Coordinate Systems in Computer Graphics: Master the Fundamentals

Question 1

In a 2D coordinate plane, which quadrant contains the point (4, 3)?

Accepted Answer

First quadrant (positive x and y)

Answer

Second quadrant (negative x and positive y)

Answer

Third quadrant (negative x and negative y)

Answer

Fourth quadrant (positive x and negative y)

Question 2

Identify the transformation matrix that represents a 3D rotation around the z-axis by an angle theta.

Accepted Answer

[cos(theta), -sin(theta), 0; sin(theta), cos(theta), 0; 0, 0, 1]

Answer

[cos(theta), 0, sin(theta); 0, 1, 0; -sin(theta), 0, cos(theta)]

Answer

[1, 0, 0; 0, cos(theta), -sin(theta); 0, sin(theta), cos(theta)]

Answer

[0, -sin(theta), cos(theta); sin(theta), 0, 0; cos(theta), 0, 0]

Question 3

Which of the following is not a valid camera projection type used in computer graphics?

Accepted Answer

Isometric

Answer

Orthographic

Answer

Perspective

Answer

Stereoscopic

Question 4

Identify the characteristic that does not apply to a homogeneous coordinate system.

Accepted Answer

Remains unaffected by scaling operations.

Answer

Allows for the representation of translation and rotation operations.

Answer

Used in 3D graphics to represent points, vectors, and transformations.

Answer

Has an additional component called the w-component.

Question 5

How do coordinate systems enable the handling of user input devices like a mouse or touchscreen?

Accepted Answer

They define a framework for translating user input into specific screen or device locations.

Answer

They store object data primarily.

Answer

They generate random numbers for various uses.

Answer

They perform complex mathematical calculations.

Question 6

In a 2D coordinate system, the horizontal movement is represented along which axis?

Accepted Answer

x-axis

Answer

y-axis

Answer

z-axis

Question 7

What is the standardized order for specifying a point in a 3D coordinate system?

Accepted Answer

(x, y, z)

Answer

(z, y, x)

Answer

(y, z, x)

Question 8

Which transformation matrix is responsible for moving an object along the z-axis?

Accepted Answer

Translation Matrix

Answer

Rotation Matrix

Answer

Scaling Matrix

Question 9

What is the determinant value of a rotation matrix?

Accepted Answer

1

Answer

-1

Answer

0

Question 10

In computer graphics, which coordinate system serves as the viewpoint of the camera?

Accepted Answer

Eye Coordinates

Answer

World Coordinates

Answer

Object Coordinates

Question 11

What is the key difference between affine and projective transformations?

Accepted Answer

Affine transformations preserve parallelism, while projective transformations do not

Answer

Projective transformations preserve parallelism, while affine transformations do not

Answer

There is no distinction between affine and projective transformations

Question 12

What is the primary function of a viewport transformation in computer graphics?

Accepted Answer

Conversion from normalized device coordinates to window coordinates

Answer

Conversion from world coordinates to normalized device coordinates

Answer

Conversion from window coordinates to world coordinates

Question 13

In computer graphics, how does a coordinate system define a camera's viewing area?

Accepted Answer

It determines the shape and orientation of the visible region.

Answer

It defines the image's resolution.

Answer

It controls how objects move within the scene.

Answer

It is not relevant to the camera's functionality.

Question 14

Which of the following is NOT a type of fundamental coordinate system utilized in computer graphics?

Accepted Answer

Polar Coordinates

Answer

2D Cartesian Coordinates

Answer

Homogeneous Coordinates

Answer

3D Cartesian Coordinates

Question 15

In a 2D Cartesian coordinate system, which axis represents horizontal displacement?

Accepted Answer

x-axis

Answer

w-axis

Answer

y-axis

Answer

z-axis

Question 16

In a 3D Cartesian coordinate system, where do the three axes intersect?

Accepted Answer

Origin

Answer

Viewer's perspective

Answer

Center of transformed object

Answer

x-axis

Question 17

Which coordinate system is commonly used to represent points on a sphere?

Accepted Answer

Spherical Coordinates

Answer

Cartesian Coordinates

Answer

Homogeneous Coordinates

Answer

Cylindrical Coordinates

Question 18

Which transformation matrix is used to scale an object by (x, y, z)?

Accepted Answer

[x 0 0; 0 y 0; 0 0 z]

Answer

[x 0 0; 0 y 0; 0 0 1]

Answer

[1 x 0; 0 y 0; 0 0 z]

Answer

[x 0 0; 0 x 0; 0 0 x]

Question 19

In a 3D coordinate system, the vector (1, 2, 3) is translated by the vector (4, 5, 6). What are the coordinates of the resulting translated vector?

