LiveGraphics3D
LiveGraphics3D is a Java applet written by Martin Kraus and licensed for commercial use by Wolfram Research, Inc. LiveGraphics3D allows 3D solids created by Mathematica to be rotated interactively right in the middle of an HTML page. For a complete listing of all applets in MathWorld, see the index of interactive illustrations.
To use LiveGraphics3D, you must use a web browser supporting Java 1.1 (e.g., Netscape Communicator 4.x, Mozilla, IE 4.x/5.x, iCab, OmniWeb). You must also activate Java in the Preferences or Options menu of your web browser.
A LiveGraphics3D solid can be rotated by dragging it with the mouse and can be continuously spun (while the mouse pointer is located in the applet frame) by dragging and letting up the mouse button in the middle of a drag.
The images depicted in LiveGraphics3D applets can be printed directly from most web browsers (e.g., Netscape 4.6 under Mac OS, Netscape 4.6 under Linux RedHat 6.0). However, under some operating system/browser/Java combinations, a blank space is obtained when printing where the image should be. If you experience this problem, turn off Java in your browser's Preferences settings and SHIFT-Reload the page. This will bring up the pages with static GIF images instead of applets, and these should print fine. Note that the presence of embedded GIFs within applet tags also allows non-Java-capable browsers to view pages without missing "live" images.
2D and 3D animations may also be rendered using LiveGraphics3D. Such animations are rotatable, but they are active only when the mouse is moved within a given animation frame. Therefore, only a single animation may be active at any given time.
In some cases, preprocessing of Mathematica graphics is necessary to put them in a form capable of being rendered correctly by LiveGraphics3D. Martin Kraus has written a Mathematica package LiveGraphics3D.m that contains routines to do preprocessing for many of the 3D graphics included in MathWorld.
Other commands recognized by LiveGraphics3D are summarized in the following tables.
| user action | applet reaction |
|---|---|
| dragging (left mouse button pressed) | rotating about an axis in the picture |
| releasing left mouse button while dragging | spinning about an axis in the picture |
| pressing SHIFT key plus vertical dragging | zooming |
| pressing SHIFT key plus horizontal dragging | rotating about an axis perpendicular to the picture |
| pressing CONTROL key plus vertical dragging | changing focal length |
| pressing CONTROL key plus horizontal dragging | changing strength of stereo effect |
| pressing META (ALT) key (or right mouse button) plus vertical dragging | stripping parts of the graphics |
| pressing "o" key | printing parameter settings to the Java console (a.k.a. Java messages window) |
| pressing "s" key | toggling between single picture, stereo pictures for diverge fusing, and stereo pictures for cross fusing |
| User interface for all graphics. | |
The META key is usually mapped to the ALTERNATE or COMMAND key. However, on some systems, it is mapped to the right mouse button.
Several additional interactions are supported for animations.
| user action | applet reaction |
|---|---|
| entering applet region | starting animation |
| leaving applet region | stopping animation |
| double clicking | stopping or restarting animation |
| pressing META (ALT) key (or right mouse button) plus horizontal dragging | switching through frames |
| Additional interface for animated graphics. | |
Additional details and documentation are given on the LiveGraphics3D Homepage. If you are experiencing difficulties using LiveGraphics3D applets in MathWorld, please consult the LiveGraphics3D FAQ.