# 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

Explanation: The process of rotation is applied on a 3 D object to rotate it about any axis from its original position. The rotation of the object can be in clockwise direction or in anti-clockwise direction. We must specify the angle of rotation and the rotational point while performing the rotation transformation.

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

Explanation: An object can be rotated in two ways – either clockwise or anticlockwise. If the rotation value of pivot point of the object is positive then the object is rotated in anti-clockwise direction and if the rotation value of pivot point of the object is negative then the object is rotated in clockwise direction.

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

Explanation: The correct matrix equation for 3 D rotation around x axis is –
$$\begin{matrix}x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = & [ 0 \; cos\theta \; -sin\theta \; 0 ] & [ y0 ]\\ z1 & 0 \; sin\theta \; cos\theta \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$
First matrix is for the final point, second matrix is the rotation matrix for x axis and the third matrix is for the original point.

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

Explanation: The correct matrix equation for 3 D rotation around x axis is –
$$\begin{matrix}x1 & cosθ \; 0 \; sinθ \; 0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0 \; 0 ]& [ y0 ]\\ z1 & -sinθ \; 0 \; cosθ \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$
First matrix is for the final point, second matrix is the rotation matrix for y axis and the third matrix is for the original point.

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

Explanation: The correct matrix equation for 3 D rotation around x axis is –
$$\begin{matrix}x1 & cosθ \; -sinθ \; 0 \; 0 & x0\\ [ y1 ] = & [ sinθ \; cosθ \; 0 \; 0 ]& [ y0 ]\\ z1 & 0 \; 0 \; 1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$
First matrix is for the final point, second matrix is the rotation matrix for z axis and the third matrix is for the original point.

6. Every vertex in a polygon is rotated with the same rotation angle.
a) True
b) False

Explanation: When we apply 3 D rotation on any three dimensional polygon then the polygon is rotated by shifting every vertex using the same rotational angle. When the object is rotated, then every point of the object is rotated by the same angle.

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

Explanation: The correct equation for the new Y co-ordinate if an object undergoes 3D rotation around x axis is – Ynew = Yold x cosθ – Zold x sinθ.
When the matrix form for 3D rotation around x axis is expanded then we get the following equations – Xnew = Xold; Ynew = Yold x cosθ – Zold x sinθ; Znew = Yold x sinθ + Zold x cosθ.

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

Explanation: The correct equation for the new Y co-ordinate if an object undergoes 3D rotation around x axis is – Znew = Yold x cosθ – Xold x sinθ.
When the matrix form for 3D rotation around x axis is expanded then we get the following equations – Xnew = Zold x sinθ + Xold x cosθ; Ynew = Yold; Znew = Yold x cosθ – Xold x sinθ

Sanfoundry Global Education & Learning Series – Computer Graphics.