3D Transformations in Computer Graphics: Master the Fundamentals

Question 1

Which of the following is a valid sequence of transformations to rotate an object 45 degrees around the z-axis, then translate it by (1, 2, 3)?

Accepted Answer

Rotation, Translation

Answer

Translation, Rotation

Answer

Scaling, Rotation, Translation

Answer

Translation, Scaling, Rotation

Question 2

What is the inverse transformation of a rotation around the y-axis by an angle θ?

Accepted Answer

Rotation around the y-axis by -θ

Answer

Rotation around the x-axis by θ

Answer

Rotation around the z-axis by -θ

Answer

Translation along the y-axis by -θ

Question 3

What is the determinant of a scaling matrix?

Accepted Answer

sx * sy * sz

Answer

1

Answer

sx + sy + sz

Answer

0

Question 4

In 3D computer graphics, what is the purpose of shearing transformations and where are they commonly used?

Accepted Answer

Skewing objects by displacing one face or edge relative to another, altering their shape.

Answer

Exclusively applicable to 2D objects, not 3D objects.

Answer

Primarily used for rotating objects around specific axes.

Answer

Have no practical significance in computer graphics.

Question 5

Which transformation translates an object along a specified vector?

Accepted Answer

Translation

Answer

Rotation

Answer

Scaling

Answer

Shearing

Question 6

What is the result of applying a rotation transformation around the z-axis?

Accepted Answer

Rotates the object around the z-axis

Answer

Translates the object along the z-axis

Answer

Rotates the object around the x-axis

Answer

Rotates the object around the y-axis

Question 7

Which transformation uniformly increases or decreases the size of an object?

Accepted Answer

Scaling

Answer

Rotation

Answer

Translation

Answer

Shearing

Question 8

What is the effect of applying a shearing transformation to an object?

Accepted Answer

Distorts the object's shape by skewing it

Answer

Translates the object along a specified vector

Answer

Rotates the object around an axis

Answer

Increases or decreases the object's size

Question 9

What is the inverse operation of a rotation transformation around the x-axis?

Accepted Answer

Rotation around the x-axis in the opposite direction

Answer

Rotation around the y-axis

Answer

Rotation around the z-axis

Answer

Scaling

Question 10

What is the purpose of a shear matrix?

Accepted Answer

To distort the object's shape by skewing it

Answer

To translate the object along a specified vector

Answer

To rotate the object around an axis

Answer

To scale the object

Question 11

What is the effect of applying a rotation transformation matrix about the z-axis by an angle of 45 degrees on an object?

Accepted Answer

Rotates the object around the z-axis by 45 degrees

Answer

Rotates the object around the x-axis by 45 degrees

Answer

Rotates the object around the y-axis by 45 degrees

Answer

Scales the object by a factor of 45

Question 12

Which of the following is NOT a fundamental 3D transformation?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Scaling

Question 13

What is the purpose of applying a shear transformation to an object?

Accepted Answer

To distort the shape of the object

Answer

To rotate the object about an arbitrary axis

Answer

To scale the object non-uniformly

Answer

To translate the object along a curved path

Question 14

Why is the order of applying transformations to an object significant?

Accepted Answer

The order matters for all transformations

Answer

The order does not affect the final result

Answer

The order matters for rotations and translations

Answer

The order matters for scaling and shearing

Question 15

What is the mathematical representation of a 3D transformation?

Accepted Answer

A 4x4 matrix

Answer

A 3x3 matrix

Answer

A 3x4 matrix

Answer

A 4x3 matrix

Question 16

What is the inverse operation of a rotation transformation about an arbitrary axis?

Accepted Answer

Another rotation transformation about the same axis

Answer

A translation transformation

Answer

A scaling transformation

Answer

A shearing transformation

Question 17

Which of the following transformations is not a fundamental 3D transformation?

Accepted Answer

Skewing

Answer

Translation

Answer

Rotation

Answer

Scaling

Question 18

The operation that moves an object along a straight line is called:

Accepted Answer

Translation

Answer

Rotation

Answer

Shearing

Answer

Reflection

Question 19

Which transformation changes the size of an object?

Accepted Answer

Scaling

Answer

Rotation

Answer

Translation

Answer

Shearing

Question 20

What is the determinant of a rotation matrix?

