Answer Happy

1. In this question a model of a simple building is to be generated by taking a series of 1x1xl cubes or diagonal half cubes and transforming them suitably. A corner of each cube or half cube is initially at the origin. Figure Q1-1 shows these as well as images of the building as well as orthographic projections. This question features the walls of the building, question 2 will feature the roof. At either end of the building, the walls consist of a cuboid above which is a half cuboid with a triangular cross section (shown in the figure). Between these ends are two walls formed from cuboids. AZ AZ y у X х 8 16 16 10 10 Z L, у Z L X 0 -- 0.- 1 0 1 Il 15 16 o''1 39" 40 Figure Q1-1 Images to help define the building our answers to the following should show all relevant working. (a) State which two operations are needed to transform the unit cube for the side wall visible in Figure Q1-1. Derive the associated single transformation matrix, and show that corner (1,0,1) on the cube is transformed correctly. (3 marks) (b) Find the matrix which transforms the cube to represent the bottom of the end wall visible in Figure Q1-1. Show that corners (0,0,0) and (1,1,1) are transformed correctly. (3 marks) (c) The top part of this wall is to be generated in stages by processing the half cuboid. First it is to be rotated by -45° about the z axis and then by -90° about the y axis. Determine the transformation matrix for these two operations and then show that corners 0,0,0; 1,0,0 and 0,1,0 of the half cube are transformed so as to form an isosceles triangle whose base is horizontal positioned below the origin. (4 marks) (d) The second stage is to scale this half cuboid and then move it so that it sits on top of the cuboid found in part b). Determine a matrix for these two transformations, apply it to the matrix found in part c) and show that corners 0,0,1; 1,0,1 and 0,1,1) are correctly transformed. (6 marks) (e) Discuss how you would use these cuboids / half cuboids to create a model of all walls of the building, and how you would draw it suitably. (4 marks)