mathematica画图指南（英文）.pdf开源计算机代数系统，可用于做符号计算，代数推导和编程，

文件名称: mathematica画图指南（英文）.pdf

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详细说明：开源计算机代数系统，可用于做符号计算，代数推导和编程，供大家学习Contents Preface IX Acknowledgments XIX 1 The Design of Mathematica's Graphics Commands 1.1 Easy to Use 1.2 General purpose 1. 3 The Evolution of Mathematica's Graphics 3679 2 Data Typ 2.1 TwO-Dimensional Graphics Objects 2.1.1 Graphics 2.1.2 Graphicsarray 2.2 Three-Dimensional Graphics Objects 2. 3 Optimized Surface Graphics objects 18 2.4 Mixed 2D and 3D Graphics Objects 2.5 Print Forms of Graphics Objects ,,23 2.6 Displaying Graphics obj 25 2.6.1 Graphics Option Settings and Show 25 2.6.2 What show rcally docs 27 2.6.3 What Show returns 2.6. 4 How Show Combines objects 2.7 Graphics Type Conversions 31 2.7.1 Conversion Quirks 32 2.7. 2 Saving Time 34 2. 8 Summary 35 vI contents 3 Graphics Primitives and Directives 37 3.1 Localization 38 3.2 Primitives and Directives for 2D Graphics 3.2.1 Color 40 3.2.2 Points 44 3.2.3 Lines and curves 46 3.2.4 Filled Regions 49 3.2.5 Text 58 3.2.6 Postscript 69 3.3 Primitives and Directives for 3D Graphics 70 3.3.1 Colors 3.3.2 Points 3.3.3 Lines 3.3.4 Cuboids 3.3.5 Polygons 3.4 Summary 78 4 Commands for Producing graphics 79 4.1 TwO-Dimensional Function Plotting 80 4.1.1 Plot 4.1.2 ParametricPlot 85 4.1.3 Sampling 86 4.1.4 No Plot 97 4.2 Three-Dimensional function plotting .102 4.2.1 Plot3d ,,,102 4.2.2 Parametricplot 3D 106 4.2.3 Options shared by plot 3d and ParametricPlot3D 4,3 Mixed 2D and 3D Plots 4.3.1 ContourPlot 114 4.3.2 Density Plot ,118 4.4 Plotting Data Sets: The listPlot Functions .121 4.4.1 Listplot 122 4.4.2 Listplot3D 124 4.4.3 ListContourPlot and listDensity plot 127 4.5 Summary ....128 5 Graphics Packages 129 5.1 Working with Packages 130 CONTEN 5.1.1 Loading a package 130 5.1.2 Package Names 132 5.1.3 Context 132 5.1.4 Forgetting to Load a Package ,135 Master Packages 137 2 A Sampling of graphics Package 140 5.2. 1 General graphics manipulations 142 5.2.2 Two-Dimensional graphics 152 5.2.3 Data Graphics 157 5. 2. 4 Three-Dimensional Graphics 165 5.2.5 Mixed 2D and 3D Graphics 171 5.2.6 Application areas 173 5.3 Summary 177 6 Coordinate systems 179 6.1 Two-Dimensional Graphics .,.180 6.1.1 The coordinate systems 180 6.1.2 An Extended example ...185 6.1.3 Display of 2D Graphics 188 6. 2 Three-Dimensional Graphics 190 6.2.1 Coordinate Systems for Specifying Objects .190 6.2.2 Coordinate Systems for Perspective projection 192 6.2.3 Coordinate Systems for Simulated Illumination 199 6.2.4 Converting Coordinates From Three to Two Dimensions 6.3 Summary 203 7 Options 205 7. 1 Options used by all graphics functions 206 7.1.1 Options for Scaling Graphics 206 7.1.2 Options for Overlays and Underlays 218 7.1.3 Options for Axes 223 7.1.4 Options for Generating postscript Code 229 7.2 Additional Axis Options for 2D Graphics 237 7.3 Other 2D Graphics options 244 7.4 Options Used by All 3D Graphics 247 7.4.1 The Bounding Box 247 7.4.2 Polygon shading 252 7.4.3 Perspective Projection ..261 viiI contents 7.5 Special 3D Graphics Options 267 7.5.1 Options for Graphics3D Objects 267 7.5.2 Options for Special 3D Graphics Types 269 7.5.3 Mesh Options for Surface and Density Graphics 272 7.5.4 Options for Contour Plots 274 7.5.5 Options for Surface Graphics 278 7.6 Options for Plotting Functions 280 7.6.1 Options Used by All Sampling Plot Functions 281 7.6.2 Options Controlling Two-Dimensional Adaptive Sampling 282 7.6.3 A Line style option for two-Dimensional plotters 284 6.4 A Special Option for ListPlot 285 7.7 Default Values for Graphics Options 285 7.8 Obsolete Graphics Options 287 7. 9 Option Manipulation 288 7.9.1 Commands for Reading Option Settings 28 9 7.9.2 Commands for Setting Options 294 7.9.3 Commands for Filtcring Options 296 7.10 Summary 298 Appendix: Code to Produce the Figures 299 A1 Graphics Primitives and Directives noo A. 2 The Loop 301 A. 3 The mathematica Ribbon 303 A. 4 The rotated text picture 304 A.5 Adaptive sampling pictures 305 A 5.1 Sampled points 305 A.5.2 Subdividing the Sampling Interval 306 A.5.3 Scaling for ax Bend 307 A6 Perspective projection pictures 309 A7 Thc Figurc for Specular Reflection ..314 Tables of Graphics Symbols 317 Suggested Readings 327 Index 331 Colophon 341 Preface Mathematica is an exceptionally flexible and powerful tool for producing mathematical graphics. Mathematica makes it easy to create graphs of functions, plots of data, pictures of geometrical solids, and other mathematical illustrations either with built-in functions or with simple programs of your own. This book tells you what you need to know to make the most of the graphics capabilities of Mathematica. Whether you are a beginner, an experienced user of Mathematica, or even someone who doesn't use mathematica at all but wants to use pictures produced by mathematica in your publications, you will find information in this book that will help you. This preface will help you figure out which parts of the book to read to find the information you need This book describes version 2.2 of mathematica, which is the current version at the time of this writing. Early versions of Mathematica(1.03, 1.04, 1.1, and 1. 