计算机图形学基础：3D渲染与OpenGL编程

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"计算机图形学（英文） - 由Steve Cunningham编著的一本关于编程、问题解决和视觉沟通的计算机图形学教材" 计算机图形学是一门涉及编程、问题解决和视觉交流的学科，它在现代科技中扮演着至关重要的角色。这本由Steve Cunningham博士编写的英文原版教材，来自加利福尼亚州立大学斯坦尼斯劳斯分校的计算机科学部门，旨在深入浅出地介绍计算机图形学的基本概念和技术。书中首先探讨了计算机图形学的核心概念。"什么是计算机图形学？"这个问题引导读者进入这个领域，理解它是如何通过计算机程序创建和操纵图像的。接着，"什么是图形API（应用程序接口）？"这一部分解释了图形API如OpenGL或DirectX在图形处理中的作用，它们为开发者提供了与硬件交互的标准化接口。作者进一步讨论了为什么我们需要计算机图形学，即它在科学可视化、游戏开发、电影制作、工程设计等多个领域的广泛应用。书中的"Overview of the Book"章节概述了全书的结构和内容，帮助读者规划学习路径。在"Getting Started"章节，Cunningham博士详细介绍了3D几何的基础知识，包括3D模型坐标系统、3D世界坐标系、3D视图坐标系以及剪裁算法。他还讲解了投影的概念，如透视投影和平行投影，以及如何将3D对象转换为2D屏幕坐标。此外，色彩理论、纹理映射和深度缓冲作为影响物体外观的重要因素也在此部分被提及。在"AbasicOpenGLprogram"中，读者将了解到如何构建一个基础的OpenGL程序，包括main()函数的结构、模型空间、建模变换、3D世界空间、视图变换、3D视图空间、投影、2D视图空间、2D屏幕空间，以及如何处理物体的外观。同时，书中还提到了OpenGL扩展，这些扩展允许开发者利用最新的硬件特性。每一章末尾都包含问题、练习和实验，以巩固学习并鼓励实践操作。第一章"Viewing and Projection"专注于观察和投影技术，这是计算机图形学中的基石，为后续更复杂的渲染和交互奠定了基础。通过这本书，读者不仅可以掌握计算机图形学的基本原理，还能了解到如何实际应用这些知识来创建动态、逼真的图像。无论你是初学者还是希望深化对计算机图形学理解的专业人士，这本书都将是你宝贵的参考资料。

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Many, if not most, of the examples in this book are taken from sources in the sciences, and we

include a chapter that discusses several kinds of scientific and mathematical applications of

computer graphics. This emphasis makes this book appropriate for courses in computational

science or in computer science programs that want to develop ties with other programs on

campus, particularly programs that want to provide science students with a background that will

support development of computational science or scientific visualization work. It is tempting to

use the word “visualization” somewhere in the title of this book, but we would reserve that word

for material that is primarily focused on the science with only a sidelight on the graphics;

because we reverse that emphasis, the role of scientific visualization is in the application of the

computer graphics.

The book is organized along fairly traditional lines, treating projection, viewing, modeling,

rendering, lighting, shading, and many other aspects of the field. It also includes an emphasis on

using computer graphics to address real problems and to communicate results effectively to the

viewer. As we move through this material, we describe some general principles in computer

graphics and show how the OpenGL API provides the graphics programming tools that

implement these principles. We do not spend time describing in depth the algorithms behind the

techniques or the way the techniques are implemented; your instructor will provide these if he or

she finds it necessary. Instead, the book focuses on describing the concepts behind the graphics

and on using a graphics API (application programming interface) to carry out graphics

operations and create images.

We have tried to match the sequence of chapters in the book to the sequence we would expect to

be used in a beginning computer graphics course, and in some cases the presentation of one

module will depend on your knowing the content of an earlier chapter. However, in other cases

it will not be critical that earlier chapters have been covered. It should be pretty obvious if other

chapters are assumed, and we may make that assumption explicit in some modules.

The book focuses on computer graphics programming with a graphics API, and in particular uses

the OpenGL API to implement the basic concepts that it presents. Each chapter includes a

general discussion of a topic in graphics as well as a discussion of the way the topic is handled in

OpenGL. However, another graphics API might also be used, with the OpenGL discussion

serving as an example of the way an API could work. Many of the fundamental algorithms and

techniques that are at the root of computer graphics are covered only at the level they are needed

to understand questions of graphics programming. This differs from most computer graphics

textbooks that place a great deal of emphasis on understanding these algorithms and techniques.

