Q)
(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:
(Jx² + y² – R)' + z² = r?
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, r are 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.
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