2) had much more limited graphics capabilities than Version 2 and later versions. The differences are great enough that we decided it would not be practical to try to describe all versions in this book. If you are using any level of Version 1 of Mathematica, we recommend that you switch to the current version Why Cameron Wrote This book I worked for Wolfram Research, Inc. for about two years, beginning in the spring of 1988 when the first version of Mathematica was in its final stage of beta-testing, shortly before it was released to the public. My job was to get information about Mathematica out to people who needed it, and to that end i gave presentations at conferences and trade shows, wrote technical reports and other end-user documentation, and provided technical support to developers of Mathematica packages and other Mathematica related software. I was privileged to get glimpses of the exciting ideas that hundreds of creative and enthusiastic people were rushing to put into practice but i also saw at first hand how the lack of complete, detailed documentation could hamper a promising project. X pREFACE During my tenure at WRi I also did a great deal of Mathematica programming, and I really came face-to-face with the information gap in the spring of 1989 when I was asked to produce about 150 illustrations for a calculus textbook. The authors wanted to create a visually engaging text, and the publisher had agreed to use four-color printing not just for a few plates, but for the entire book. This was a new idea in calculus textbook design, and the authors had many ideas for ways to use photographs, diagrams, and other visual aids to communicate the ideas of the calculus. They needed dozens of attractive and accurate figures depicting plots of functions, curves, and surfaces, solids of revolution, and other mathematical objects. Mathematica was an obvious choice to make these illustrations, and the then-new version 1.2 with many new graphics features, promised to make the job easy and fun Well, parts of it were fun, but none of it was easy! Even though i had by then read Stephen Wolfram's book, Mathematica: A System for Doing Mathematics by Computer, from cover to cover several times I found that there were many features of mathematica graphics that i just didn't understand until I tried to use them. Stephen couldnt document every feature of every function without bloating his book to the size of the Manhattan telephone directory, but keeping the book to a manageable length forced him to leave some odd corners of mathematica graphics unexplored, and I found that I needed to explore them if i wanted to produce publication-quality graphics. If I hadn't had access to the developers of Mathematica to get questions answered (and occasionally, to get workarounds for bugs)I don't know whether I could have finished the project When the idea of writing a book about Mathematica graphics was presented to me, I thought of that textbook project, and i determined to write the kind of book that I shed I had had then. Given a function to plot or an object to draw, it's easy to get Mathematica to produce some graphical representation, but to get a particular image that makes a particular point you must simultaneously control coloring, lighting and shading, sampling, scaling, labeling, and all the other factors that go into producing an image with Mathematica. To do that you need a thorough understanding of how Mathematica graphics are produced and a complete and detailed reference guide with plenty of practical examples to follow. That's what I've tried to give you in this book Why nancy Wrote This book I developed an interest in computer graphics when I took a graduate-level course on this topic from Leo Guibas at Stanford University during the winter of 1986. In the summer of 1988 I taught that course. At the end of the summer i went to the computer graphics conference siggraPh, where I saw Stephen Wolfram demonstrate Mathematica. I was PREFACE xi favorably impressed with the software, and subsequently went to work for Wolfram Research, Inc, the developer of mathematica In 1989 I lett Wolfram Research to start my own company, Variable Symbols, Inc. to provide consulting and training in mathematical software. In 199 1 i wrote the tu- torial book Mathematica: A Practical Approach to help people learn to use Mathematica effectively. This book has been well received. Though I was already familiar with Mathematica, I learned more about this software package when writing the book When Cameron asked me in the fall of 1992 to join him as co-author of the Mathematica Graphics Guidebook, I was delighted. Writing this book has given me an opportunity to learn more about Mathematica's graphics capabilities. I hope this book enables you to take better