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2. (a) This part refers to one of the roof panels of the building which is to sit on top of the walls. A cross section of the panel is shown in Figure Q2-1, where the transformations shown are to sheer suitably and then rotate about the x axis, so that the relevant edges are vertical. 11 0.4 * 6 8 10 0 0.3 Figure Q2-1 Shows operations needed for roof panel (i) Define the scaling, sheering, rotating and move operations which are needed. (ii) Hence show that the relevant transformations can be found 140 0 0 0 0 8 0 0 using the matrix 0 6 0.5 10 0 0 0 1 (iii) Apply this matrix to points 0,0,0; 1,0,0; 1,0,1 and 1,1,0 and so show that the transformed cube has the correct size, sits on the walls, and that the relevant edge is vertical. (8 marks) (b) This roof panel is illuminated and you are to calculate the light reflected from it. In the left of Figure Q2-2 is shown the panel, one corner at 40,0,10.5, the corner below it which touches the top of the wall at 40,0,10, the midpoint of the upper side of the panel P, and vectors a and b between two corners and P. In the right figure are shown relevant unit vectors originating at P: V is towards the eye at 26, 12, 21, L is towards the light at position 10, -2, 18, N is normal to the panel and R is the reflection vector. b L N P a V P R 40, 0, 10 40, 0, 10.5 Figure Q2-2 (i) Show that P is at point 20,4,13.5 and hence find a and b. (ii) Compute the unit vectors N, V, L and R. (iii) Suppose the roof has diffuse reflection coefficient 0.3, specular coefficient W = 0.4 and specular reflection exponent ng = 5. Find the proportion of the light received by the viewer. (9 marks) (c) In addition to modelling the light, how else would you make the building look more realistic. (3 marks)