3D计算机图形学实用算法第二版概览

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"Practical Algorithms for 3D Computer Graphics, Second Edition" 是一本专注于三维计算机图形学算法实践的书籍，由R. Stuart Ferguson撰写，他在英国女王大学贝尔法斯特分校工作。该书由CRC Press（Taylor & Francis Group的一个印记）出版。这本书详细探讨了3D计算机图形学中的实用算法，这些算法是游戏开发、电影特效、虚拟现实以及许多其他领域的基础。作者旨在通过实际案例和应用，使读者理解并掌握这些复杂的数学和编程概念。虽然提供的内容主要是书籍的版权信息，但可以推测书中可能包含以下核心知识点： 1. **坐标系统与变换**：包括三维空间中的点、向量表示，坐标转换（平移、旋转、缩放）以及矩阵运算在3D图形中的应用。 2. **图形管线**：介绍OpenGL或DirectX等图形库的工作原理，涵盖顶点处理、几何渲染、光栅化和像素操作等步骤。 3. **图形建模**：讨论如何创建和编辑3D模型，如多边形建模、细分表面、NURBS曲线和曲面。 4. **光照与着色**：深入讲解光照模型（如Phong模型）、阴影投射、纹理映射以及高级着色技术，如法线贴图和置换贴图。 5. **摄像机与视图控制**：涵盖透视投影、正交投影，以及摄像机运动和视口变换。 6. **动画与物理模拟**：包括关键帧动画、骨骼绑定、物理引擎基础，以及刚体和软体动力学。 7. **图形渲染算法**：如Z缓冲、蒙特卡洛方法、光线追踪以及实时渲染技巧。 8. **交互式图形用户界面**：设计和实现用户友好的图形界面，用于控制和展示3D场景。 9. **图形编程**：可能涉及C++、OpenGL和GLSL（OpenGL着色语言）等相关编程知识。 10. **实例项目**：书中可能包含实际项目，让读者能够将所学应用于实践中，如创建简单的3D游戏或模拟。本书适合计算机图形学的学生、软件工程师和对3D图形感兴趣的爱好者阅读，通过理论与实践相结合的方式提升在3D图形领域的技能。

Introduction

Computer grap h ics embraces a broad spectrum of topics including such things

as image processing, photo editing, a myriad of ty pes of computer games and of

course special eﬀects for the movies and TV. Even a word processor or presen-

tation package could be said to fall into the category of a graphics program.

Three-dimensional computer graph ics (3DCG), the topic covered in this book,

began as a separate discipline in the early 1980s where those few fortunate in-

dividuals who had access to computing hardware costing tens or hundreds of

thousands of dollars began to experiment with the wondrous science of pro-

ducing, through mathematics alone, pictures that in many cases could not be

distinguished from a photograph. The “Voyager” animations of Jim Blinn for

NASA were perhaps the ﬁrst really well publicized use of computer graphics.

The title from a television program of the period sums up perfectly the subject

of computer graphics: It was Painting by Number s.

We can think of four main applications for 3D CG : computer-aided design,

scientiﬁc visualization, the ever growing entertainment businesses (cinema and

TV animation) and computer games.

There is some overlap between th es e categories. At the level of the mathe-

matical theory on which graphics algorithms are based th ey are ex actly the same.

At the program level h owever it is usually possible to identify an application as

belonging to one of these four categories.

1. In a computer-aided design (CAD) application the most important featu r e

is to be able to use the graphics to present accurate and detailed plans that

have the potential to be used for fu r th er engineering or architectural work.

2. Scientiﬁc visualization is the process of using graphics to illustrate ex-

perimental or theoretical data with the aim of bringing into focus trends,

anomalies, or special features that might otherwise go unnoticed if they are

presented in simple tabular form or by lists of numbers. In this category

one might include medical imaging, interpreting physical phenomena and

presentations of weather or economic forecasts.

3. Compu ter animation for the entertainment ind u s tr y is itself a broad subject

where the primary driver is to produce realistic pictures or sequences of

4 1. Introduction

pictures that would be very diﬃcult, impos s ib le or too expensive to obtain

by conventional means. The movie, TV and advertising industries have

adopted this use of 3D computer animation with great enthusiasm and

therefore perhaps it is they who provided the main driving force behind

the rapid improvements in realism that can be achieved with 3DCG.

4. In the case of computer game development fast and furious is the watch-

word, with as many twists and turns as can be accomplished in real-time.

The quality of images produced from game renderin g engines improves at

what seems like a constantly accelerating pace and the ingenuity of the

game programmers ensures that th is is a very active area of computer

graphics research and development.