advantage of Mathematica and spend less time fighting it How This book was written Since the original reason for writing this book was the lack of documentation for many features of Mathematica graphics you won't be surprised to learn that we didn 't write the book simply by referring to other printed sources. We started with stephen wol fram's book but whenever it was vague or unclear, or whenever we saw mathematica producing results that differed from what Stephen's book led us to expect, we pursued other sources of information in an attempt to understand fully what was happening so that we could explain it to you. We interviewed the developers at wolfram research who write and maintain the graphics code in mathematica, and we are grateful to them (especially Henry Cejtin and Tom Wickham-Jones) for their assistance in puzzling out the rationale underlying Mathematica's graphics features. In a few cases we were even vouchsafed a glimpse of Mathematica's source code We didnt stop there, either All the information we include in this book has been substantiated by extensive testing; on average, we created a dozen or more trial graphics for cach onc that appears in the book. We exercised somc hitherto unexplored aspects of Mathematica's graphics, including some undocumented features; in fact, we uncovered a few bugs in the program(or discrepancies in the documentation, depending on how you look at it) in the course of doing experimental research for this book For this reason, the information here records the performance of mathematica what actually happened, whether or not we thought that was what was supposed to happen. If this book disagrees with other references on some point, it is safe to assume that the other book is describing what Mathematica was intended to do and this book describes what mathematica actually does This means, of course, that some of the odd phenomena documented here will (we hope) disappear in future versions of Mathematica, as enhancements and bug fixes bring the perfor mance of the program closer into line with the design specifications. As Mathematica Xi1 preface evolves, this book may fall out of step with future versions, but for now, it is as accurate and complete a description of Mathematica's graphics as you will find any- where Who should read This book Anyone who uses Mathematica can benefit from the information in this book. For example, scientists and engineers who work with large data sets find that a single well-designed plot is far more informative than a huge table of numbers. Teachers at tempting to convey complicated ideas can capture students' attention by using still and animated displays to enliven lectures handouts and textbooks. Researchers can turn abstruse concepts into pictures that make mathematics almost tangible, stimulating the imagination in ways that symbol manipulations never could. One of Mathemat- ica's greatest strengths is its smooth integration of symbolic, numerical, and graphical capabilities. Even if your work is primarily involved with numbers or formulas you will quickly come to appreciate the ability to translate your ideas into vivid and accurate mages Of course, some people's primary reason for using Mathematica is its graphical abilities. To be useful, a book or journal that treats topics in the sciences must have illustrations that not only are appealing to the eye but also are faithful to the concepts they illustrate. Professional technical illustrators and production specialists find mathe- matica valuable for producing diagrams of geometric figures, graphs of functions, plots of data sets, and other mathematical illustrations that are both beautiful and accurate And it is not only publishing professionals who need these capabilities. As desktop publishing systems become more versatile and more faithful to the standards of fine publishing, more and more authors (including the authors of this book) are electing to compose and typeset thcir own work. Mathematica is an excellent tool for preparing technical illustrations for publication, but anyone who uses it for that purpose will need the information in this book Perhaps youve never used mathematica before-maybe it was the prospect of drawing beautiful mathematical graphics that attracted your interest, and this book is your first exposure to mathematica. Graphics programming is a good introduction to mathematica, or to programming in general, because there's a special satisfaction in getting a program correct and being rewarded with a beautiful picture. You can skim this book to get an idea of what you can accomplish with Mathematica, but before you begin programming you should read the introductory chapters and try out some of the examples in Stephen Wolfram's book, Mathematica: A System for doing Mathematics by Computer, which we refer to as"Thc Mathematica Book. You should keep The mathematica Book at hand as you read this one so you can look up any

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