We recognize the importance of these for persons who want to develop a deep knowledge of the

subject and suggest that a second graphics course can provide that knowledge. We believe that

the experience provided by API-based graphics programming will help you understand the

importance of these algorithms and techniques as they are developed and will equip you to work

with them more fluently than if you met them with no previous background.

This book includes several features that are not found in most beginning textbooks. These

features support a course that fits the current programming practice in computer graphics. The

discussions in this book will focus on 3D graphics and will almost completely omit uniquely 2D

3/15/03 Page 5

techniques. It has been traditional for computer graphics courses to start with 2D graphics and

move up to 3D because some of the algorithms and techniques have been easier to grasp at the

2D level, but without that concern it is easier to begin by covering 3D concepts and discuss 2D

graphics as the special case where all the modeling happens in the X-Y plane.

Modeling is a very fundamental topic in computer graphics, and there are many different ways

that one can model objects for graphical display. This book uses the standard beginning

approach of focusing on polygon-based modeling because that approach is supported by

OpenGL and most other graphics APIs. The discussion on modeling in this book places an

important emphasis on the scene graph as a fundamental tool in organizing the work needed to

create a graphics scene. The concept of the scene graph allows the student to design the

transformations, geometry, and appearance of a number of complex components in a way that

they can be implemented quite readily in code, even if the graphics API itself does not support

the scene graph directly. This is particularly important for hierarchical modeling, but it also

provides a unified design approach to modeling and has some very useful applications for

placing the eye point in the scene and for managing motion and animation.

A key feature of this book is an emphasis on using computer graphics to create effective visual

communication. This recognizes the key role that computer graphics has taken in developing an

understanding of complex problems and in communicating this understanding to others, from

small groups of working scientists to the general public. This emphasis is usually missing from

computer graphics textbooks, although we expect that most instructors include this somehow in

their courses. The discussion of effective communication is integrated throughout several of the

basic chapters in the book, because it is an important consideration in graphics modeling,

viewing, color, and interaction. We believe that a systematic discussion of this subject will help

prepare students for more effective use of computer graphics in their future professional lives,

whether this is in technical areas in computing or is in areas where there are significant

applications of computer graphics.

This book also places a good deal of emphasis on creating interactive displays. Most computer

graphics textbooks cover interaction and the creation of interactive graphics. Historically this

was a difficult area to implement because it involved writing or using specialized device drivers,

but with the growing importance of OpenGL and other graphics APIs this area has become much

more common. Because we are concerned with effective communication, we believe it is

critically important to understand the role of interaction in communicating information with

graphics. Our discussion of interaction includes a general treatment of event-driven

programming and covers the events and callbacks used in OpenGL, but it also discusses the role

of interaction in creating effective communications. This views interaction in the context of the

task that is to be supported, not just the technology being studied, and thus integrates it into the

overall context of the book.

This book’s approach, discussing computer graphics principles without covering the details of

the algorithms and mathematics that implement them, differs from most computer graphics

textbooks that place a much larger emphasis on understanding these graphics algorithms and

techniques. We recognize the importance of these ideas for persons who want to develop a deep

knowledge of the subject and suggest that a second graphics course can provide that knowledge.

Chapter 0: Getting Started

This chapter is intended to give you a basic overview of the concepts of computer graphics so that

you can move forward into the rest of the book with some idea of what the field is about. It gives

some general discussion of the basis of the field, and then has two key content areas.

The first key area is the discussion of three-dimensional geometry, managed by the 3D geometry

pipeline, and the concept of appearance for computer graphics objects, managed by the rendering

pipeline. The geometry pipeline shows you the key information that you must specify to create an

image and the kind of computation a graphics system must do in order to present that image. We

will also discuss some of the ways appearance can be specified, but we will wait until a later

chapter to discuss the rendering pipeline.

The second key area is a presentation of the way a graphics program is laid out for the OpenGL

graphics API, the key API we will use in this book. In this presentation you will see both the

general structure of an OpenGL program and a complete example of a program that models a

particular problem and produces a particular animated image. In that example you will see how the

information for the geometry pipeline and the appearance information are defined for the program

and will be able to try out various changes to the program as part of the chapter exercises.

