# Computer Graphics Questions & Answers – 3D Reflection and Shear

This set of Computer Graphics Multiple Choice Questions & Answers (MCQs) focuses on “3D Reflection and Shear”.

1. Which of the following transformation is a rotation where angle of rotation is 180°?
a) Rotation
b) Shearing
c) Reflection
d) Translation

Explanation: Reflection is a kind of rotation where the angle of rotation is 180 degree. The reflected object is always formed on the other side of mirror. The laws of reflection are also applicable on the newly formed object and the original object.

2. How many types of reflection is possible in a 3-dimensional environment?
a) 1
b) 3
c) 6
d) 9

Explanation: There are three different types of reflections that are possible in a 3-dimensional environment. These reflections are relative to XY plane, reflection relative to YZ plane and reflection reflective to ZX plane.

3. Which of the following matrix equation is correct for 3 D reflection relative to XY plane?
a) $$\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0 \; 0 ]& [ y0 ]\\ z1 & 0 \; 0\; -1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \;1 & 1\end{matrix}$$

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

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

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

Explanation: The correct matrix equation for 3 D reflection relative to XY plane is –
$$\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0 \; 0 ]& [ y0 ]\\ z1 & 0 \; 0\; -1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \;1 & 1\end{matrix}$$
First matrix is for the final point, second matrix is the reflection matrix for XY plane and the third matrix is for the original point.

4. Which of the following matrix equation is correct for 3 D reflection relative to YZ plane?
a) $$\begin{matrix}x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = & [ 0\; 1 \; 0 \; 0 ] &[ y0 ]\\ z1 & 0 \; 0 \; -1\; 0 & z0\\ 0 & 0 \; 0 \; 0 \;1 & 0\end{matrix}$$

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

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

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

Explanation: The correct matrix equation for 3 D reflection relative to YZ plane is –
$$\begin{matrix}x1 & -1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0 \; 0 ]& [ y0 ]\\ z1 & 0 \; 0 \; 1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$
First matrix is for the final point, second matrix is the reflection matrix for YZ plane and the third matrix is for the original point.

5. Which of the following matrix equation is correct for 3 D reflection relative to XZ plane?
a) $$\begin{matrix}x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0 \; 0 ] &[ y0 ]\\ z1 & 0 \; 0\; -1 \; 0 & z0\\ 0 & 0 \; 0\; 0 \;1 & 0\end{matrix}$$

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

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

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

Explanation: The correct matrix equation for 3 D reflection relative to XZ plane is –
$$\begin{matrix}x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = &[ 0 \; -1 \; 0 \; 0 ]& [ y0 ]\\ z1 & 0 \; 0 \; 1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$
First matrix is for the final point, second matrix is the reflection matrix for XZ plane and the third matrix is for the original point.
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6. Given a 3D shape with coordinates A(6, 4, -2), B(5, -3, 6), C(2, 1, -5) and D(-2, 4, 7), what will be the new coordinates if the shape undergoes 3D reflection relative to XZ plane?
a) A(-6, -4, -2), B(-5, -3, -6), C(-2, -1, -5), D(-2, -4, -7)
b) A(6, 4, 2), B(5, 3, 6), C(2, 1, 5), D(2, 4, 7)
c) A(6, 4, 2), B(-5, 3, -6), C(-2, -1, 5), D(2, 4, -7)
d) A(6, -4, -2), B(5, 3, 6), C(2, -1, -5), D(-2, -4, 7)

Explanation: The newly formed coordinates would be – A(6, -4, -2), B(5, 3, 6), C(2, -1, -5), D(-2, -4, 7)
For 3D reflection relative to XZ plane –
Xnew = Xold; Ynew = -Yold; Znew = Zold
So, A(6, 4, -2) = A(6, -4, -2)
B(5, -3, 6) = B(5, 3, 6)
C(2, 1, -5) = C(2, -1, -5)
D(-2, 4, 7) = D(-2, -4, 7)

7. Which of the following transformation can be used to change the shape of a 3D object in any particular axis?
a) Scaling
b) Rotation
c) Shearing
d) Translation

Explanation: The Shearing transformation is used to change the shape of a 3 D object in any specified axis. In shearing, the position of the object remains same but its shape gets changed. The shape of the object can be changed with respect to the X or Y or Z axis or any combination of these three.

