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MathGroup Archive 1995

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Just Published: The Mathematica Graphics Guidebook

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg469] Just Published: The Mathematica Graphics Guidebook
  • From: nb at Eeyore.Stanford.EDU
  • Date: Tue, 14 Feb 95 10:11:32 -0800

I am pleased to announce the publication of

                    The Mathematica Graphics Guidebook 
                                    by                 
                     Cameron Smith and Nancy Blachman
                        Published by Addison-Wesley
                            ISBN 0-201-53280-8


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 geometric 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.  

Cameron Smith, a long-time expert on Mathematica graphics, conceived this 
guide to satisfy user demand for more detailed graphics information than 
is elsewhere available.  This book was written with the assistance of 
Nancy Blachman, a well-known author and lecturer on Mathematica.  Readers 
will find this book offers both a thorough tutorial introduction to 
Mathematica graphics and a comprehensive reference manual for the graphics 
functions.  This book is filled with  examples illustrating the software's 
graphics capabilities.  A DOS disk in the back of the book contains 
Mathematica Notebooks with the input needed to reproduce the examples 
in this book.

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 Mr. Smith and Ms. Blachman didn't write 
the book simply by referring to other printed sources.  They started 
with Stephen Wolfram's book "Mathematica: A System of Doing Mathematics 
by Computer" (Addison-Wesley), but whenever it was vague or unclear, or whenever they saw Mathematica producing results that differed from what 
Stephen Wolfram's book led them to expect, they pursued other sources 
of information in an attempt to understand fully what was happening so 
that they could explain it to you.  They interviewed the developers at 
Wolfram Research who write and maintain the graphics code in Mathematica.  
In a few cases they were even vouchsafed a glimpse of Mathematica's 
source code! 

They didn't stop there, either.  All the information they include in this 
book has been substantiated by extensive testing; they created at least
a dozen  trial graphics for each one that appears in the book.  They 
exercised some hitherto unexplored aspects of Mathematica's graphics.

For this reason, the information here records Mathematica's actual 
performance.  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.  
As Mathematica 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 anywhere.

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 attempting 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 
Mathematica'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 images.

The Mathematica Graphics Guidebook

* Provides a hands-on tutorial for using Mathematica graphics
* Contains detailed reference information for all of Mathematica's
  built-in graphics functions
* Describes key Mathematica algorithms to show how the software can 
  be used more effectively to produce desired results
* Includes a 3.5" DOS disk that allows readers to reproduce examples
  from the book.  This disk is readable on Macintosh, DOS, and Windows-
  based computers as well as on workstations.

About the Authors:

Cameron Smith is a recognized authority on Mathematica graphics.
He was formerly affiliated with Wolfram Research, Inc., and he now 
consults independently on computer graphics and computer typesetting.  
He is a particularly popular resource for authors and publishers
converting Mathematica files to LaTeX and other formats.

Nancy Blachman, the founder of Variable Symbols, Inc., provides
both individual and group training in the use of Mathematica and
teaches Mathematica classes at Stanford University.  She is a prolific 
author of books, help software, and articles on Mathematica.

The list price for the Mathematica Graphics Guidebook is $39.75.  This
guidebook can be ordered from your local bookstore, from Addison-Wesley
(telephone 800-447-2226, fax 617 944 8964), or from Variable Symbols 
(telephone 510 652 8462, fax 510 652 8461).

--------------------------------------------------------------------------
Below is the table of contents of the book.