Essentially, this book is targeted at those who work on applications un-

der the broad heading of computer animation, rendering and 3D modeling. If

you are interested in scientiﬁc visualization the book by Schroeder, Martin and

Lorensen [77] is an extensive an d valuable resource. Many of their algorithms

complement those described here (in chapter 10) and they provide readily adapt-

able code. In the en gin eer in g arena, 3D modeling software is used to design

everything from plastic bottles to aircraft. Nowadays the CAD design tools

also oﬀer some ex cellent product visualizations as well as the rigorous technical

drawings and plans. With the drawing parts of packages such as Solid Edge [73]

achieving maturity the latest developments in these packages has tended to take

them into the realm of analysis, for such things as stresses an d strains, using

mathematical techniques such as ﬁ n ite elements. Fr om the graphics point of

view visualizing the r es u lts of analysis closes the cir cle into scientiﬁc visualiza-

tion again . As a result CAD type software lies somewhat outside the scope of

this book. Our discussions on the topic will be limited to modeling with prim-

itive planar shapes. The essentials of computer-aided geometric design are well

covered in Farin’s book [29] an d information on solid modelin g for CAD/CAM

(computer-aided manufacture) can be fou n d in the book by Mortenson [62].

For computer game developers the key element is the ability to render large

numbers of polygons in real time. This is probably the most rapidly ad van cin g

area of application development and virtually every computer game now relies

on the dedicated graphics hardware. A clear dis tin ction is starting to emerge

with, on one hand , ever more powerful console systems , whilst on the other hand,

3D games are starting to become popular as cell phone apps. Nearly everything

that we discuss in this book has utility on the technical side of the computer

games business.

1.1 A note on mathematics for 3D computer graphics

Geometry is the foundation on which computer graphics and speciﬁcally 3DCG

is built. A familiarity with the basic concepts of geometry and what I can only

1.2. Getting up to speed and following up 5

express as a “feel” for three dimensions will make the understanding of existing,

and creation of new, 3D algorithms much more straightforward.

In this book only two assumptions are made ab ou t the reader’s mathematical

prowess. First, that you have an appreciation of the Cartesian frame of reference

which is used to map three-dimensional space and second, you know the rules

for manipulating vectors and matrices. For any reader who wishes to brush up

on their vector geometry a general intr oduction is given by Kindle [49].

A recent and excellent compendium of all aspects of the mathematics used in

computer graphics is given by Lengyel [54], and the timeless classic Numerical

Recipes by Press et al. [74] is a hugely valuable resource of source code for algo-

rithms that solve more mathematical problems than we need to think about for

computer graphics. And it has ex cellent accompanying computer codes as well.

1.2 Getting up to speed and following up

This book is not a general introduction to the subject of computer graphics (CG)

or even to 3DCG. If you want to acquire background knowledge of hardware,

software packages or the current state of what is now a huge industry there are

many other excellent sources of information available.

The quantity of reference material that is available and our access to it has

changed utterly since the ﬁrst edition of th e book was published. I thin k it is

fair to say that there is nothing you cannot ﬁnd out about 3D computer graphics

in the semi-inﬁnite universe of the the World W ide Web. A search engine may

be a magniﬁcent and powerful tool, but on ly if you have a clue about what you

are looking for. So there remains a real need for the carefully crafted book, and

the classic references have as much value today as they did a decade ago.

Of course, it would be quite ridiculou s to dismis s the Wor ld Wide Web ’s

semi-inﬁnite library and resources, but its real value comes about because it lets

you get what you need, when you need it. But we must be selective and have

a p ointer to follow. This is not as easy as it sound, becaus e pages move, pages

get changed, and pages get deleted or become outd ated . Our aim is to preserve

as much longevity in this book as we can, so all our web references will appear

through our online content. There are only two web addresses you need to open

the door: the book’s website (the address is quoted in the Preface) and that of

our open-source 3D application OpenFX (also referenced in the Preface).

As we’ve just discussed, there will always be a need to refer to some of the

classic texts of compu ter graphics. They not only oﬀer an insight into how

the topic evolved but they also provide some of the best explanations for the

major breakthrough s in 3D graphics. The following sections cover books that I

personally have found very usefu l in my work.

