Question 1D (January 1998).
Using one of the methods of Constructive Solid Geometry, describe a childs toy consisting of solids with different cross-sections (e.g square, circular, triangular and possibly others) and a board with suitably shaped holes into which the solids fit. The parts of the toy will be made of plastic in a variety of different bright colours, so you will need to provide a separate description of each part.

(a) Give a detailed description of at least two of the solids. (20%)

(b) Give a detailed description of that part of the board which contains the matching holes and indicate how the rest of the parts will be included. You should ensure that the holes are large enough for the correct part to slide in and out easily while being too small to accept the wrong shaped solid.(15%)

(This should take about 50 mins.)

Question 2D (June 1997).
Describe the three main methods used for Constructive Solid Geometry. (10%)

State which you consider the most suitable for the bracket (consisting of two metal plates at right angles containing circular holes) shown below and give a full description using your chosen method. (25%)

(This should take about 40 mins.)

Question 3D
Describe briefly the three types of modeller for use in CAD solid modelling packages. Explain how Euler's Equation may be used to check the boundary representation of an object.

Using a boundary representation, show in detail how you would design an upright chair suitable for use at a desk or dining table. Check each of your steps using Euler's equation and explain, using diagrams where relevant, how a solid object is built up using this type of modeller.

(This should take about 45 mins.)

Question 4D
Give a brief description of the three main techniques used in geometric modelling.

An object consists of a right circular cylinder of radius 2 inches and length 1 inch, with a square cylinder of side 1 inch removed from it. The axes of the two cylinders coincide.

(This should take about 40 mins.)

Question 5D.
Using a half-space method and a boundary-representation method, give a description of the desk at which you are sitting.

(Note: in an examination you would be sitting at a desk. If you are not so seated when attempting this question, make sure you have a clear idea (possibly produce a sketch or look at a photograph) of the desk you are going to describe.)

(This should take about 40 mins.)

Question 6D
Consider the drawing of a scene in three-dimensions involving a number of coloured bricks against a white background. The first is a red cube whose vertices are at the positions (10,20,0), (20,20,0), (20,10,0), (10,10,0), (10,20,10), (20,20,10), (20,10,10) and (10,10,10). The second is a green pyramid whose vertices are at positions (15,15,15), (15,35,15), (35,35,15), (35,15,15) and (25, 25,35). The third is a yellow sphere whose centre is at the position (20,20,-20) and whose radius is of length 10.

Describe these objects using the methods of C.S.G.

(This should take about 40 mins.)