SuperGraph is a powerful, easy-to-use, inexpensive program to graph explicit and implicit mathematical functions. Implicit expressions, ones that cannot easily be solved for either x or y, have presented a challenge to visualize. SuperGraph makes that a thing of the past.
SuperGraph differs from Apple’s Graphing Calculator in its flexibility and customizability when dealing with implicit expressions (which Graphing Calculator does not directly support) and in its ability to run on 680x0 (non-PowerPC) Macintosh computers.
SuperGraph is especially suited to demonstrating various implicit expressions and techniques of sketching them in a classroom situation.
Complete instructions on using SuperGraph are provided below, in the section “Using SuperGraph.” Information about registration and payment is in the section “SuperGraph is shareware.”
System requirements
SuperGraph requires a Macintosh with System 7.0 or higher and a 68020 or higher processor. SuperGraph is accelerated for Power Macintosh and ships as a “fat binary” application. 32-Bit QuickDraw is also required, as is a color or grayscale monitor. At least 4 grays or colors should be used; 256 grays or millions of colors produce the best-looking contour maps. (Images that are copied or saved will be of the same quality no matter what the screen can display.) A PowerPC or a 68040 with a math coprocessor is recommended for faster graphing.
On 68K Macs, SuperGraph will use a math coprocessor (FPU) if one is available. Otherwise, it will use the main processor. Mathematical operations are significantly faster with math coprocessors.
Using SuperGraph
For basic assistance with general concepts of SuperGraph, choose “SuperGraph Help” from the Help menu. In addition, Balloon Help is available for all menus and dialog boxes.
The window that appears after the splash screen disappears is a graphing window. To create an additional graphing window, select “New” from the File menu. At any time, you can select “Copy Image” from the Edit menu to copy the current image to the Clipboard or select “Save” or “Save As…” from the File menu to save the current graph to disk.
To scroll around a graphing window, either hold down the Option key and then drag the window contents around, or click the arrows (the third button from the left) in the lower left-hand side of the graphing window. Clicking the arrows is functionally equivalent to holding down the Option key.
Each graphing window has a number of settings associated with it, such as whether axes are drawn and the maximum and minimum x and y coordinates contained within the window. To edit these settings, select “Graph Settings…” from the Graphing menu. To change the default settings for new windows, select “Default Graph Settings…” from the Options menu. Changes to the default graph settings will not be saved after you quit the program unless you select “Save Default Settings” from the Options menu.
The Preferences dialog, on the other hand, contains two settings that will be saved automatically. Choosing “Follow Mouse Position” tells SuperGraph to constantly report (in the bottom of each window) the numerical coordinate underneath the pointer’s position on the graph. Selecting “I Paid” signifies that you have registered SuperGraph and paid the shareware fee. It turns off the annoying messages and allows the program to launch faster. Please be honest; don’t turn on this checkbox unless you really have paid. See the section “SuperGraph is shareware” below for information about registering.
To graph an expression, first select “Edit Expression…” from the Graphing menu. In the dialog box that appears, type or paste a mathematical expression. (For information about the format of expressions, select “Entering Expressions” from the Help menu on the right side of the menu bar or press the Help button in the dialog box.) Then either press the Graph Now button to graph it immediately, or press OK and then choose “Graph Expression” from the Graphing menu.
Each window created by SuperGraph is always in either implicit mode, contour-map mode or function mode. Implicit mode should be used with complicated equations, such as y^2(y-1)-x^2(y^2-1)+2xy^2-x^4=0 or 2x^2(y^2+x^2-y-x-13) = 9(y^2-2y-2x-8), that cannot easily be solved for y. However, when you are graphing a function of x, such as y = 3x + 3, function mode gives faster, more precise graphs. Contour mapping is useful for a view of the dynamics of a function or relation, but it is slower than the other graphing methods and produces less precise (but more visually pleasing) results. To switch among graphing modes, use the Graph Settings dialog box, available under the Graphing menu.
The “Zoom In” and “Zoom Out” commands in the Graphing menu and the two zooming buttons at the lower left-hand side of each graphing window zoom in and out by a factor of two. For more precise scaling, or to change the contour-map tolerance or the distance between tick marks on the axes, use the Graph Settings dialog box.
The following mathematical operators, functions, and constants are recognized:
Arithmetic and logarithmic: + - * / ^ π e log() ln() exp()
(Note: Type the π character by pressing Option-P.)
If your computer is connected to the Internet and you have installed Internet Config, you can use the items on the Help menu to access information about SuperGraph. If these items do not work properly, you should set up Internet Config according to the instructions provided with it. Specifically, the “http:” and “mailto:” helper applications should be set to your web browser and email program, respectively.
If the appropriate software is installed on your system, SuperGraph supports Macintosh Drag and Drop. When the arrows in the lower left-hand corner of a graphing window are off, you can drag the current graph to the desktop or to another application. Only the picture representation of the graph, and not the settings or equation used to create the graph, is sent to the other programs. Using drag and drop requires System 7.5, or an earlier version of System 7 with the Macintosh Drag and Drop extension installed.
SuperGraph is shareware
SuperGraph is distributed as shareware under the honor system. If you continue to use it after trying it, you must purchase a license by registering with the author. The fee is $15 per computer. Source code (in Pascal for CodeWarrior) is free with registration if you provide an email address where I can send the latest version and source code; a disk with the latest version and other goodies is $5 additional with registration. (If you don’t provide an email address and do not order a disk, I will be unable to send you the latest version or the source code.) Please use the enclosed Register program or the registration form if you have it. Contact me for information on institutional use or site licensing.
Once you have registered, you are entitled to click the “I Paid” checkbox in the Preferences dialog box. This will make the program launch faster and eliminate the registration reminders. Of course, you could check that box without registering. But that would be dishonest.
