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(chatquestion)...The process of generating primitive shapes in computer-aided design (CAD) software is often mathematical-based. Case in point: a torus surface (commonly known as the 'doughnut'). This has the shape and Cartesian equation as follows: (x2 + y2 -R)+ z? = r2 Figure 1: Description of a torus surface (source: web resource) In CAD software, this surface is usually generated by the following procedures: (1) The values of major radius, R and minor radius, rare fixed by the user. (2) Revolve a point on the x-axis for one round until a circle (line) is formed. (3) Revolve the circle (line) for one round about the z-axis until the torus (surface) is formed. Figure 2: Common process flow of generating a torus surface 1 Question (a): [4 marks] With the introduction as a hint, parameterize a torus surface with two parameters, u and v. State the parameterization as x(u, v), y(u, v), z(u, v), along with the range of u and v. Question (b): [6 marks] A surface integral has the form of fS f(x,y, z) dS. At its simplest, f(x,y, z) = 1, this integral simply gives the area of the entire surface S. Use the surface integral method to determine the surface area of a torus. Refer to the information below for values of R and r: Table 1: Substitution of Rand r based on last two digits of student number (e.g. KIX1900 R Digit Rorr 1 6 3 4 5 10

asked May 19, 2020 by balaji.thirumalai

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