Introduction 1

Question 1

What are the major areas of computer graphics?

Answer 1

Modelling
Rendering
Animation
User interaction
Virtual reality
Visualization
Image processing
3D scanning
Computational photography

Question 2

Define modelling

Answer 2

deals with the mathematical specification of shape and appearance properties in a way that can be stored on the computer. For example,
a coffee mug might be described as a set of ordered 3D points along with some interpolation rule to connect the points and a reflection model that describes how light interacts with the mug.

Question 3

Define rendering

Answer 3

a term inherited from art and deals with the creation of

shaded images from 3D computer models

Question 4

Define animation

Answer 4

a technique to create an illusion of motion through sequences of images. Animation uses modeling and rendering but adds the key issue of movement over time, which is not usually dealt with in basic modeling and rendering

Question 5

Define user interaction

Answer 5

deals with the interface between input devices such as mice and tablets, the application, feedback to the user in imagery, and other sensory feedback. Historically, this area is associated with graphics largely because graphics researchers had some of the earliest access to the input/output devices that are now ubiquitous.

Question 6

Define virtual reality

Answer 6

attempts to immerse the user into a 3D virtual world. This typically requires at least stereo graphics and response to head motion. For true virtual reality, sound and force feedback should be provided as well. Because this area requires advanced 3D graphics and advanced display technology, it is often closely associated with graphics.

Question 7

Define visualization

Answer 7

attempts to give users insight into complex information via visual display. Often there are graphic issues to be addressed in a visualization problem.

Question 8

Define Image processing

Answer 8

deals with the manipulation of 2D images and is used in both the fields of graphics and vision.

Question 9

Define 3D scanning

Answer 9

uses range-finding technology to create measured 3D models. Such models are useful for creating rich visual imagery, and the processing of such models often requires graphics algorithms.

Question 10

Define computational photography

Answer 10

the use of computer graphics, computer vision, and image processing methods to enable new ways of photographically capturing objects, scenes, and environments

Question 11

What’s a key part of using graphics libraries?

Answer 11

A key part of using graphics libraries is dealing with a graphics API.

Question 12

Define an API

Answer 12

An application program interface (API) is a standard collection of functions to perform a set of related operations

Question 13

Define a graphics API

Answer 13

a set of functions that perform basic operations such as drawing images and 3D surfaces into windows on the screen.

Question 14

Every graphics program needs to be able to use…

Answer 14

two related APIs:
a graphics API for visual output and
a user-interface API to get input from the user.

Question 15

There are currently two dominant paradigms for graphics and user-interface APIs…

Answer 15

The first is the integrated approach, exemplified by Java, where the graphics and user interface toolkits are integrated and portable packages that are fully standardized and supported as part of the language.

The second is represented by Direct3D and OpenGL.

Question 16

geometric manipulation used in the graphics pipeline can be accomplished almost entirely in a….

Answer 16

4D coordinate space composed of three traditional geometric coordinates and a fourth homogeneous coordinate that helps with perspective viewing.

These 4D coordinates are manipulated using 4 × 4 matrices and 4-vectors.

The graphics pipeline, therefore, contains much machinery for efficiently processing and composing such matrices and vectors.

Question 17

Infinity operations

Answer 17

\+a/(+∞) = +0
−a/(+∞) = −0
\+a/(−∞) = −0
−a/(−∞) = +0
∞ + ∞ = +∞
∞−∞ = NaN
∞×∞ = ∞
∞/∞ = NaN
∞/a = ∞
∞/0 = ∞
0/0 = NaN
\+a/ +0 = +∞
−a/ +0 = −∞

Question 18

A reasonable approach to making code fast is to proceed in the following order, taking only those steps which are needed:

Answer 18

1. Write the code in the most straightforward way possible. Compute intermediate results as needed on the fly rather than storing them.
2. Compile in optimized mode.
3. Use whatever profiling tools exist to find critical bottlenecks.
4. Examine data structures to look for ways to improve locality. If possible, make data unit sizes match the cache/page size on the target architecture.
5. If profiling reveals bottlenecks in numeric computations, examine the assembly code generated by the compiler for missed efficiencies. Rewrite source code to solve any problems you find.

Question 19

What are the basic classes for designing and coding graphics programs

Answer 19

Vector2. 
Vector3
Hvector
RGB 
Transform
Image

Question 20

Describe a vector2 class’ purpose and functionality

Answer 20

A 2D vector class that stores an x- and y-component. It should store these components in a length-2 array so that an indexing operator can be well supported. You should also include operations for vector addition, vector subtraction, dot product, cross product, scalar multiplication, and scalar division.

Question 21

Describe a vector3 class’ purpose and functionality

Answer 21

A 3D vector class analogous to vector2.

Question 22

Describe a hvector class’ purpose and functionality

Answer 22

A homogeneous vector with four components (see Chapter 7).

Question 23

Describe a RGB class’ purpose and functionality

Answer 23

An RGB color that stores three components. You should also include
operations for RGB addition, RGB subtraction, RGB multiplication, scalar
multiplication, and scalar division.

Question 24

Describe a Transform class’ purpose and functionality.

Answer 24

A 4 × 4 matrix for transformations. You should include a
matrix multiply and member functions to apply to locations, directions, and surface normal vectors. As shown in Chapter 6, these are all different.

Question 25

Describe a image class’ purpose and functionality.

Answer 25

A 2D array of RGB pixels with an output operation.

Question 26

Common sets of interest include:

Answer 26

• R—the real numbers;
• R+—the non-negative real numbers (includes zero);
• R^2—the ordered pairs in the real 2D plane;
• R^n—the points in n-dimensional Cartesian space;
• Z—the integers;
• S^2—the set of 3D points (points in R3) on the unit sphere

Question 27

Differentiate loga x

Answer 27

d/dx loga x = 1/x ln a

Question 28

Differentiate a^x

Answer 28

d/dx a^x = a^x ln a.

Question 29

Sec and tan identity

Answer 29

sec2 A − tan2 A = 1

Question 30

cosec and cot identity

Answer 30

csc2 A − cot2 A = 1

Question 31

Product identities for sinAsinB

Answer 31

sin A sin B = −(cos(A + B) − cos(A − B))/2

Question 32

Product identities for sinAcosB

Answer 32

sin A cos B = (sin(A + B) + sin(A − B))/2

Question 33

Product identities for cosAcosB

Answer 33

cos A cos B = (cos(A + B) + cos(A − B))/2

Question 34

Law of tangents

Answer 34

(a + b)/(a − b) = tan ((A+B)/2) / tan ((A−B)/2)

Question 35

Area of triangle formula with square root

Answer 35

triangle area = 1/2 x ((a + b + c)(−a + b + c)(a − b + c)(a + b − c))^0.5