3D Geometry and the Geometry Pipeline

Computer graphics, at least as we will treat it in this book, is fundamentally three-dimensional, so

a graphics system must deal with three-dimensional geometry. Computer graphics systems do this

by creating the 3D geometry pipeline, a collection of processes that convert 3D points, the basic

building blocks of 3D geometry, from those that are most convenient for the application

programmer into those that are most convenient for the display hardware. We will explore the

details of the steps for the geometry pipeline in chapter on viewing and projection, but here we

outline the steps of the geometry pipeline to help you understand how it operates. This pipeline is

diagrammed in Figure 0.1, and we will start to sketch some stages in the pipeline in this chapter.

A great deal more detail will be given in the next few chapters.

3D Model

Coordinates

3D Eye

Coordinates

3D Eye

Coordinates

2D Eye

Coordinates

2D Screen

Coordinates

3D World

Coordinates

Modeling

Transformation

Viewing

Transformation

Clipping Projection Window-to-Viewport

Mapping

Figure 0.1: The geometry pipeline’s stages and mappings

model

coordinate

systems

In order to create an image, we must define the geometry that represents each part of the image.

The process of creating and defining this geometry is called modeling, and is described in the

chapters below on principles of modeling and on modeling in OpenGL. This is usually done by

defining each object in terms of a coordinate system that makes sense for that particular object, and

then using a set of modeling transformations that places that object in a single world coordinate

system that represents the common space in which all the objects will live. Modeling then creates

the 3D model coordinates for each object, and the modeling transformations place the objects in the

world coordinate system that contains the entire scene.

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world

coordinate

system

The 3D coordinate system that is shared by all the objects in the scene is called the world

coordinate system. By placing every component of the scene in this single shared world, we can

treat the scene uniformly as we develop the presentation of the scene through the graphics display

device to the user. The scene is a master design element that contains both the geometry of the

objects placed in it and the geometry of lights that illuminate it. Note that the world coordinate

system often is considered to represent the actual dimensions of a scene because it may be used to

model some real-world environment. This coordinate system exists without any reference to a

viewer, as is the case with any real-world scene. In order to create an image from the scene, the

viewer is added at the next stage.

eye

coordinate

system

Once the 3D world has been created, an application programmer would like the freedom to allow

an audience to view it from any location. But graphics viewing models typically require a specific

orientation and/or position for the eye at this stage. For example, the system might require that the

eye position be at the origin, looking in –Z (or sometimes +Z). So the next step in the geometry

pipeline is the viewing transformation, in which the coordinate system for the scene is changed to

satisfy this requirement. The result is the 3D eye coordinate system. We can think of this process

as grabbing the arbitrary eye location and all the 3D world objects and sliding them around to

realign the spaces so that the eye ends up at the proper place and looking in the proper direction.

The relative positions between the eye and the other objects have not been changed; all the parts of

the scene are simply anchored in a different spot in 3D space. Because standard viewing models

may also specify a standard distance from the eyepoint to some fixed “look-at” point in the scene,

there may also be some scaling involved in the viewing transformation. The viewing

transformation is just a transformation in the same sense as modeling transformations, although it

can be specified in a variety of ways depending on the graphics API. Because the viewing

transformation changes the coordinates of the entire world space in order to move the eye to the

standard position and orientation, we can consider the viewing transformation to be the inverse of

whatever transformation placed the eye point in the position and orientation defined for the view.

We will take advantage of this observation in the modeling chapter when we consider how to place

the eye in the scene’s geometry.

Clipping

At this point, we are ready to clip the object against the 3D viewing volume. The viewing volume

is the 3D volume that is determined by the projection to be used (see below) and that declares what

portion of the 3D universe the viewer wants to be able to see. This happens by defining how much

of the scene should be visible, and includes defining the left, right, bottom, top, near, and far

boundaries of that space. Any portions of the scene that are outside the defined viewing volume

are clipped and discarded. All portions that are inside are retained and passed along to the

projection step. In Figure 0.2, it is clear that some of the world and some of the helicopter lie

outside the viewable space to the left, right, top, or bottom, but note how the front of the image of

the ground in the figure is clipped—is made invisible in the scene—because it is too close to the

viewer’s eye. This is a bit difficult to see, but if you look at the cliffs at the upper left of the scene

you will see a clipped edge.

Clipping is done as the scene is projected to the 2D eye coordinates in projections, as described

next. Besides ensuring that the view includes only the things that should be visible, clipping also

increases the efficiency of image creation because it eliminates some parts of the geometry from the

rest of the display process.

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