Accepted Answer

(5, 7, 9)

Answer

(3, 4, 5)

Answer

(1, 2, 3)

Answer

(4, 5, 6)

Question 20

In a homogeneous coordinate system, each point is represented as:

Accepted Answer

A vector with four components

Answer

A vector with three components

Answer

A scalar

Question 21

What is the key difference between an orthonormal basis and a non-orthonormal basis?

Accepted Answer

Orthonormal basis vectors are perpendicular to each other and have unit length, while non-orthonormal basis vectors may not have these properties.

Answer

Orthonormal basis vectors are used in 2D, while non-orthonormal basis vectors are used in 3D

Question 22

In computer graphics, a projection matrix is primarily used for:

Accepted Answer

Transforming 3D coordinates into 2D coordinates for display on a screen

Answer

Transforming 2D coordinates into 3D coordinates

Answer

Translating objects in a 3D scene

Question 23

The use of a left-handed coordinate system in computer graphics is advantageous because:

Accepted Answer

It simplifies cross-product calculations and aligns with the conventions of most graphics APIs

Answer

It reduces computational complexity

Answer

It makes it easier to visualize 3D objects

Question 24

Which of the following is NOT a property of a coordinate system?

Accepted Answer

Curvature

Answer

Skew

Answer

Scale

Answer

Translation

Question 25

In a 2D coordinate system, which axis is used to represent horizontal displacement?

Accepted Answer

x-axis

Answer

y-axis

Answer

w-axis

Answer

z-axis

Question 26

Which transformation tool is used to change the position of an object within a coordinate frame?

Accepted Answer

Translation matrix

Answer

Shear transformation

Answer

Rotation matrix

Answer

Scale transformation

Question 27

Which coordinate system type is commonly used in computer graphics?

Accepted Answer

Right-handed

Answer

Oblique

Answer

Left-handed

Answer

Polar

Question 28

What is the primary function of a world coordinate system?

Accepted Answer

To define the global scene and camera placement

Answer

To represent individual object transformations

Answer

To store user interactions

Answer

To handle collisions

Question 29

Which matrix operation is used to move an object along a specified axis?

Accepted Answer

Translation

Answer

Rotation

Answer

Shearing

Answer

Scaling

Question 30

Which coordinate system is used to represent an object's intrinsic orientation and position?

Accepted Answer

Object coordinate system

Answer

Screen coordinate system

Answer

Normalized device coordinate system

Answer

World coordinate system

Question 31

What is the key difference between homogeneous and non-homogeneous coordinates?

Accepted Answer

Homogeneous coordinates have an additional element representing scale

Answer

Non-homogeneous coordinates are used for 2D transformations

Answer

Only homogeneous coordinates can be used for 3D transformations

Question 32

In a 2D Cartesian coordinate system, the origin is defined as the point:

Accepted Answer

(0, 0)

Answer

(1, 1)

Answer

(0, 1)

Answer

(1, 0)

Question 33

The conversion factor from degrees to radians is:

Accepted Answer

π / 180

Answer

180 / π

Answer

π / 360

Question 34

One limitation of using Cartesian coordinates in computer graphics is:

Accepted Answer

Difficulty in representing curved surfaces

Answer

Intuitive representation

Answer

Widely accepted standard

Answer

Ease of performing transformations

Question 35

The primary purpose of a homogeneous coordinate system is:

Accepted Answer

To represent transformations and projections using matrix operations

Answer

To reduce the number of dimensions

Answer

To improve the accuracy of calculations

Question 36

Determine the correct transformation matrix for translating an object by (2, 3) in a 2D Cartesian coordinate system:

Accepted Answer

[1 0 2; 0 1 3; 0 0 1]

Answer

[0 1 2; 1 0 3; 0 0 1]

Answer

[2 0 1; 3 0 1; 1 1 1]

Answer

[1 2 0; 0 1 3; 0 0 1]

Question 37

Describe the perspective projection matrix used in computer graphics.

Accepted Answer

A matrix that transforms 3D coordinates into 2D coordinates, with a perspective effect

Answer

A matrix that rotates an object around a specified axis

Answer

A matrix that transforms 2D coordinates into 3D coordinates

Question 38

Which of the following coordinate systems is commonly used in computer graphics for representing 2D objects?

Accepted Answer

Cartesian Coordinate System

Answer

Cylindrical Coordinate System

Answer

Geographic Coordinate System

Answer

Spherical Coordinate System

Question 39

What is the primary advantage of using homogeneous coordinates in computer graphics?

