. (8)

b. Explain painter’s algorithm for solving hidden-surface problem. (8)

Q.7 a. A polygon has three vertices, V₀ = (1, 1), V₁ = (5, 5), and V₂ = (11, 2). (10)

(i) What will be the intensity at (7, 3) using Gouraud shading if the

intensities at the three vertices are I₀ = 2, I₁ = 12, and I₂ = 9?

(ii) What will be the unit normal vector at (4, 3) using Phong shading if

if the normal vectors at the three vertices are N₀ = (0, 1, 0), N₁

= (1, 0, 0), and N₂ = (1, 1, 1)?

b. Explain object-space methods for identifying the back faces of a polyhedron. (6)

Q.8 a. Use the seedfill algorithm for 4-connected boundary defined region to fill a polygon (2, 2), (2, 7), (5, 7), (5, 2). Use the point (4, 6) as seed. (6)

b. Use the cubic B-spline matrix formula to compute the parametric formula of the curve segment that approximates P4 to P5 in the figure above, and confirm that your locations for Q4 and Q5 are correct. Assume that the origin is in the lower left and that a unit grid is shown e.g., P1 is at (3, 3) (6)

c. If a system has eight control points, give the open uniform knot vector (4)

(i) for a quadratic B-spline

(ii) for a cubic B-spline

Q.9 a. What is meant by fractals? Explain any one construction method used for constructing ‘Affine Fractals’. (6)

b. Explain the following two modeling or construction techniques used to construct solid objects in solid modeling packages. (10)

(i) Sweep representations

(ii) Constructive solid geometry methods.