Mathlets: Java[TM] Applets for Math Explorations -- Notes

Mathlets: Java^TM Applets for Math Explorations

Written by Tom Leathrum

Notes

Another big update, although this still uses Java5 code -- I have added to all of the graphing applets the ability to change the colors of the graphed items. I still have not had a chance to update the source code pages.

I have upgraded the applets to use the features of Java5, especially the new generic classes. This means that, in order to run the applets, you will need a Java5-compatible runtime/plug-in (version 1.5 or later) for your browser. I have not yet had a chance to update the source code page, but there will be many changes there, as well. The Addison-Wesley materials still use the older Java2-compatible versions (use runtime-plug-in version 1.3 or later with these).

The particularly intrepid user may also wish to read the source code for some of these applets.

The Limits applet and the exploration of Exponential Functions and Their Derivatives appear in the January 2001 issue of the Journal of Online Mathematics and its Applications (JOMA), published online under the auspices of the Mathematics Association of America (MAA). Judy Holdener of Kenyon College wrote a review of my materials in the second issue. Since then, I have been working on a series of articles in the Developers Area of JOMA, under the title "Writing Mathlets: A Call to Working Math Professionals" ( part 1, part 2, and part 3 available so far).

I have entered into a publication agreement with Addison-Wesley, which includes a pretty substantial subset of the Mathlets package. By the terms of the publication agreement, though, the content of these Web pages will not be seriously affected by the publication -- I have altered the copyright notifications to include the Addison-Wesley copyright on their materials, but I will still be able to maintain and further develop the materials here.

The Latest Changes:

A new applet, Combinations and Transformations of Functions, required some revisions to the parser code in order to allow one defined function to be used in the definition of another function. I patched up a few inconsistencies in the parser when I did that. I have also shaken a few minor bugs out of the recently upgraded code.
Big Upgrade and Rewrite Now Complete! I have been working on bringing the applets up to Java 2 standards, with all that entails. Changes include:
- Making the JavaScript-to-Java communications two-way -- in particular, I have included a public method in the Java code which allows a JavaScript command to get the contents of a field from the applet. This was done largely at the suggestion of the WeBWorks people. In particular, now you can take the contents of an applet input field and load them directly into an HTML form's text input field for CGI processing.
- Internationalization -- I have put all displayed strings into separate Java "properties" files. This, along with the ability to change the applet's Locale using HTML parameters, makes the work of translating the applets into other languages much easier. I have contact with people interested in translating the applets and materials into Spanish and Portuguese. Addison-Wesley has agreed to let these translations apply to their materials.
- Consolidation -- much of the code for event-handling, JavaScript communication, and HTML parameters was nearly identical between applets, so I developed a set of mechanisms to handle them in a single shared abstract "AMathlet" class, which all of the applets will now extend and use. This class handles keyboard events (to shift focus between input fields), some common button-triggered events (making sure to do graph redrawing at the right times), methods for JavaScript-to-Java communications (now two-way, see above), HTML parameters, and Locale configuration (for internationalization, again see above). Some of the code (for keyboard event handling, button events, and window closing events) was so common even in the shared classes that I further consolidated it into a small set of utility classes which now handle those events.
- Swing interface elements -- I have been looking for a long time at doing this, but various problems kept me away from it until now. This has had some far-reaching consequences, including the elimination of double-buffering code in the 3D graphing applets (Swing elements automatically double-buffer). I am also moving to Swing Timer objects for animations and button-repeat actions.
- Java 2D API -- with the move to Swing, I also moved from the AWT Graphics objects to AWT Graphics2D objects for custom graphing contexts. This allowed me to use the AWT Shapes in the geometry package, and Affine Transforms for coordinate conversions. These changes have been by far the most far-reaching and difficult parts of the upgrade, but they have allowed me to totally rethink how graphs are generated and stored.
- JavaCC version 3.2 -- this didn't actually affect the parser's source code at all (although other aspects of the update did), but does seem to affect the compiled bytecode in some subtle ways.
- All of the upgraded applets are online now.
It is unclear to me at this point how these changes will affect the Addison-Wesley materials. They have agreed to accept the upgrade into their materials, but that has not happened yet. Their copyright applies to the compiled bytecode for the applets, not the source code, by agreement. However, the changes in the source code for this upgrade have been so extensive that I cannot see how the new bytecode would bear much resemblance to the old bytecode. Until Addison-Wesley has the upgraded applets in their materials, their copyright may not apply to the new versions. (This applies to the applets, not the HTML -- Addison-Wesley still holds copyright on their HTML materials.)
The work with Addison-Wesley prompted me to fix some things in the applets and HTML, in particular to bring the HTML up to their visual standards. Their materials use a frames-based presentation for the HTML, and they are pretty picky about things like fonts and colors. This work has dramatically improved the applets, but mostly in small ways. There are still some gaps in the non-frames materials that I use and maintain separate from the Addison-Wesley materials, but I hope to fill them soon.
I have implemented a new mode of presentation for surfaces in 3D -- faceted surfaces with surface-hiding, rather than simple wireframes. Both presentations are now available, but the faceted hidden surface presentation is the primary mode.
The HTML files for the applets have been updated to include click-and-load examples for all of the applets and better instructions (this was part of the preparations for publication).
The JavaScript-to-Java interface has been expanded to include the fields common to the 2D and 3D graphing classes, and now also handles HTML parameters.
Hitting the "Return" key in a text input field now moves the input focus to another field and (in most applets) redraws the graph.
Many bugs have been fixed, mostly having to do with the JavaScript-to-Java interface and making sure that graphs are erased and redrawn correctly when that interface is being used.
The previously available "sample" of applets (which started the JavaScript-to-Java interfacing and the click-and-load examples) has been removed.
The Power User's Guide has been made available and linked to the main page, and with completion of the big rewrite, the Guide has also been completed and updated with new features.

The applets in the Mathlets package are designed to work in all current browsers using the Java Plug-In version 1.3 or later. The applets have been tested in Netscape version 7.x, Microsoft Internet Explorer version 6.x, and Mozilla versions 1.5 and later, with Java Plug-In version 1.4. All previous issues, involving older versions of the browsers and Plug-In, no longer apply. Look instead for new issues....