MCQs of 3D transformation and viewing (Computer Graphics - 3150712)

Computer Graphics (3150712) MCQs

MCQs of 3D transformation and viewing

Showing 1 to 10 out of 30 Questions

Which is a correct equation for 3D translation?

(a)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ t_{x} & t_{y} & t_{z} & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$
(b)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} t_{x} & t_{y} & t_{z} & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$
(c)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} t_{x} & 0 & 0 & 1 \\ 0 & t_{y} & 0 & 1 \\ 0 & 0 & t_{z} & 1 \\ 0 & 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$
(d)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 & t_{x} \\ 0 & 1 & 0 & t_{y} \\ 0 & 0 & 1 & t_{z} \\ 0 & 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$

What are the final coordinates after a translation of point P (10, 10, 10) into 3D space with translation factor T (10, 20, 5)?

(a)	(20, 30, 15)
(b)	(20, 20, 25)
(c)	(15, 30, 25)
(d)	(15, 20, 25)

Which is a correct equation for 3D rotation about X-axis?

(a)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \cos θ & - \sin θ & 0 \\ 0 & \sin θ & \cos θ & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$
(b)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} \cos θ & - \sin θ & 0 & 0 \\ \sin θ & \cos θ & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$
(c)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} \cos θ & 0 & \sin θ & 0 \\ 0 & 1 & 0 & 0 \\ - \sin θ & 0 & \cos θ & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$
(d)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} \cos θ & 0 & \sin θ & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ - \sin θ & 0 & \cos θ & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$

What are the final coordinates after rotation of the point P(5, 5, 5)

90^{o}

about Z-axis?

(a)	(5, -5, -5)
(b)	(-5, 5, 5)
(c)	(-5, -5, -5)
(d)	(5, -5, 5)

Arrange steps of general 3D rotations in the correct order :
1. Apply inverse rotations to bring the rotation axis back to its original orientation.
2. Apply the inverse translation to bring the rotation axis back to its original position.
3. Rotate the object so that the axis of rotation coincides with one of the coordinate axes.
4. Perform the specified rotation about that coordinate axis.
5. Translate the object so that the rotation axis passes through the coordinate origin.

(a)	3, 5, 4, 2, 1
(b)	3, 2, 4, 5, 1
(c)	5, 3, 4, 1, 2
(d)	1, 2, 3, 4, 5

Which is a correct equation for 3D scaling?

(a)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ s_{x} & s_{y} & s_{z} & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$
(b)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} s_{x} & 0 & 0 & 0 \\ s_{y} & 0 & 0 & 0 \\ s_{z} & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$
(c)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} s_{x} & s_{y} & s_{z} & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$
(d)	$[\begin{matrix} x^{'} \\ y^{'} \\ z' \\ 1 \end{matrix}] = [\begin{matrix} s_{x} & 0 & 0 & 0 \\ 0 & s_{y} & 0 & 0 \\ 0 & 0 & s_{z} & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] \cdot [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]$

Which is a correct matrix for 3D fixed-point scaling(for column-major matrix)?

(a)	$[\begin{matrix} s_{x} & (1 - s_{x}) x_{f} & (1 - s_{y}) y_{f} & (1 - s_{z}) z_{f} \\ 0 & s_{y} & 0 & 0 \\ 0 & 0 & s_{z} & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$
(b)	$[\begin{matrix} s_{x} & 0 & 0 & (1 - s_{x}) x_{f} \\ 0 & s_{y} & 0 & (1 - s_{y}) y_{f} \\ 0 & 0 & s_{z} & (1 - s_{z}) z_{f} \\ 0 & 0 & 0 & 1 \end{matrix}]$
(c)	$[\begin{matrix} s_{x} & 0 & 0 & 0 \\ 0 & s_{y} & 0 & 0 \\ 0 & 0 & s_{z} & 0 \\ (1 - s_{x}) x_{f} & (1 - s_{y}) y_{f} & (1 - s_{z}) z_{f} & 1 \end{matrix}]$
(d)	$[\begin{matrix} s_{x} & 0 & 0 & 0 \\ (1 - s_{x}) x_{f} & s_{y} & 0 & 0 \\ (1 - s_{y}) y_{f} & 0 & s_{z} & 0 \\ (1 - s_{z}) z_{f} & 0 & 0 & 1 \end{matrix}]$

Which is a correct matrix for 3D reflection about XZ-plane(for column-major matrix)?

(a)	$[\begin{matrix} - 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$
(b)	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & - 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$
(c)	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & - 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$
(d)	$[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & - 1 \end{matrix}]$

Which is a correct matrix for 3D shearing about X-axis(for column-major matrix)?

(a)	$[\begin{matrix} 1 & 0 & a & 0 \\ 0 & 1 & b & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$
(b)	$[\begin{matrix} 1 & a & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & b & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$
(c)	$[\begin{matrix} 1 & 0 & 0 & 0 \\ a & 1 & 0 & 0 \\ b & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$
(d)	$[\begin{matrix} 1 & 0 & 0 & a \\ 0 & 1 & 0 & b \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$

10.

Arrange transformation sequence of 3D viewing pipeline in a correct order :
1. Viewing Transformation
2. Workstation Transformation
3. Modeling Transformation
4. Projection Transformation

(a)	1, 2, 3, 4
(b)	1, 3, 4, 2
(c)	3, 1, 2, 4
(d)	3, 1, 4, 2

Showing 1 to 10 out of 30 Questions