1. The Design of Mathematica's Graphics Commands                         1
    1.1 Easy to Use                                                      3
    1.2 General Purpose                                                  6
    1.3 The Evolution of Mathematica's Graphics                          7
2. Data Types                                                            9
    2.1 Two-Dimensional Graphics Objects                                10
        2.1.1 Graphics                                                  10
        2.1.2 GraphicsArray                                             12
    2.2 Three-Dimensional Graphics Objects                              16
    2.3 Optimized Surface Graphics Objects                              18
        Combining SurfaceGraphics Objects                               19
        Erroneous Values                                                20
        Surface Shading                                                 22
    2.4 Mixed 2D and 3D Graphics Objects                                22
    2.5 Print Forms of Graphics Objects                                 23
    2.6 Displaying Graphics Objects                                     25
        2.6.1 Graphics Option Settings and Show                         25
        2.6.2 What Show Really Does                                     27
        2.6.3 What Show Returns                                         28
        2.6.4 How Show Combines Objects                                 28
    2.7 Graphics Type Conversions                                       31
        2.7.1 Conversion Quirks                                         32
        2.7.2 Saving Time                                               34
    2.8 Summary                                                         35 
3. Graphics Primitives and Directives                                   37
    3.1 Localization                                                    38
    3.2 Primitives and Directives for 2D Graphics                       39
        3.2.1 Colors                                                    40
            GrayLevel                                                   40
            RGBColor                                                    40
            CMYKColor                                                   41
            Hue                                                         42
            Other Color Specifications                                  43
            Why So Many Systems?                                        43
        3.2.2 Points                                                    44
            Point                                                       44
            PointSize                                                   44
            AbsolutePointSize                                           45
        3.2.3 Lines and Curves                                          46
            Line                                                        46
            Circle                                                      46
            Thickness and AbsoluteThickness                             48
            Dashing and AbsoluteDashing                                 49
        3.2.4 Filled Regions                                            49
            Polygon                                                     49
            Rectangle                                                   52
            Raster                                                      54
            RasterArray                                                 57
            Disk                                                        57
        3.2.5 Text                                                      58
            A Quirk in Text Offsets                                     59
            Text in Different Directions                                60
            Text in Different Fonts                                     64
            Multiple Lines of Text                                      66
            Truncated Text                                              68
        3.2.6 PostScript                                                69
    3.3 Primitives and Directives for 3D Graphics                       70
        3.3.1 Colors                                                    71
        3.3.2 Points                                                    71
        3.3.3 Lines                                                     71
        3.3.4 Cuboids                                                   72
        3.3.5 Polygons                                                  72
            Polygon                                                     72
            EdgeForm                                                    74
            Lighting and SurfaceColor                                   74
            FaceForm                                                    77
    3.4 Summary                                                         78 
4. Commands for Producing Graphics                                      79
    4.1 Two-Dimensional Function Plotting                               80
        4.1.1 Plot                                                      81
            Plotting More Than One Function                             82
            Taking Control of Plot                                      82
        4.1.2 ParametricPlot                                            85
        4.1.3 Sampling                                                  86
            Using Caution with the Sampling Algorithm                   87
            Graphing the Same Function on Different Machines            88
            Adaptive Sampling                                           89
            Aliasing: One Function Impersonating Another                93
            Why Is the Right Half Sometimes Better Than the Left Half?  95
        4.1.4 No Plot                                                   97
            The Order of Evaluation                                     97
            Single versus Multiple Expressions                         100
    4.2 Three-Dimensional Function Plotting                            102
        4.2.1 Plot3D                                                   102
            Options Accepted by Plot3D                                 104
        4.2.2 ParametricPlot3D                                         106
        4.2.3 Options Shared by Plot3D and ParametricPlot3D            109
            Viewpoint                                                  109
            Bounding Box and Axes                                      112
            Lighting                                                   113
    4.3 Mixed 2D and 3D Plots                                          114
        4.3.1 ContourPlot                                              114
        4.3.2 DensityPlot                                              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 ListDensityPlot                      127
    4.5 Summary                                                        128 
5. Graphics Packages                                                   129
    5.1 Working with Packages                                          130
        5.1.1 Loading a Package                                        130
        5.1.2 Package Names                                            132
        5.1.3 Context                                                  132
            The Current Context and the Default Context                134
            Where to Look for Symbols                                  134
        5.1.4 Forgetting to Load a Package                             135
        5.1.5 Master Packages                                          137
            Making Your Own Master Packages                            140
    5.2 A Sampling of Graphics Packages                                140
        5.2.1 General Graphics Manipulations                           142
            Colors                                                     142
            Combined Graphics                                          145
            Labeled Plots                                              146
            Animations                                                 148
        5.2.2 Two-Dimensional Graphics                                 152
            Logarithmic Scales                                         152
            Arrows                                                     153
            Splines                                                    155
            Filled Plots                                               155
            Complex Mappings                                           156
        5.2.3 Data Graphics                                            157
            Bar Charts and Pie Charts                                  157
            Labeled Data                                               162
            Error Bars                                                 164
            Multiple Data Sets                                         164
        5.2.4 Three-Dimensional Graphics                               165
