Fakultät II
Institut für Mathematik

Virtual Math Labs: Virtual Reality

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Contents:
 JRBullet CMC tori: Wente and Twisty Imaginary Surfaces of Constant Gaussian Curvature Boy's surface Minimal Surfaces 3D-XplorMath-J Meets jReality Plateau Problem Sphere Eversion Elastic Space Curves

To start a lab just click on the screenshot. If the application does not start, have a look at our Help page.

JRBullet

See how the JBullet physics engine has been integrated into jReality.

Experience mathematical objects as physical objects: use middle mouse to shoot balls, left mouse to move an object, right mouse to apply momentum to an object and the scroll wheel to change the direction of the applied momentum.

Includes real-time synthesized audio. This may require a fast computer to run smoothly. You can turn off audio, uncheck "sound" in the "Main Physics Controls" panel on the left.

CMC tori: Wente and Twisty

This lab is an interactive remake of Matthias Heil's famous movie of CMC tori (mp4 72.3MiB) or (avi 66.8MiB). Double click on the surface opens the interaction panel. Tip: To simplify puzzling one might set the magnetism to 20 to get the pieces in the right position. Then set magnetism to 0 and move (middle mouse) the pieces apart. Setting magnetism back to 5 it is now easier to finish the puzzle.

The labs front end uses ViewerVR from our jReality project. You may wish to have a look at the ViewerVR User Manual.

This lab was implemented by Felix Knoeppel during the practice sessions of the course "Mathematische Experimente in Virtual Reality" winter 2006/07 using the jReality java package.

Imaginary

This lab is part of the exhibition Imaginary 2008. You may switch between the six different geometries using the "1" and "2" key.

The labs front end uses ViewerVR from our jReality project. You may wish to have a look at the ViewerVR User Manual.

Surfaces of Constant Gaussian Curvature

In this lab you may investigate surfaces of constant negative Gaussian curvature (K-surfaces). Double click on the surface allows you to change the curvature and the length of the surface. The initial curve may be changed (at the bottom when the lab comes up). Just drag the yellow points of the initial curve. Double click on the initial curve to add more control points and change the interpolation parameters. Double click on the initial curve to open a panel that allows to change the number of control points and subdivision parameters. More ... .

The labs front end uses ViewerVR from our jReality project. You may wish to have a look at the ViewerVR User Manual.

For the theoretical background consult Designing Cylinders with Constant Negative Curvature.

Boy's surface

In this lab you may explore a version of Boy's surface that minimizes Willmore energy. Double click on the surface opens a panel which allows to adjust some exploration parameters. In particular you may start an animation, which draws the surface stretching a Möbius band until only one small disc is missing. This surface is the Möbius inversion of a minimal sphere with three planar ends. Adjusting the parameters called "Add in x,y,z" under "Appearance" you may alter the center of this Möbius inversion.

The labs front end uses ViewerVR from our jReality project. You may wish to have a look at the ViewerVR User Manual.

This lab was implemented by Elisabeth Guenther during the practice sessions of the course "Mathematische Experimente in Virtual Reality" winter 2006/07 using the jReality java package.

Minimal Surfaces

In this lab you may explore some minimal surfaces. It is an interactive version of some of Matthias Weber's Mathematica notebooks, see Matthias Weber's minimal surface museum. Double click on the surface opens the exploration panel.

The labs front end uses ViewerVR from our jReality project. You may wish to have a look at the ViewerVR User Manual.

This lab was implemented by Martin Beckmann during an intenship using the jReality java package.

3D-XplorMath-J Meets jReality

This webstart application integrates 3D-XplorMath-J into jReality's ViewerVR.

To explore a 3D-Object in jReality press the button "View in jReality" in the "3DXploreMath" panel. JBullet and jReality sound is enabled.

Consult ViewerVR User Manual for the usage of ViewerVR.

JBullet interaction: use middle mouse to shoot balls, left mouse to move an object, right mouse to apply momentum to an object and the scroll wheel to change the direction of the applied momentum.

Plateau Problem

This lab solves the Plateau Problem interactively, i.e., finds the minimal surfaces with a given boundary. Double click on the surface opens the exploration panel, in which you may manipulate the parameters of the boundary curve. The yellow points on the boundary are draggable.

The labs front end uses ViewerVR from our jReality project. You may wish to have a look at the ViewerVR User Manual.

This lab was implemented by Simon Weiss during the practice sessions of the course "Mathematische Experimente in Virtual Reality" winter 2006/07 using the jReality java package.

Sphere Eversion

This lab is an interactive version of The Optiverse. Double click on the surface opens the animation panel.

The labs front end uses ViewerVR from our jReality project. You may wish to have a look at the ViewerVR User Manual.

Elastic Space Curves

You may explore elastic curves in space with this lab. Double click on a red point of the curve (re)opens the animation panel. All points are draggable. Drag the green point to add segments to the curve.

The labs front end uses ViewerVR from our jReality project. You may wish to have a look at the ViewerVR User Manual.

This lab was implemented by Ronny Guenther during the practice sessions of the course "Mathematische Experimente in Virtual Reality" winter 2006/07 using the jReality java package.

 Ulrich Pinkall . 24.11.2009.