Master Geometric Transformations in Computer Graphics: Interactive Learning Quizzes

Question 1

Determine the equation for translating an object in 2D space.

Accepted Answer

T(x, y) = [x + dx, y + dy]

Answer

T(x, y) = [x - dx, y - dy]

Answer

T(x, y) = [x * dx, y * dy]

Answer

T(x, y) = [dx, dy]

Question 2

Distinguish clearly between **rigid** and **non-rigid** transformations. Provide an example of each type.

Accepted Answer

**Rigid transformations** preserve the shape and size of an object, while **non-rigid transformations** do not.

Accepted Answer

Scaling is a rigid transformation, while shearing is a non-rigid transformation.

Answer

Rigid transformations only apply to 2D objects, while non-rigid transformations can be applied to both 2D and 3D objects.

Answer

Translation is a non-rigid transformation, while rotation is a rigid transformation.

Question 3

Which geometric transformation moves an object without changing its size or orientation?

Accepted Answer

Translation

Answer

Scaling

Answer

Rotation

Answer

Shearing

Question 4

A rotation transformation is uniquely defined by its:

Accepted Answer

Angle and center of rotation

Answer

Scaling factor and angle

Answer

Shearing angle and center

Answer

Translation vector and angle

Question 5

Scaling an object by a factor less than 1 will:

Accepted Answer

Reduce its size

Answer

Increase its size

Answer

Rotate it

Question 6

Which transformation results in a parallelogram from a rectangle?

Accepted Answer

Shearing

Answer

Scaling

Answer

Translation

Answer

Rotation

Question 7

In a typical graphics pipeline, transformations are typically applied in the following order:

Accepted Answer

Modeling -> Viewing -> Projection

Answer

Projection -> Viewing -> Modeling

Answer

Projection -> Modeling -> Viewing

Answer

Viewing -> Projection -> Modeling

Question 8

Which transformation matrix type is used to translate an object in a 2D space?

Accepted Answer

Translation matrix

Answer

Rotation matrix

Answer

Scaling matrix

Answer

Shearing matrix

Question 9

What is the determinant of a rotation matrix?

Accepted Answer

1

Answer

Depends on the rotation angle

Answer

0

Answer

-1

Question 10

Which transformation is used to create a mirror image of an object around the y-axis?

Accepted Answer

Scaling by -1 in the x-direction

Answer

Shearing along the x-axis

Answer

Translation by half the object's width

Answer

Rotation by 180 degrees

Question 11

What is the key distinction between affine and non-affine transformations?

Accepted Answer

Affine transformations preserve lines and parallelism, while non-affine transformations do not.

Answer

Affine transformations are only used in 2D, while non-affine transformations are used in 3D.

Answer

Affine transformations are always invertible, while non-affine transformations are not.

Question 12

Which of the following transformations is not commonly used in 3D graphics?

Accepted Answer

Shearing

Answer

Translation

Answer

Scaling

Answer

Rotation

Question 13

Which transformation consistently moves every point of an object by the same distance in a specific direction?

Accepted Answer

Translation

Answer

Shearing

Answer

Rotation

Answer

Scaling

Question 14

A scaling transformation with scaling factors Sx = 2 and Sy = 0.5 applied to a 2D object will:

Accepted Answer

Stretch the object horizontally and compress it vertically

Answer

Compress the object horizontally and stretch it vertically

Answer

Rotate the object 45 degrees counterclockwise

Answer

Shear the object along the x-axis

Question 15

What are the coordinates of the point (x, y) after a 90-degree counterclockwise rotation around the origin?

Accepted Answer

(-y, x)

Answer

(-x, -y)

Answer

(y, -x)

Answer

(x, y)

Question 16

Which matrix represents a shear transformation along the x-axis?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 17

Why are homogeneous coordinates used in transformation matrices?

Accepted Answer

To represent translations using matrix multiplication

Answer

To eliminate the need for scaling factors

Answer

To make matrix operations more efficient

Answer

To simplify rotation calculations

Question 18

The process of converting an object from its local coordinate system to the world coordinate system is called:

Accepted Answer

World transformation

Answer

Viewport transformation

Answer

View transformation

Answer

Projection transformation

Question 19

Which transformation is used to resize an object?

Accepted Answer

Scaling

Answer

Translation

Answer

Rotation

Answer

Shearing

Question 20

What type of transformation results from combining a shear and a translation?

Accepted Answer

Affine transformation

Answer

Linear transformation

Answer

Perspective transformation

Answer

Orthographic transformation

Question 21

In 3D graphics, which axis typically represents depth information?

Accepted Answer

Z-axis

Answer

W-axis

Answer

Y-axis

Answer

X-axis

Question 22

What is the result of applying a transformation matrix to a vector?

Accepted Answer

The vector is transformed according to the matrix

Answer

The matrix is transformed according to the vector

Answer

The vector and matrix are multiplied element-wise

Answer

The result is a new matrix