What Is LiveGraphics3D?
LiveGraphics3D is a non-commercial Java 1.1 applet to display and rotate three-dimensional graphics produced by Mathematica in HTML pages. It may be used without charge for any non-commercial purposes. Mathematica is a program for symbolic and numeric mathematics by Wolfram Research, Inc.. Wolfram Research is also responsible for licensing LiveGraphics3D for commercial purposes.
LiveGraphics3D enables all Mathematica users to put almost any three-dimensional graphics computed by Mathematica directly onto a HTML page, such that everyone with a web browser supporting Java 1.1 (e.g. Communicator 4.0 or Internet Explorer 4.0 or higher) can view and interactively rotate the graphics without any additional software.
Additionally LiveGraphics3D is able to show animations, calculate stereo graphics, integrate hyperlinks, and display bitmap backgrounds.
Since version 1.00 LiveGraphics3D supports parametrized graphics, i.e. simple Mathematica expressions in places of coordinates, and animations with Animate. These features are not described in detail in this documentation; however, some examples and my talk at the Mathematica Developer Conference are available online.
In order to learn how to rotate, zoom, strip, and animate graphics displayed by LiveGraphics3D you should read the User Interface section. (A subsection about Trouble Shooting is included.)
Quick Start
In order to view LiveGraphics3D applets you have to use a web browser supporting Java 1.1 (e.g. Communicator 4.0 or Internet Explorer 4.0) and activate Java in the options or preferences menu (if not activated already).
After a LiveGraphics3D applet has successfully initialized itself the following interactions are always supported.
| 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 |
| SHIFT key pressed plus vertical dragging | zooming |
| SHIFT key pressed plus horizontal dragging | rotating about an axis perpendicular to the picture |
| CONTROL key pressed plus vertical dragging | changing focal length |
| CONTROL key pressed plus horizontal dragging | changing strength of stereo effect |
| META (ALT) key (or right mouse button) pressed plus vertical dragging | stripping parts of the graphics |
| "o" key | printing parameter settings to the Java console (aka Java messages window) |
| "s" key | toggling between single picture, stereo pictures for diverge fusing and stereo pictures for cross fusing |
| HOME key | restoring original perspective (no spinning) |
The META key is usually mapped to the ALTERNATE or COMMAND key. However, on some systems it is emulated by the right mouse button. Rotation about an axis perpendicular to the picture is not possible if a rotating background is included.
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 |
| META (ALT) key (or right mouse button) pressed plus horizontal dragging | switching through frames |
Details
This subsection presents some details of the user interface. First the determination of the axis of rotation is described.
The axis of rotation is usually in the plane of the two-dimensional picture and perpendicular to the virtual line you moved with the mouse (starting from the point on which you clicked). The angle of rotation is determined by the length of that line. This allows to view the graphics from all directions. However, the presence of rotating bitmap backgrounds changes this prescription as in this case horizontal dragging will rotate about the fixed vertical axis and vertical dragging about the horizontal axis in the plane of the picture
Pressing SHIFT and dragging vertically will change the value of the parameter MAGNIFICATION. Pressing CONTROL and dragging horizontally will change the parameter STEREO_DISTANCE. (Negative values indicate the need to cross fuse while positive values are appropriate for diverge fusing.) The current settings of MAGNIFICATION, STEREO_DISTANCE and the Graphics3D options ViewPoint and ViewVertical can be printed to the Java console by pressing the "o" key while the mouse cursor is in the region of the Java applet. Web browsers supporting Java should be (and usually are) able to display the Java console. If you are using LiveGraphics3D on your own HTML page, you may copy the line containing MAGNIFICATION or STEREO_DISTANCE into the applet call and/or the settings of ViewPoint and ViewVertical into the Graphics3D definition to use them as initial values. This is probably the best way to find appropriate values for these parameters.
Martin Kraus, October 8, 2001