Please read through this exam paper thoroughly before you start the exam April/May 2023 CS3VR16 2022/3 A 800
VIRTUAL REALITY (CS3VR16)
One and a half hours
Answer ANY TWO out of THREE questions.
If a word limit is not specified next to a QUESTION then EACH QUESTION (e.g. Q1, Q2, Q3, etc.) has a word limit of 1000 words.
This limit excludes scanned images of diagrams or hand-written formulas but includes images with hand-written text.
Submit your answers to EACH QUESTION SEPARATELY to the relevant submission point on Blackboard.
EACH Question is worth 20 marks.
V2
Page 2
Questions 1 and 2 related to amodel of a desk as shown in Figure Q1&2- 1 below. The desk is to be created by taking a series of 1x1x1 cubes or diagonal
half cubes and transforming them suitably. One corner of each cube or half cube is initially at the origin, as shown in the Figure. An image of the desk together
with orthographic projections are also shown, the latter include the dimensions and positions of relevant parts of the desk.
Figure Q1&2- 1 Images to help define the desk
The desk has two legs, above which is a horizontal surface. On top of this
surface are the back of the desk and two sides of triangular cross section. The desk has a hinged lid which is shown in its open position protruding from the horizontal surface, but which can be rotated to sit on top of the sides.
CS3VR16 2022/3 A 800
Page 3
1. In this question, suitable transformations are to be undertaken so as to construct the desk. Your answers to the following should show all relevant working.
(a) Without giving detailed numbers, give the scaling and translating operations needed to transform the cube for one leg, the back, the horizontal surface and the hinged lid. Similarly, what operations are needed for one of the triangular shaped sides?
(3 marks)
(b) Find the matrix which transforms the cube to represent the right handleg shown in Figure Q1&2- 1. Show that corners (0,0,0) and
(1,1,1) are transformed correctly.
(c) Find the matrix needed to transform the cube for the back and
demonstrate that it is correct.
(3 marks)
(2 marks)
(d) Find the matrix needed to transform the cube lid for the lid in its
position shown in Figure Q1&2- 1 and demonstrate that it is correct. (2 marks)
(e) As regards the triangular cross sectioned sides, they are to be
generated by first rotating the half cube about the x axis, and then making them the right size and at the correct position.
Find to where the points (0,0,0); (0,0,1); (1,0,0) and (0,1,1) are transformed if the half cube is rotated by 900 around the x axis. Hence determine by how much the half cube needs to be scaled. Finally, for the side on the left, determine the overall
transformation and show that these four points are transformed
(7 marks)
(f) Explain how you would use these transformation matrices, and others, so as to draw the desk on the screen when viewed from
CS3VR16 2022/3 A 800
Turn Over
correctly.
position (25, 12, 20).
(3 marks)
Page 4
2. This question refers to the lid of the desk shown in F]igure Q1&2- 1. Two opposite corners of the lid are at (9,0,9) and (19,20,10). If the lid is to be closed, then it should be rotated by angle a, where cos(a) is -0.8 and
sin(a) is 0.6, about the axis parallel with they axis going through point (9,0,10).
(a) Outline the transformation operations needed to do this rotation and show that the transformation matrix below rotates the lid.
(4 marks)
(b) Use the above to find to where point (9,0,10) as well as points (9,0,9) and (19,20,10) are transformed. Explain why these
calculations show that the lid is closed.
(c) A light illuminating the desk is reflected off the closed lid. Figure Q2-2 shows the lid and relevant unit vectors emanating from point P at the centre of the lid. V is towards the eye at (19.6,12,36.8), L is towards the light at position (-1.4,8,39.8), N is normal to the lid and R is the reflection vector.
CS3VR16 2022/3 A 800
Figure Q2-2
Use the matrix in (b), or otherwise, to show P is at (5.6,10,13.8)
and explain how using your answer to (b) N is 0.6i + 0.8k.
Determine L and hence the proportion of the light received by the viewer due to diffuse reflection if the surface diffuse reflection
coefficient 0.2.
(6 marks)
(Question continues on next page)
(4 marks)
Page 5
(d) Find R and then V and the proportion of the light due to specular reflection assuming the lid has specular coefficient W = 0.1 and
specular reflection exponent ns = 4. Find the proportion of the light
received by the viewer due to specular reflection.
(3 marks)
(e) In addition to modelling the light, how else would you make the desk look more realistic? (3 marks)
3. (a) You are asked to design a VR system to help train someone to learn to navigate abuilding, such as that you created in the first
coursework, using a wheelchair. Initially assume that the user is in an electronic wheelchair with suitable steerage say a joystick.
If you were asked to design such a system, what features would
you provide? Could it be adapted for anon-wheelchair user so they could appreciate relevant issues?
Suppose a real wheelchair is available, which the user steers using ‘hand rims’. How might you utilize that considering relevant
haptics?
(7 marks)
(b) Some people have special needs which mean they struggle
encountering new people or surroundings. They can in principle be helped if they have first visited a virtual version of say an airport or railway station, which gives them the opportunity to experience what might happen when they visit the real version.
Choose atypical application and give an outline design, describing
facilities and scenarios your world would contain.
(7 marks)
(c) Games are often considered useful ways of engaging people in
learning. They can also be useful for children with autism or other special needs. Thinking about the game you developed in the
coursework, or choosing a different game, give an outline of the game, explain how it could be suitable and describe how it could
CS3VR16 2022/3 A 800
be adapted for such a child.
(End of Question Paper)
(6 marks)
