Tight and overtwisted contact structures

The idea of a contact structure is to attach a plane to every point of a 3-manifold in a twisty way. In particular, no surface can be everywhere tangent to the contact planes. This condition translates roughly into a non-integrability condition, so we say that a contact structure is a maximally non-integrable 2-plane distribution.

There are two kinds of contact structures: tight and overtwisted. The idea is that a tight contact structure doesn't contain any "unnecessary twisting," whereas an overtwisted one contains a disk such that, as we look at planes along radial rays, the contact planes twist all the way around (i.e., 180 degrees around).

Use the mouse to rotate. To toggle automatic rotating, click or press the space bar.

• t: Toggles visibility of the solid torus (defaults to visible)
• o: Toggles tight vs. overtwisted contact structures (defaults to tight)

If this doesn't work, you can view the animation here: https://editor.p5js.org/jessicajzhang03/present/GBfUBUJo. (Note: This will open in a new tab.)