Accepted Answer

They allow for the representation of both points and vectors in a single mathematical framework.

Answer

They simplify the implementation of perspective projection.

Answer

They reduce the computational cost of matrix operations.

Question 40

In a 3D Cartesian coordinate system, what is the vector representing the direction of the positive z-axis?

Accepted Answer

(0, 0, 1)

Answer

(1, 1, 1)

Answer

(0, 1, 0)

Answer

(1, 0, 0)

Question 41

Which transformation would you apply to scale an object in a 2D Cartesian coordinate system by a factor of 2 along the x-axis?

Accepted Answer

A scaling matrix with (2, 1) as the diagonal entries.

Answer

A rotation matrix by 90 degrees.

Answer

A translation matrix by (2, 0).

Question 42

Given a point P(2, 3) in a 2D Cartesian coordinate system, what would be its coordinates after a translation by vector (1, -1)?

Accepted Answer

(3, 2)

Answer

(1, 4)

Answer

(2, -1)

Question 43

In a 3D coordinate system, what is the effect of a rotation around the y-axis?

Accepted Answer

It changes the x and z coordinates of the object while preserving the y-coordinate.

Answer

It changes the y and z coordinates of the object while preserving the x-coordinate.

Answer

It changes the x and y coordinates of the object while preserving the z-coordinate.

Question 44

What is the purpose of a view matrix in computer graphics?

Accepted Answer

It defines the position and orientation of the camera or viewer in the 3D scene.

Answer

It transforms objects from world space to screen space.

Answer

It performs perspective projection.

Question 45

Which of the following is NOT a standard component of a graphics pipeline?

Accepted Answer

Animation

Answer

Modeling

Answer

Shading

Answer

Rendering

Question 46

What is the primary difference between orthographic and perspective projection?

Accepted Answer

Orthographic projection maintains parallel lines, while perspective projection simulates depth by converging lines.

Answer

Orthographic projection is used for 2D graphics, while perspective projection is used for 3D graphics.

Question 47

In a 3D scene, how do you change the field of view (FOV) using a perspective projection matrix?

Accepted Answer

By adjusting the aspect ratio of the projection matrix.

Answer

By rotating the camera around its axis.

Answer

By translating the camera position.

Question 48

Which coordinate system is primarily used to represent points on a 2D screen?

Accepted Answer

Screen coordinates

Answer

World coordinates

Answer

Object coordinates

Question 49

What does a positive value for the z-coordinate indicate in a right-handed 3D coordinate system?

Accepted Answer

A point located in front of the xy-plane

Answer

A point with a negative y-coordinate

Answer

A point located behind the xy-plane

Answer

A point with a positive x-coordinate

Question 50

Which transformation matrix would you use to scale an object by a factor of 2 in the x-direction and 0.5 in the y-direction?

Accepted Answer

[ [2, 0, 0], [0, 0.5, 0], [0, 0, 1] ]

Answer

[ [1, 0, 0], [0, 1, 0], [0, 0, 2] ]

Answer

[ [2, 0.5, 0], [0, 0, 1], [0, 1, 0] ]

Answer

[ [0.5, 0, 0], [0, 2, 0], [0, 0, 1] ]

Question 51

What is the purpose of the view transformation in the graphics pipeline?

Accepted Answer

Transforms objects from world space to camera space

Answer

Projects 3D objects onto a 2D screen

Answer

Transforms objects from object space to world space

Question 52

In a perspective projection, objects further away from the camera appear ______.

Accepted Answer

Smaller

Answer

The same size

Answer

Distorted

Answer

Larger

Question 53

Which of the following is NOT a component of a homogeneous coordinate?

Accepted Answer

Color

Answer

Y-coordinate

Answer

X-coordinate

Question 54

What is the purpose of using normalized device coordinates (NDC)?

Accepted Answer

To provide a consistent coordinate system independent of screen resolution and aspect ratio

Answer

To represent object coordinates in their original space

Answer

To define the position of the camera in the world

Question 55

What type of transformation combines a rotation and a translation?

Accepted Answer

Rigid body transformation

Answer

Shear transformation

Answer

Scaling transformation

Answer

Perspective transformation

Question 56

The process of converting a 3D object representation into a set of lines and polygons is called ______.

Accepted Answer

Rasterization

Answer

Interpolation

Answer

Transformation

Answer

Clipping

Question 57

What is the role of barycentric coordinates in computer graphics?

Accepted Answer

To interpolate vertex attributes across a triangle

Answer

To define the position of the camera in world space

Answer

To control the intensity of a light source

Answer

To represent the color of a pixel on the screen