Virtual Math Labs: planar elastic nets

Planar elastic domain

Start the java web start application.

This application simulates a planar elastic sheet. While you drag some vertices, the rest of the mesh moves in order to lower its elastic energy.

Right click on the background to open a menu. There are two types if objects solids and holes, which you can add and edit in "Domain" mode. In "Selection" mode you can use the green "Brush" (brush needs to be in "select" mode) to select vertices. Mark selected vertices as "fixed" or "movable". Finally, in "Physics" mode you can drag the movable vertices around and the rest of the mesh moves like a rubber sheet. Since there is no friction you always need some fixed vertices.

• Start with an empty session and right click in the middle of nowhere. Study the menu entries and see how different selections in the "Mode" submenu influence the available menu entries.
• Change to Mode->Domain and make a new solid, new->Solid. Every so often encompass by pressing 'e' and scale the image dragging with middle mouse on the background. Dragging with middle mouse on the solid scales and rotates it.
• Change the shape of the solid by dragging the control points of its boundary curve.
• Change to Mode->Selection then there appears a green dot, the "Brush", appears at the origin. Change to Brush->select and select some vertices dragging the brush around with left mouse. Mark the selected vertices as fixed, Mark as->fixed.
• Change to Brush->move and move the brush to another place, then select some vertices as before and Mark as->movable.
• Change to Mode->Physics and drag the movable points around.

Lab author: Ulrich Pinkall