## Computer Graphics & Virtual Reality - Dec 2016

### Information Technology (Semester 5)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1(a)** If 8 bits pixel, per color scheme is used for a RGB diplay device, How much memory is required to hold picture data worth one screen . If the resolution is 800×600. If the refresh rate 50Hz, How much memory is required to hold picture data for duration of one sec.(5 marks)
**1(a)** What are different application of computer graphics(5 marks)
**1(b)** Prove that the two successive rotation Transformations are additive.(5 marks)
**1(b)** Explain even odd method for inside test for polygone(5 marks)
**1(c)** Explain different ways of performing text clipping.(5 marks)
**1(c)** Expain parallel and perspective projections(5 marks)
**1(d)** What is VRML, what is the meaning of six degrees of freedom in 3D graphics. How to define any shape (say cylinder) in VRML.(5 marks)
**1(d)** Various application of VR(5 marks)
**2(a)** Given 4 control points (10,

10),

(15,

15),

(20,

15) and (30,

10), find the points to plot bezier curve by using step size as 0.2.(10 marks)
**2(a)** Explain Cohen Sutherland line clipping algorithm with example(10 marks)
**2(b)** Explain Boundary fill and flood fill Algorithm. Whih algorithm cannot be used to fill the Region R2 which is bounded by Blue color and Red color boundary, justify.

!mage(10 marks)
**2(b)** Derive the DDA line drawing algorithm. Take suitable example and draw a line between two points.(10 marks)
**3(a)** Find sequence of Transformating required to rotate a solid object w.r.t a line y=mx+c, in anticlockwise manner by angle θ.(10 marks)
**3(a)** Write a short note on Homogenous co-ordinate system.(10 marks)
**3(b)** Explain Morphing and warping mechanism.(10 marks)
**3(b)** List various types of computing archiectures of VR and explain any one in detail.(10 marks)
**4(a)** What are the important components of VR system. Explain different types of VR systems.(10 marks)
**4(a)** Explain Flood Fill Algorithm using 8-connected approach. What are its advantages over Boundary Fill Algorithm?(10 marks)
**4(b)** What is projection, what are its different types? Derive transformation Matrix for oblique projection.(10 marks)
**4(b)** Derive the matrix for Rotation about an arbitrary point for 2D Rotation.(10 marks)
**5(a)** Explain Geometric and kinematic modeling in detail.(10 marks)
**5(a)** Let ABCD be the rectangular window with A(20,

20), B(90,

20), C(90,

70), and D(20,

70). Find region codes for endpoints and use Cohen Sutherland alorithm to clip the lines P1P2 with P1(10,

30), P2(80,

90) and q1q2 with q1(10,

tO),

q2(70,

60)(10 marks)
**5(b)** Explain an algorithm which uses parametric equation for the propose of line clipping, using the same algorithm, find the coordinates of the line segment A(10,

10),

B (70,

40), after it is clipped against a window with two diagonal vertices at (20,

20)

(40,

50).(10 marks)
**5(b)** Explain B spline curve(10 marks)

### Solve any 2 question Q6(a,b,c)

**6(a)** Fractals(10 marks)
**6(a)** Show that transformation matrix for reflection about line y-x is equivalent to reflection to X axis followed by counter clockwise rotation of 90 degree.(10 marks)
**6(b)** Applications of VR(10 marks)
**6(b)** Derive mathematical representation for Beziers curve and state their property(10 marks)
**6(c)** 3D position Trackers.(10 marks)