Assignment 1 (Total marks = 100)Qn 1 (30 marks)
a) Use 3 quadrilateral meshes to represent the following simple object. The top face shall be mesh 1. The bottom face shall be mesh 2. The rest of the object shall be mesh 3. For each mesh, draw a 2D array and put the vertex (e.g. a) at the corner to illustrate your idea.
h (-15, 5, -12)
d(-15,0 ,-12)
a(0, 0, 0)
b) Derive a set of linear inequalities using which we can determine whether an arbitrary point (𝑋𝑋, 𝑌𝑌, 𝑍𝑍) is inside the object or not.
acgf is simply 𝑍𝑍 = 0.] Qn 2 (20 marks)
a) Convert the equation to its parametric form (steps required)
�(𝑋𝑋2)25 + (𝑌𝑌2)25�12 + (𝑍𝑍4)15 = 1
f (0, 5, 0)
Y
X
Z
b (11, 5, -12)
g(10, 5, 0) e (11, 0, -12)
c(10, 0, 0)
[Hint: the equation of most faces can be determined easily. For example, the equation of
(15 marks)
(15 marks)
b) What is the name of the shape?
c) Why there is a need to convert the equation to parametric form?
(20 marks)
1
Qn 3 (50 marks)
ii) Name the 3D shape.
a) The non-parametric equation of a 3D shape is
�𝑋𝑋2�2/𝑠𝑠1 + �𝑌𝑌2�2/𝑠𝑠1 − 𝑍𝑍2 = −1
i) Using the identity 𝑠𝑠𝑠𝑠𝑠𝑠2𝛼𝛼 − 𝑡𝑡𝑡𝑡𝑡𝑡2𝛼𝛼 = 1, convert the equation to its parametric form.
(10 marks)
b) Represent the 3D object below by three quadrilateral meshes: the top face, the bottom face and the rest of the object. [You only need to draw a 2D grid and specify the vertex number e.g. “a” at each corner.] (15 marks)
g
f
c
h
d
𝑡𝑡(1, −1, −5)
𝑠𝑠(10, −10, −50) 𝑓𝑓(10, 10, −50) 𝑔𝑔(−10,10, −50) h(−10, −10, −50)
c) Derive the equation of the plane aefb. [The plane equation should give positive left hand side if (X,Y,Z) is on the air side and vice versa.] (15 marks)
d) [This question requires you to read ahead Lecture 5 and find out how gluPerspective works.] If Fig. 1 is a clipping volume, write down the corresponding gluPerspective command.
b
e a
Fig. 1
𝑏𝑏(1, 1, −5) 𝑠𝑠(−1,1, −5) 𝑑𝑑(−1, −1, −5)
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(10 marks)
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