8. Which of the following matrix equation is correct for 3D shearing in X axis?
a) $$\begin{matrix}x1 & 1 \; 0 \; 0\; 0 & x0\\ [ y1 ] = & [ Sh_y \;1 \; 0\; 0 ]& [ y0 ]\\ z1 & Sh_z \; 0 \; 1 \; 0 & z0\\ 1 & 0 \; 0 \;0 \; 1 & 1\end{matrix}$$

b) $$\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = & [ Sh_y \;1 \; 0 \; 0 ]& [ y0 ]\\ z1 & Sh_z \; 0 \; 1\; 0 & z0\\ 0 & 0 \; 0 \; 0 \; 1 & 0\end{matrix}$$

c) $$\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = &[ 0 \; 1 \; 0 \; 0 ] &[ y0 ]\\ z1 & Sh_y \; Sh_z \; 1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$

d)$$\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0\; Sh_y ] &[ y0 ]\\ z1 & 0 \; 0 \; 1\; Sh_z & z0\\ 1 & 0 \; 0\; 0 \; 1 & 1\end{matrix}$$

Explanation: The correct matrix equation for 3D shearing in X axis is –
$$\begin{matrix}x1 & 1 \; 0 \; 0\; 0 & x0\\ [ y1 ] = & [ Sh_y \;1 \; 0\; 0 ]& [ y0 ]\\ z1 & Sh_z \; 0 \; 1 \; 0 & z0\\ 1 & 0 \; 0 \;0 \; 1 & 1\end{matrix}$$
First matrix is for the final point, second matrix is the shearing matrix for X axis and the third matrix is for the original point.

9. Which of the following matrix equation is correct for 3D shearing in Y axis?
a) $$\begin{matrix} x1 & 1 \; Sh_x \; Sh_z \;0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0 \; 0 ]& [ y0 ]\\ z1 & 0 \; 0 \; 1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$

b) $$\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = &[ 0 \; 1 \; 0 \; 0 ]& [ y0 ]\\ z1 & 0 \; Sh_z \; 1\; 0 & z0\\ 1 & 0 \; Sh_x \; 0 \; 1 & 1\end{matrix}$$

c) $$\begin{matrix} x1 & 1 \; Sh_x \; 0 \; 0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0 \;0 ] &[ y0 ]\\ z1 & 0 \; Sh_z \; 1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$

d) $$\begin{matrix} x1 & 1 \; Sh_x \; 0 \; 0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0 \; 0 ] &[ y0 ]\\ z1 & 0 \; Sh_z \; 1\; 0 & z0\\ 0 & 0 \; 0 \; 0\; 0 & 0\end{matrix}$$

Explanation: The correct matrix equation for 3D shearing in Y axis is –
$$\begin{matrix} x1 & 1 \; Sh_x \; 0 \; 0 & x0\\ [ y1 ] = & [ 0 \; 1 \; 0 \;0 ] &[ y0 ]\\ z1 & 0 \; Sh_z \; 1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$
First matrix is for the final point, second matrix is the shearing matrix for Y axis and the third matrix is for the original point.

10. Which of the following matrix equation is correct for 3D shearing in Z axis?
a) $$\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 & x0\\ [ y1 ] = &[ 0 \; 1 \; 0 \; 0 ] &[ y0 ]\\ z1 & Sh_x \; 0 \;1 \; 0 & z0\\ 1 & Sh_y \; 0 \; 0 \; 1 & 1\end{matrix}$$

b)$$\begin{matrix} x1 & 1 \; 0 \; Sh_x \;Sh_y & x0\\ [ y1 ] = &[ 0\; 1 \; 0 \; 0 ]& [ y0 ]\\ z1 & 0 \; 0 \; 1 \; 0 & z0\\ 1 & 0 \;0 \; 0 \; 1 & 1\end{matrix}$$

c) $$\begin{matrix}x1 & 1 \;0 \; Sh_x \;0 & x0\\ [ y1 ] = & [ 0 \; 1 \; Sh_y \; 0 ]& [ y0 ]\\ z1 & 0 \; 0 \; 1 \; 0 & z0\\ 0 & 0 \; 0 \; 0 \; 1 & 0\end{matrix}$$

d)$$\begin{matrix}x1 & 1 \; 0\; Sh_x \; 0 & x0\\ [ y1 ] = &[ 0 \; 1 \; Sh_y \; 0 ] &[ y0 ]\\ z1 & 0\; 0 \; 1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$

Explanation: The correct matrix equation for 3D shearing in Z axis is –
$$\begin{matrix}x1 & 1 \; 0\; Sh_x \; 0 & x0\\ [ y1 ] = &[ 0 \; 1 \; Sh_y \; 0 ] &[ y0 ]\\ z1 & 0\; 0 \; 1 \; 0 & z0\\ 1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}$$
First matrix is for the final point, second matrix is the shearing matrix for Z axis and the third matrix is for the original point.

Sanfoundry Global Education & Learning Series – Computer Graphics.

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