Registering supports me and the shareware system. It will help pay my tuition and encourage me to write more useful Mac software. And it’ll make you feel good about yourself. It might even help cure diseases, although this product has not been evaluated by the Food & Drug Administration.
To register, run the enclosed Register program. Registration is handled through Kagi Shareware, which accepts credit cards, First Virtual, money orders, and U.S. checks. You may register by fax, postal mail or email. Online registration via credit card is available at <http://kagi.direct.net/cgi-bin/register1.cgi?BE> (or choose “Register Online” from the Help menu to access this page using the web browser you have set in Internet Config). (For secure, encrypted registration, if your browser supports it, follow the link at the top of that page.)
You may also register by sending a check or money order in the appropriate amount (U.S. currency drawn on U.S. banks only, or a postal money order in U.S. currency) to Mike Epstein at 90 Maple Drive, Great Neck, NY 11021.
Please include your email address and the version you are currently using to allow me to notify you of new versions. Specify whether you want me to email you a copy of the latest version. A disk with the latest version is $5 additional. The latest version can always be downloaded from the SuperGraph information page, which is located at <http://www.bozosoft.com/supergraph/>.
Troubleshooting
If you experience out-of-memory messages, or if you open many windows or graph very large images, you should raise SuperGraph’s memory allocation by selecting its icon in the Finder and choosing Get Info from the File menu. Raise the “Preferred size” until the problem stops. (This will only work when SuperGraph is not running.)
If you experience any problems, please report them to the author so that they can be corrected for a future version.
Support
Technical support is available via electronic mail at mike@kagi.com or epstein@bozosoft.com. Comments are always welcome. Registered users who either include an email address with their registration or pay for a disk with the latest version will receive my phone number for support.
Thanks
Special thanks to Mr. Albert F. Cavallaro, my Computer Science teacher, for his support and encouragement during this project. I am indebted to Matt Gieselman for development help. Thanks to my beta testers (Dennis T. Cheung, “JD,” Matt Gieselman, Tim Kelly, Dick Palais, Stephen Ryan, and several others who preferred that their names not be used here) for their invaluable efforts. Thanks also to Tonya Engst for her exposition of the attributes of a good Read Me file in TidBITS, a weekly Macintosh e-zine. Information about TidBITS is available on the World Wide Web at <http://www.tidbits.com>.
The code used to implement the standard implicit-graphing algorithm is in the public domain and was written by Angel Montesinos Amilibia of the Department of Geometry and Topology of the University of Valencia, Spain. The code is available for FTP from <ftp://topologia.geomet.uv.es/pub/montesin/>.
Legal
While I believe SuperGraph to be quite robust, I cannot be held responsible for any damage or data loss caused by its use. It has been tested under several Macintosh platforms with good results. Still, as with all software, all use is at your own risk.
SuperGraph is provided for your evaluation. If, after a reasonable amount of period (not to exceed 30 days), you continue to use SuperGraph, you are required to purchase a license from the author (or his agent, Kagi Shareware). See above for information on how to register. Single user licenses ($15 US) are valid for one person’s use, or for a single workstation. Multiple-user discounts, site licenses, and worldwide licenses are available; please ask for information if you are interested in purchasing licenses for more than one user. Thank you.
For information about this and other fine Bozosoft products, please send email to <bozosoft@bozosoft.com>, or see the Bozosoft home page at <http://www.bozosoft.com/>.
The installer for this product was created using Installer VISE Lite from MindVision Software. For more information on Installer VISE Lite, contact:
MindVision Software
840 South 30th Street, Suite C
P.O. Box 81886
Lincoln, NE 68510
Voice: (402) 477-3269
Fax: (402) 477-1395
Internet: mindvision@mindvision.com
AOL: MindVision
AppleLink: MindVision
CompuServe: 70253,1437
ftp://ftp.mindvision.com
I’d like to thank Steve Kiene and MindVision for their extraordinary support of shareware authors and the shareware system.
Version History
Version 1.5.1: 1 September 1996.
Multiple consecutive equals signs are treated as a single equals sign.
Fixes two bugs.
Version 1.5: 15 August 1996.
New graphing method is 20 to 50 times faster and produces better-looking results for nearly all curves.
Has zoom-in, zoom-out, and arrows buttons in each graphing window.
Adds live dragging of window contents.
Windows keep their scale when they are resized.
Abs(), Min(), and Max() functions are supported.
Doubles precision for calculations.
Pictures can be dragged to the desktop or to other applications (requires appropriate system software).
Adds option for online registration on the Web.
The minimum display is 2-bit instead of 4-bit.
Includes assorted bug fixes and cosmetic changes.
And more!
Version 1.1.1: 18 July 1996.
Fixes a bug that would not allow certain types of input in certain dialog boxes.
Fixes a minor error in the read me file.
Version 1.1: 16 July 1996.
Supports multiple windows.
Saved documents contain all relevant information about the graph yet are still standard PICT files for use by other programs.
Can open files (including its own files and standard PICT files).
Supports stationery and preferences files.
Sqr(), Sqrt(), Abs() and hyperbolic functions are supported.
Implicit graphing is approximately 300% faster on PowerPC and 50% faster on 68K.
The PowerPC version includes Motorola’s LibMoto for faster mathematical computation.
Directly supports 68K Macs with and without FPU math coprocessors.
Background graphing is possible.
Better memory management.
System 7.0 is required.
Version 1.0a: 25 June 1996.
Fixes a problem with the installer that would sometimes prevent successful installation.
Version 1.0: 19 June 1996.
First public release.
Mike Epstein, 90 Maple Drive, Great Neck, NY 11021, mike@kagi.com or epstein@bozosoft.com