            Scatter Plots                                              165
            Parametrized Curves and Surfaces                           166
            Surfaces of Revolution                                     167
            Contour Surfaces                                           168
            Mathematical Solids                                        169
        5.2.5 Mixed 2D and 3D Graphics                                 171
            Curves Defined Implicitly (Plots of Equations)             171
            Vector Fields                                              172
        5.2.6 Application Areas                                        173
            Graph Theory and Combinatorics                             173
            Computational Geometry                                     173
            Maps of the World                                          173
            Mathematica and AutoCAD                                    176
    5.3 Summary                                                        177
6. Coordinate Systems                                                  179
    6.1 Two-Dimensional Graphics                                       180
        6.1.1 The Coordinate Systems                                   180
            Object Coordinates                                         180
            Scaled Coordinates                                         181
            Text Coordinates                                           183
            PlotRegion                                                 185
        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
            Object Coordinates                                         190
            Scaled Coordinates                                         190
            Text Coordinates                                           191
        6.2.2 Coordinate Systems for Perspective Projection            192
            The Theory of Perspective Projection                       192
            Perspective Projection Coordinates                         195
        6.2.3 Coordinate Systems for Simulated Illumination            199
        6.2.4 Converting Coordinates From Three to Two Dimensions      201
    6.3 Summary                                                        203 
7. Options                                                             205
    7.1 Options Used by All Graphics Functions                         206
        7.1.1 Options for Scaling Graphics                             206
            AspectRatio                                                206
            PlotRegion                                                 210
            PlotRange                                                  212
        7.1.2 Options for Overlays and Underlays                       218
            Background                                                 219
            Prolog                                                     219
            Epilog                                                     221
            PlotLabel                                                  222
        7.1.3 Options for Axes                                         223
            Axes                                                       223
            AxesLabel                                                  224
            AxesStyle                                                  225
            Ticks                                                      226
        7.1.4 Options for Generating PostScript Code                   229
            ColorOutput                                                229
            DefaultColor                                               232
            DefaultFont                                                233
            DisplayFunction                                            233
            StringConversion                                           235
    7.2 Additional Axis Options for 2D Graphics                        237
            AxesOrigin                                                 237
            Frame, FrameStyle, FrameTicks, FrameLabel and RotateLabel  241
    7.3 Other 2D Graphics Options                                      244
            GridLines                                                  244
            GraphicsSpacing                                            246
    7.4 Options Used by All 3D Graphics                                247
        7.4.1 The Bounding Box                                         247
            AxesEdge                                                   247
            Boxed                                                      248
            BoxRatios                                                  249
            BoxStyle                                                   250
            FaceGrids                                                  251
        7.4.2 Polygon Shading                                          252
            Shading and Lighting                                       252
            AmbientLight and LightSources                              254
        7.4.3 Perspective Projection                                   261
            ViewPoint                                                  261
            ViewVertical                                               263
            ViewCenter                                                 263
            SphericalRegion                                            264
    7.5 Special 3D Graphics Options                                    267
        7.5.1 Options for Graphics3D Objects                           267
            PolygonIntersections                                       267
            RenderAll                                                  269
        7.5.2 Options for Special 3D Graphics Types                    269
            ColorFunction                                              269
            MeshRange                                                  271
        7.5.3 Mesh Options for Surface and Density Graphics            272
        7.5.4 Options for Contour Plots                                274
            ContourLines                                               274
            Contours                                                   275
            ContourShading                                             276
            ContourSmoothing                                           276
            ContourStyle                                               277
        7.5.5 Options for SurfaceGraphics                              278
            HiddenSurface                                              278
            ClipFill                                                   279
    7.6 Options for Plotting Functions                                 280
        7.6.1 Options Used by All Sampling Plot Functions              281
            Compiled                                                   281
            PlotPoints                                                 282
        7.6.2 Options Controlling Two-Dimensional Adaptive Sampling    282
            MaxBend                                                    282
            PlotDivision                                               283
        7.6.3 A Line Style Option for Two-Dimensional Plotters         284
        7.6.4 A Special Option for ListPlot                            285
    7.7 Default Values for Graphics Options                            285
            DefaultFont                                                285
            Display and DisplayFunction                                286
            SoundDisplay and SoundDisplayFunction                      286
            StringConversion                                           286
    7.8 Obsolete Graphics Options                                      287
    7.9 Option Manipulation                                            288
        7.9.1 Commands for Reading Option Settings                     289
            Options                                                    289
            FullOptions and FullGraphics                               291
            PlotRange as a Function                                    293
        7.9.2 Commands for Setting Options                             294
            SetOptions                                                 294
            Show                                                       295
            Options                                                    295
            ClearAll and Remove                                        296
        7.9.3 Commands for Filtering Options                           296
    7.10 Summary                                                       298
Appendix: Code to Produce the Figures                                  299
    Tables of Graphics Symbols                                         317
    Suggested Readings                                                 327
Index                                                                  331
Colophon                                                               341



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