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At this point we hope you have learned the basics of using LiveGraphics3D to create mathlets without any low-level computer programming. You should be aware that we have only covered the essential concepts and features of LiveGraphics3D. We have made no attempt to discuss every parameter of the applet, nor have we tried to describe the complete syntax of the underlying graphics format. A more complete discussion of these topics may be found in the documentation at the LiveGraphics3D homepage (Kraus) and in the second, more advanced section of this article; see the table of contents below. If you are contemplating using LiveGraphics3D in your courses, you might also be interested in what the future holds for LiveGraphics3D.

LiveGraphics3D allows you to create and display mathlets with nothing more than a text editor and a web browser supporting Java 1.1. While Mathematica is not required to create, display, or interact with a mathlet, the use of a CAS such as Mathematica to generate interactive, three-dimensional illustrations for online mathematics is extremely helpful. Therefore, one of the directions for future work is certainly to extend LiveGraphics3D to support other computer algebra systems such as Maple, Mathcad, or MuPAD.

Further possibilities for future extensions are support for complex numbers as well as vector and matrix variables. Moreover, control structures such as loops and functions could be implemented in the future. Furthermore, an implementation as a J# browser control and an improved implementation of the graphics rendering exploiting the features of Java 1.4 will be considered. Beyond a Java-based implementation, one might also think about alternative implementations based on other web standards, such as the XML-based X3D. However, the wide support for Java applets in today's web browsers proves that the original decision to implement LiveGraphics3D in Java (made about eight years ago) was extremely fortunate.

It is impossible to tell what the Internet and online interactive mathematical visualizations will look like in the future. Nonetheless, the steadily increasing number of applications and enthusiastic reactions of users of LiveGraphics3D certainly let us hope that some of the concepts and ideas discussed in this article will be part of it in one form or another. We wish you luck in constructing mathlets for your own use, and look forward to seeing your creations online.

This page finishes the general portion of our article. From here, you may go to the references or to the advanced topics.

Jonathan Rogness and Martin Kraus, "Constructing Mathlets Quickly using LiveGraphics3D - Future Directions," *Convergence* (May 2006)

Journal of Online Mathematics and its Applications