Accepted Answer

1

Answer

0

Answer

-1

Answer

2

Question 21

What is the purpose of using perspective projection in 3D graphics?

Accepted Answer

To create a realistic effect by simulating depth

Answer

To reduce computational complexity

Answer

To improve object visibility

Answer

To eliminate hidden surfaces

Question 22

Which transformation matrix translates a point along the x-axis by a distance of 'tx'?

Accepted Answer

[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [tx, 0, 0, 1]]

Answer

[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, ty, 0, 1]]

Answer

[[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, tz, 1]]

Answer

[[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]]

Question 23

When scaling a point (x, y, z) by factors (sx, sy, sz), what are the resulting coordinates?

Accepted Answer

(sx * x, sy * y, sz * z)

Answer

(x * sx, y * sy, z * sz)

Answer

(sx + x, sy + y, sz + z)

Answer

(sx / x, sy / y, sz / z)

Question 24

Which transformation is not considered rigid?

Accepted Answer

Shearing

Answer

Translation

Answer

Rotation

Answer

Scaling

Question 25

In homogeneous coordinates, how is the point (x, y, z) represented?

Accepted Answer

(x, y, z, 1)

Answer

(x, y, z, 0)

Answer

(1, x, y, z)

Answer

(0, x, y, z)

Question 26

Which of the following is NOT a fundamental 3D transformation?

Accepted Answer

Reflection

Answer

Scaling

Answer

Rotation

Answer

Translation

Question 27

What is the resultant transformation of applying a sequence of translations (2, 3, 0) followed by (0, 4, 5)?

Accepted Answer

Translation: (2, 7, 5)

Answer

Translation: (4, 7, 5)

Answer

Translation: (2, 3, 5)

Answer

Translation: (0, 7, 5)

Question 28

Which type of transformation is characterized by a change in the size of an object?

Accepted Answer

Scaling

Answer

Shearing

Answer

Translation

Answer

Rotation

Question 29

What is the effect of applying a translation transformation with a negative value in the x-axis?

Accepted Answer

Shifting the object to the left

Answer

Shifting the object down

Answer

Shifting the object to the right

Answer

Shifting the object up

Question 30

What is the primary effect of applying a translation transformation to an object?

Accepted Answer

Moves the object in 3D space

Answer

Scales the object uniformly

Answer

Deforms the object by shearing

Answer

Rotates the object around a specific axis

Question 31

Which axis is used by default for rotation transformations in a right-handed coordinate system?

Accepted Answer

Z-axis

Answer

Y-axis

Answer

W-axis

Answer

X-axis

Question 32

What is the purpose of a composite transformation matrix?

Accepted Answer

To apply multiple transformations to an object in a single operation

Answer

To store the individual transformation matrices

Answer

To invert the order of transformations

Question 33

Which transformation is used to create the effect of stretching or squeezing an object?

Accepted Answer

Shear

Answer

Scaling

Answer

Translation

Answer

Rotation

Question 34

Which 3D transformation involves moving an object from one position to another without altering its shape or size?

Accepted Answer

Translation

Answer

Scaling

Answer

Shearing

Answer

Rotation

Question 35

What effect does a scaling transformation with a scale factor of 2 applied in the x-direction have on an object?

Accepted Answer

The object's width will be doubled.

Answer

The object's volume will be quadrupled.

Answer

The object's height will be doubled.

Answer

The object's depth will be doubled.

Question 36

Describe the resulting composite transformation when a rotation of 60 degrees around the x-axis is followed by a translation of 5 units along the y-axis.

Accepted Answer

A roto-translation where the rotation matrix R is applied first, followed by the translation matrix T.

Answer

A translation of 5 units along the y-axis, followed by a rotation of 60 degrees around the x-axis.

Question 37

Which property is NOT characteristic of homogeneous transformations?

Accepted Answer

They maintain the object's center.

Answer

They can be applied in any sequence.

Answer

They can be applied to both points and vectors.

Answer

They are represented by 4x4 matrices.

Question 38

What is the determinant of a rotation matrix representing a rotation around any axis?

Accepted Answer

1

Answer

The scale factor

Answer

-1

Answer

0

Question 39

Which 3D transformation is used to flip an object across a plane?

