Computer Graphics Questions & Answers – 3D Rotation – 1

This set of Computer Graphics Multiple Choice Questions & Answers (MCQs) focuses on “3D Rotation – 1”.

1. Which of the following operation can be applied on a 3 D object to rotate it about any axis from its original position?
a) Translation
b) Scaling
c) Rotation
d) Shearing
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2. The positive value of the pivot point rotates an object in which of the following position?
a) Clockwise
b) Anti-Clockwise
c) Both Clockwise and Anti-Clockwise
d) Neither Clockwise nor Anti-Clockwise
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3. Which of the following matrix equation is correct for 3 D rotation around x axis?
a) \(\begin{matrix}x1 & 1 \; 0 \; 0 \; 0 & x0\\
[ y1 ] = & [ 0 \; cos\theta \; -sin\theta \; 0 ] & [ y0 ]\\
z1 & 0 \; sin\theta \; cos\theta \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)

b) \(\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 \; & x0\\
[ y1 ] = & [ 0 \; cosθ \; sinθ \; 0 ] & [ y0 ]\\
z1 & 0 \; -sinθ \; cosθ \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 \; & 1\end{matrix}
\)

c) \(\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 & x0\\
[ y1 ] = & [ 0 \; sinθ \; -cosθ \; 0 ] &[ y0 ]\\
z1 & 0 \; cosθ \; sinθ \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 \;& 1\end{matrix}
\)

d) \(\begin{matrix}x0 & 1 \; 0 \; 0 \; 0 & x1\\
[ y0 ] = & [ 0 \; cosθ \; -sinθ \; 0 ]& [ y1 ]\\
z0 & 0 \; sinθ \; cosθ \; 0 & z1\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)
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4. Which of the following matrix equation is correct for 3 D rotation around y axis?
a)\(\begin{matrix} x1 & cosθ \; 0 \; sinθ \; 1 & x0\\
[ y1 ] = & [ 1 \; 0 \; 1 \; 1 ]& [ y0 ]\\
z1 & -sinθ \; 0 \; cosθ \; 0 & z0\\
1 & 1 \; 0 \; 0 \; 0 & 1\end{matrix}
\)

b) \(\begin{matrix}x1 & sinθ \; 0 \; sinθ \; 0 & x0\\
[ y1 ] = & [ 0 \; 1 \; 0 \; 0 ] &[ y0 ]\\
z1 & -cosθ \; 0 \; cosθ \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)

c) \(\begin{matrix}x1 & cosθ \; 0 \; sinθ \; 0 & x0\\
[ y1 ] = & [ 0 \; 1 \; 0 \; 0 ]& [ y0 ]\\
z1 & -sinθ \; 0 \; cosθ \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)

d) \(\begin{matrix}x1 & cosθ \; 0 \; sinθ \; 0 & x0\\
[ y1 ] = & [ 0 \; 1 \; 0 \; 0 ]& [ y0 ]\\
z1 & -sinθ \; 0 \; cosθ \; 0 & z0\\
0 & 1 \; 1 \; 1 \; 0 & 0\end{matrix}
\)

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5. Which of the following matrix equation is correct for 3 D rotation around z axis?
a) \(\begin{matrix}x1 & sinθ \; -cosθ \; 0 \; 0 & x0\\
[ y1 ] = & [ cosθ \; sinθ \; 0 \; 0 ] &[ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)

b) \(\begin{matrix}x1 & cosθ \; -sinθ \; 1 \; 1 & x0\\
[ y1 ] = & [ sinθ \; cosθ \; 1 \; 1 ] &[ y0 ]\\
z1 & 0 \; 0 \; 0 \; 1 & z0\\
1 & 0 \; 0 \; 1 \; 0 & 1\end{matrix}
\)

c) \(\begin{matrix}x1 & cosθ \; -sinθ \; 0 \; 0 & x0\\
[ y1 ] = & [ sinθ \; cosθ \; 0 \; 0 ]& [ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
0 & 1 \; 1 \; 1 \; 0 & 0\end{matrix}
\)

d) \(\begin{matrix}x1 & cosθ \; -sinθ \; 0 \; 0 & x0\\
[ y1 ] = & [ sinθ \; cosθ \; 0 \; 0 ] &[ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}
\)

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6. Every vertex in a polygon is rotated with the same rotation angle.
a) True
b) False
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7. Which of the following equation is correct for the new Y co-ordinate if an object undergoes 3D rotation around x axis?
a) Ynew = Yold x cosθ – Zold x sinθ
b) Ynew = Yold x sinθ – Zold x cosθ
c) Ynew = Yold x cosθ + Zold x sinθ
d) Ynew = Yold x sinθ + Zold x cosθ
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8. Which of the following equation is correct for the new Z co-ordinate if an object undergoes 3D rotation around y axis?
a) Znew = Yold x cosθ + Xold x sinθ
b) Znew = Yold x cosθ – Xold x sinθ
c) Znew = Yold x sinθ + Xold x cosθ
d) Znew = Yold x sinθ – Xold x cosθ
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Sanfoundry Global Education & Learning Series – Computer Graphics.

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