______________________________________________________________________________
Course code & title Session
Time allowed ______________________________________________________________________________
Copy the following on the first page of your test answer sheet.
“I pledge that the answers in this examination are my own and that I will not seek or obtain an unfair advantage in producing these answers. Specifically,
1. I will not plagiarize (copy without citation) from any source;
2. I will not communicate or attempt to communicate with any other person during the
examination; neither will I give or attempt to give assistance to another student taking the
examination; and
3. I will use only approved devices (e.g., calculators) and/or approved device models.
4. I understand that any act of academic dishonesty can lead to disciplinary action.”
Name _________________ SID _____________ Signature ________________
Qn 1 (25 marks)
a) The general equation of hyperboloid of revolution of one sheet is
: Topics for Computer Graphics : Semester B 2020/21 Quiz 1
: 65 minutes
𝑋𝑋2 + 𝑌𝑌2 − 𝑍𝑍2 = 1 22 22 42
Use the identity 𝑠𝑠𝑠𝑠𝑠𝑠2𝛼𝛼 − 𝑡𝑡𝑡𝑡𝑡𝑡2𝛼𝛼 = 1, convert to parametric form. Specify the angle ranges. b) If you were asked to create a “super”-hyperboloid of revolution of one sheet by including
parameters 𝑠𝑠 , 𝑠𝑠 , how would you do it? 12
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Qn 2 (25 marks)
Given
gluPerspective (60, 1, sqrt(3), 100)
Derive a set of inequalities, in camera coordinates, that can determine whether a 3D point is inside the clipping volume.
Qn 3 (25 marks)
The coordinate systems of the control tower and an airplane are shown below:
Up Z
(0,0,0)
Control Tower
Y North
X
East
Suppose the plane is banking to the right 300, facing North West at a declination of 10𝑜𝑜, and at position (10, 10, 10).
Using glRotate and glTranslate, express the transformation from control tower to the plane using OpenGL commands.
Qn 4 (25 marks)
gluLookAt( 0,30,30, 0,0,0, 0,1,0 )
What are the world coordinates for a point (0, 1, −1) expressed in camera coordinates?
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