6 1. Introduction

1.2.1 Classic references

Many of the references cited in the ﬁrst edition are timeless classics , and although

some may be out of print, all can be obtained in a good library or with the click

of a mouse from a secondhand bookstore. Some of the most useful ones , then

and now are: Real-Time Rendering by Akenine-M¯oller and Haines [1], which

describes the most important algorithms in the rend er in g pipeline and provides

links to a wealth of research material. It has proved very popular and several

revisions continue to be printed regularly. Watt [89] provides a good introduction

to the main concepts of 3D computer graphics, and a comprehensive (but a bit

dated) reference on all aspects of CG is that of Foley, Van Dam, Feiner an d

Hughes [31]. The book by Watt and Watt [87] is useful for ﬁlling in s peciﬁc

details on rendering and animation. For the mathematically inclined a rigorous

evaluation on a very broad range of CG algorithms can be found in Eberly’s

book [21].

1.2.2 Specialist references

If you can n ot ﬁnd the algorithm you are looking for in the ch ap ter s forming

part III then try looking into the ﬁve volumes of the Graphics Gems series [6,

34, 41, 50, 66].

The GPU Gems series [30, 64, 71] and the GPU Pro [27] series reinvigorate

many of the classic Graphics Gems and packages th em for GPU programming.

Unfortunately, the GPU Gems series tend to be a bit hard to follow in places

and it takes a bit more eﬀor t to get good value from the ideas presented there.

As already alluded, computer graphics p u b lication s have, in recent years,

been carrying titles referring to the programmable graphics hardware (the Graph-

ics Processing Unit, GPU) or to programming for computer games, but unless

they are practical works focusing on Open G L or DirectX programming, they are

pretty much presenting the same material as in the classics. However there can

be subtle diﬀerences of emp h as is and terminology and reading the way diﬀerent

authors present the same idea can often lead to a eureka moment. Game En-

gine Architecture by Gregory [36] was one of the ﬁrst books to pu t the focus on

rendering algorithms speciﬁcally tailored for comp u ter games programs.

Writing programs for the GPU (called shaders) has virtually become a science

in itself and many of the ideas put forward in Programming Vertex and Pixel

Shaders [28], Shaders for Game Programmers and Artists [53], ShaderX

[24],

ShaderX

[25] and Shader X

[26] provide fascinating reading. Some gems of

particular use for game developers can be found in Deloura’s volume, Game

Programming Gems [20].

For background and to complement the procedural textures described in

chapter 11, the b ook by Ebert et al. [23] is ideal. It goes on to explor e the

use of fractals in computer graphics and demon s tr ates the techniques of volume

shading and hypertextures with which realistic images of hair and fur can be

created.

1.3. Assumed knowledge 7

1.2.3 Practical references

Probably the best and most practically useful book in relation to geometric

modeling algorithms is O’Rourke’s Computational Geometry [65], which pr ovides

a useful alternative view of some of the modeling algorithms that we discuss in

chapter 10 and its C code is a masterful implementation of the algorithms.

We already mentioned The Visualization Toolkit by Martin and Lorensen [77],

an extremely useful library of software and not just a book. And of course the

(code with) Numerical Recipes in C++ [74] is a delight to have on hand when

you need code for a mathematical algorithm.

The OpenGL books, the Red Book [82] and the OpenGL SuperBible [78],

form a powerful duo of reference and how-to material. There is nothing these

books will not show you how to do in real-time 3D graphics with OpenGL.

There are many practically useful references one can call on in the arena of

programming the mobile and tablet devices. These speciﬁc texts will be identiﬁed

in chapter 8.

And of course, we could not end this section without mentioning the World

Wide Web, but there are just far too many useful references to acknowledge here.

And anyway, who wants a 256 character web reference in a book? Consult our

website for a collection of our favorite links.

1.3 Assumed knowledge

As stated earlier the assumption is that the reader is familiar with the concepts

of the vector and has a basic knowledge of coordinate geometry. Some experience

of using 3D grap h ics application software would also be an advantage, at least

enough to know the signiﬁcance of the terms vertex, face/facet, polygon and pixel.

For the programming sections, a knowledge of a C like programming lan-

guage is essential, but since most languages have C (or C++) like s y ntax some

programming experience in any language should let you get to grips with all the

practical material. The biggest real challenge in developing computer programs

comes in devising algorithms for tasks so that they can be carried out by the

rather stupid computer, which after all can only do three things : move, add, and

decide which of two things to do next, depending on what the outcome of the add

was, think about it!

The chapter on graphics programming for mobile devices has to develop its

examples us in g the the C++ like languages of: Objective-C, in the case of Apple’s

iOS devices, and JAVA for the myriad of Android phones and tablets.

And the second biggest challenge is not in coding up the algorithm in C, Java, Fortran ,

Python, Basic and so on. It is in knowing what Application Programmer Interface (API)

function to use to get the computer’s operating system or library to give you control of its user

interface and peripherals: screen, disk, mouse, keyboard, WiFi and so forth.

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