UNIVERSITY OF EDINBURGH

FACULTY OF SCIENCE AND ENGINEERING

MASTER OF SCIENCE IN COMPUTER SCIENCE

COMPUTER GRAPHICS

Wednesday 18 April 2001 14:00 to 15:30

Examiners: I. Watson (External)

R.N. Ibbett (Chairman)

INSTRUCTIONS TO CANDIDATES

Answer any TWO questions. All questions carry equal weight.

1. (a) Explain why a homogeneous coordinate system is used to represent affine transformations. [2 marks ]

(b) State the role or significance of each of the elements in a single, 3D coordi-

nate, homogeneous, transformation matrix.

[8 marks ]

(c) What are canonical view-volumes and why are they used? [5 marks ]

(d) The perspective canonical view-volume is often transformed to the parallel canonical view-volume since processing of the latter is much easier. A transformation matrix for achieving this is:

( \begin{matrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \frac{1}{(1−d)} & \frac{−d}{(1−d)} \\ 0 & 0 & 1 & 0 \end{matrix} )

Show how this matrix may be derived.

[10 marks ] 2. (a) A Bézier curve is defined by the set of control points: {(0,0),(2,8),(6,3),(7,5)}

and the point half way along the curve is at approximately (4,4.75). Sketch the curve, its control points and its convex hull and explain how it is possible to draw a close approximation to the curve given only these five points.

[7 marks ]

(b) Briefly outline how you would extend the Bézier method to generate surfaces, giving expressions for the coordinates of a point on the surface. Define the terms used.

[7 marks ]

(c) Describe how to generate large, arbitrary-shaped, Bézier surfaces. [5 marks ]

(d) Sketch the Bézier cubic blending functions and hence explain how curve

endpoints are interpolated.

[6 marks ] 3. (a) An alphabet used to define rendering techniques makes use of the letters:

E - eye; L - light source; D - diffuse reflection; and S - specular reflection. Each of the regular expressions listed below fully defines a rendering technique. Name them.

i. LDS*E ii. LD*E iii. L(S|D)*E iv. LDE

[2 marks ]

(b) Compare bidirectional ray tracing with standard ray tracing, clearly stating the advantages of the former. Note that you do not need to describe the general ray tracing algorithm.

[10 marks ]

(c) The goal of Image Based Rendering (IBR) is to generate a continuous representation of the plenoptic function. Briefly describe the plenoptic function and its role in IBR.

[7 marks ]

(d) Image Based Lighting is an IBR technique. Describe this process in general

terms.

[6 marks ]