Accepted Answer

Reflection

Answer

Translation

Answer

Scaling

Answer

Rotation

Question 40

Determine the inverse transformation of a scaling operation with a scale factor of 2.

Accepted Answer

A scaling transformation with a scale factor of 1/2.

Answer

A rotation transformation around the x-axis.

Answer

A scaling transformation with a scale factor of 4.

Question 41

What is the 4x4 transformation matrix that translates a point in 3D space by a vector (tx, ty, tz)?

Accepted Answer

[[1, 0, 0, tx], [0, 1, 0, ty], [0, 0, 1, tz], [0, 0, 0, 1]]

Answer

[[tx, 0, 0, 0], [0, ty, 0, 0], [0, 0, tz, 0], [0, 0, 0, 1]]

Answer

[[0, 0, 0, tx], [0, 0, 0, ty], [0, 0, 0, tz], [0, 0, 0, 1]]

Answer

[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [tx, ty, tz, 1]]

Question 42

When a point (x, y, z) is rotated around the z-axis by an angle of theta, what are the new coordinates of the point?

Accepted Answer

(x*cos(theta) - y*sin(theta), x*sin(theta) + y*cos(theta), z)

Answer

(x*cos(theta) - y*sin(theta), x*cos(theta) + y*sin(theta), z)

Answer

(x*cos(theta), x*sin(theta), z*cos(theta) - y*sin(theta))

Answer

(x*cos(theta) + y*sin(theta), x*sin(theta) - y*cos(theta), z)

Question 43

Which of the following matrices correctly represents a 3D scaling transformation with factors sx, sy, and sz along the x, y, and z axes respectively?

Accepted Answer

[[sx, 0, 0, 0], [0, sy, 0, 0], [0, 0, sz, 0], [0, 0, 0, 1]]

Answer

[[sx, 0, 0, tx], [0, sy, 0, ty], [0, 0, sz, tz], [0, 0, 0, 1]]

Answer

[[1, Hxy, 0, 0], [Hxy, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]

Answer

[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [sx, sy, sz, 1]]

Question 44

What is the geometric effect of applying a shear transformation matrix with a shear factor Hxy in the xy-plane?

Accepted Answer

It skews the object along the x-axis proportionally to its y-coordinate.

Answer

It scales the object by a factor of Hxy.

Answer

It translates the object by a vector (Hxy, 0, 0).

Answer

It rotates the object around the z-axis by an angle Hxy.

Question 45

What is the inverse of a translation matrix T that translates a point by (tx, ty, tz)?

Accepted Answer

T^(-1) = [[1, 0, 0, -tx], [0, 1, 0, -ty], [0, 0, 1, -tz], [0, 0, 0, 1]]

Answer

T^(-1) = [[1, 0, 0, tx], [0, 1, 0, ty], [0, 0, 1, tz], [0, 0, 0, 1]]

Answer

T^(-1) = [[cos(theta), -sin(theta), 0, tx], [sin(theta), cos(theta), 0, ty], [0, 0, 1, tz], [0, 0, 0, 1]]

Answer

T^(-1) = [[sx, 0, 0, -tx], [0, sy, 0, -ty], [0, 0, sz, -tz], [0, 0, 0, 1]]

Question 46

Which of the following transformations preserves both the shape and size of an object?

Accepted Answer

Rigid transformation

Answer

Non-linear transformation

Answer

Affine transformation

Answer

Projective transformation

Question 47

What is the determinant of a valid 3x3 rotation matrix?

Accepted Answer

1

Answer

-1

Answer

0

Answer

sx * sy * sz

Question 48

Which of the following is NOT a characteristic of shear transformations?

Accepted Answer

They preserve distances between points.

Answer

They can be represented by a matrix.

Answer

They skew the object along one axis while keeping the other axis fixed.

Answer

They can be applied to both 2D and 3D objects.

Question 49

What is the effect of applying a transformation matrix to a point represented in homogeneous coordinates?

Accepted Answer

It transforms both the position and the scale of the point.

Answer

It transforms only the position of the point.

Answer

It has no effect on the point.

Answer

It transforms only the scale of the point.

Question 50

Which of the following matrices represents a 3D translation by the vector (tx, ty, tz) in homogeneous coordinates?

