Fundamentals of Computer Graphics

Steve Marschner, Peter Shirley

• Publisher: A K Peters/CRC Press
• Year: 2018
• ISBN:
  9781315360201
• Edition: 4
• Topic: Computer Science
• Subtopic: Computer Graphics
• Index: Computer Science

Drawing on an impressive roster of experts in the field, Fundamentals of Computer Graphics, Fourth Edition offers an ideal resource for computer course curricula as well as a user-friendly personal or professional reference.

Focusing on geometric intuition, the book gives the necessary information for understanding how images get onto the screen by using the complementary approaches of ray tracing and rasterization. It covers topics common to an introductory course, such as sampling theory, texture mapping, spatial data structure, and splines. It also includes a number of contributed chapters from authors known for their expertise and clear way of explaining concepts.

Highlights of the Fourth Edition Include:

• Updated coverage of existing topics
• Major updates and improvements to several chapters, including texture mapping, graphics hardware, signal processing, and data structures
• A text now printed entirely in four-color to enhance illustrative figures of concepts

The fourth edition of Fundamentals of Computer Graphics continues to provide an outstanding and comprehensive introduction to basic computer graphic technology and theory. It retains an informal and intuitive style while improving precision, consistency, and completeness of material, allowing aspiring and experienced graphics programmers to better understand and apply foundational principles to the development of efficient code in creating film, game, or web designs.

Key Features

• Provides a thorough treatment of basic and advanced topics in current graphics algorithms
• Explains core principles intuitively, with numerous examples and pseudo-code
• Gives updated coverage of the graphics pipeline, signal processing, texture mapping, graphics hardware, reflection models, and curves and surfaces
• Uses color images to give more illustrative power to concepts

1

Introduction

The term computer graphics describes any use of computers to create and manipulate images. This book introduces the algorithmic and mathematical tools that can be used to create all kinds of images—realistic visual effects, informative technical illustrations, or beautiful computer animations. Graphics can be two- or three-dimensional; images can be completely synthetic or can be produced by manipulating photographs. This book is about the fundamental algorithms and mathematics, especially those used to produce synthetic images of three-dimensional objects and scenes.

Actually doing computer graphics inevitably requires knowing about specific hardware, file formats, and usually a graphics API (see Section 1.3) or two. Computer graphics is a rapidly evolving field, so the specifics of that knowledge are a moving target. Therefore, in this book we do our best to avoid depending on any specific hardware or API. Readers are encouraged to supplement the text with relevant documentation for their software and hardware environment. Fortunately, the culture of computer graphics has enough standard terminology and concepts that the discussion in this book should map nicely to most environments.

This chapter defines some basic terminology and provides some historical background, as well as information sources related to computer graphics.

API: application program interface.

1.1 Graphics Areas

Imposing categories on any field is dangerous, but most graphics practitioners would agree on the following major areas of computer graphics:

• Modeling 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.

• Rendering is a term inherited from art and deals with the creation of shaded images from 3D computer models.

• Animation is 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.

There are many other areas that involve computer graphics, and whether they are core graphics areas is a matter of opinion. These will all be at least touched on in the text. Such related areas include the following:

• User interaction 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.

• Virtual reality 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.

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

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

• 3D scanning 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.

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

1.2 Major Applications

Almost any endeavor can make some use of computer graphics, but the major consumers of computer graphics technology include the following industries:

• Video games increasingly use sophisticated 3D models and rendering algorithms.

• Cartoons are often rendered directly from 3D models. Many traditional 2D cartoons use backgrounds rendered from 3D models, which allow a continuously moving viewpoint without huge amounts of artist time.

• Visual effects use almost all types of computer graphics technology. Almost every modern film uses digital compositing to superimpose backgrounds with separately filmed foregrounds. Many films also use 3D modeling and animation to create synthetic environments, objects, and even characters that most viewers will never suspect are not real.

• Animated films use many of the same techniques that are used for visual effects, but without necessarily aiming for images that look real.

• CAD/CAM stands for computer-aided design and computer-aided manufacturing. These fields use computer technology to design parts and products on the computer and then, using these virtual designs, to guide the manufacturing process. For example, many mechanical parts are designed in a 3D computer modeling package and then automatically produced on a computer-controlled milling device.

• Simulation can be thought of as accurate video gaming. For example, a flight simulator uses sophisticated 3D graphics to simulate the experience of flying an airplane. Such simulations can be extremely useful for initial training in safety-critical domains such as driving, and for scenario training for experienced users such as specific fire-fighting situations that are too costly or dangerous to create physically.

• Medical imaging creates meaningful images of scanned patient data. For example, a computed tomography (CT) dataset is composed of a large 3D rectangular array of density values. Computer graphics is used to create shaded images that help doctors extract the most salient information from such data.

• Information visualization creates images of data that do not necessarily have a “natural” visual depiction. For example, the temporal trend of the price of ten different stocks does not have an obvious visual depiction, but clever graphing techniques can help humans see the patterns in such data.

1.3 Graphics APIs

A key part of using graphics libraries is dealing with a graphics API. An application program interface (API) is a standard collection of functions to perform a set of related operations, and a graphics API is a set of functions that perform basic operations such as drawing images and 3D surfaces into windows on the screen.

Every graphics program needs to be able to use two related APIs: a graphics API for visual output and a user-interface API to get input from the user. There are currently two dominant paradigms for graphics and user-interface APIs. 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, where the drawing commands are part of a software library tied to a language such as C++, and the user-interface software is an independent entity that might vary from system to system. In this latter approach, it is problematic to write portable code, although for simple programs it may be possible to use a portable library layer to encapsulate the system specific user-interface code.

Whatever your choice of API, the basic graphics calls will be largely the same, and the concepts of this book will apply.

1.4 Graphics Pipeline

Every desktop computer today has a powerful 3D graphics pipeline. This is a special software/hardware subsystem that efficiently draws 3D primitives in perspective. Usually these systems are optimized for processing 3D triangles with shared vertices. The basic operations in the pipeline map the 3D vertex locations to 2D screen positions and shade the triangles so that they both look realistic and appear in proper back-to-front order.

Although drawing the triangles in valid back-to-front order was once the most important research issue in computer graphics, it is now almost always solved using the z-buffer, which uses a special memory buffer to solve the problem in a brute-force manner.

It turns out that the geometric manipulation used in the graphics pipeline can be accomplished almost entirely in a 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. This 4D coordinate system is one of the most subtle and beautiful constructs used in computer science, and it is certainly the biggest intellectual hurdle to jump when learning computer graphics. A big chunk of the first part of every graphics book deals with these coordinates.

The sp...