Accepted Answer

[[1, 0, 0, tx], [0, 1, 0, ty], [0, 0, 1, tz], [0, 0, 0, 1]]

Answer

[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [tx, ty, tz, 1]]

Answer

[[0, 0, 0, tx], [0, 0, 0, ty], [0, 0, 0, tz], [0, 0, 0, 1]]

Answer

[[tx, 0, 0, 1], [0, ty, 0, 1], [0, 0, tz, 1], [0, 0, 0, 1]]

Question 51

A scaling transformation with factors (Sx, Sy, Sz) = (2, 1, 0.5) is applied to a 3D object. How does this affect the object's dimensions?

Accepted Answer

The object is stretched twice its original size along the x-axis, remains the same size along the y-axis, and is compressed to half its original size along the z-axis.

Answer

The object is stretched twice its original size along the x-axis and z-axis, and compressed to half its original size along the y-axis.

Answer

The object is stretched twice its original size along all three axes.

Answer

The object is compressed to half its original size along all three axes.

Question 52

In 3D graphics, applying multiple transformations to an object can significantly impact the final result. Why is this the case?

Accepted Answer

The order in which transformations are applied matters. Different orders can lead to different final positions and orientations of the object.

Answer

The order of transformations only matters for specific types of transformations, such as rotation.

Answer

The order of transformations does not matter as long as all transformations are applied to the object.

Answer

Transformations are applied in the order they are defined in the code, so the order doesn't matter.

Question 53

Which of the following matrices represents a 3D rotation of an object around the y-axis by an angle of θ?

Accepted Answer

[[cos(θ), 0, sin(θ), 0], [0, 1, 0, 0], [-sin(θ), 0, cos(θ), 0], [0, 0, 0, 1]]

Answer

[[1, 0, 0, 0], [0, cos(θ), 0, 0], [0, 0, sin(θ), 0], [0, 0, 0, 1]]

Answer

[[cos(θ), -sin(θ), 0, 0], [sin(θ), cos(θ), 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]

Answer

[[cos(θ), 0, -sin(θ), 0], [0, 1, 0, 0], [sin(θ), 0, cos(θ), 0], [0, 0, 0, 1]]

Question 54

What is the primary advantage of using a homogeneous coordinate system in 3D transformations?

Accepted Answer

It allows us to represent both translation and other transformations (scaling, rotation) using a single matrix multiplication, simplifying calculations.

Answer

It makes it easier to represent 3D objects in a 2D coordinate system.

Answer

It simplifies the calculation of inverse transformations.

Answer

It allows for more efficient storage of 3D object data.

Question 55

To rotate an object by 45 degrees around the z-axis, followed by a translation of (2, 3, 1), what is the correct order of applying these transformations?

Accepted Answer

Apply the rotation first, followed by the translation.

Answer

The order depends on the specific software being used.

Answer

The order doesn't matter, as both transformations are applied to the object.

Answer

Apply the translation first, followed by the rotation.

Question 56

What is the key distinction between a shear transformation and a scaling transformation?

Accepted Answer

Scaling uniformly changes the size of an object, while shearing distorts its shape by shifting points along a specific direction.

Answer

Shearing and scaling both change the shape of an object, but shearing does so in a more controlled manner.

Answer

Shearing changes the size of an object, while scaling distorts its shape.

Answer

Shearing and scaling are essentially the same transformation, with different names.

Question 57

A 3D object is represented by a set of vertices. How are 3D transformations applied to this object?

Accepted Answer

The transformation matrix is multiplied with each vertex's homogeneous coordinates.

Answer

Each vertex is individually transformed by applying the transformation matrix to its coordinates.

Answer

The transformation matrix is added to each vertex's coordinates.

Answer

The transformation is applied to the object's center of mass, and all vertices are moved accordingly.

Question 58

Which of the following is NOT a commonly used type of 3D transformation?

Accepted Answer

Reflection across a line.

Answer

Translation.

Answer

Rotation.

Answer

Scaling.

Question 59

What is the most efficient method to create an animation of a cube continuously rotating around the y-axis?

Accepted Answer

Apply a rotation transformation with increasing angle values over time, updating the cube's orientation in each frame.

Answer

Use a pre-recorded animation sequence to display the rotation.

Answer

Manually move each vertex of the cube for every frame of the animation.

Answer

Create a new cube object for each frame of the animation, with the desired rotation.