Ever since the first time I saw Herwig Hauser’s gallery of singular algebraic surfaces, I have wanted to render them live and interactive in the browser. This presentation loads slowly as the surfaces are initially evaluated using the default marching cubes algorithm of MathCell. A bit of patience is required, but the result is rather pleasant.

The data for each surface is generated as the MathCell scrolls into view and retained for subsequent reloading. Since browsers limit the number of simultaneous WebGL contexts, each containing iframe is unloaded when not visible, then reloaded using JavaScript’s InteractionObserver. Even this has a noticeable lag for the amount of data needed to produce relatively nice surfaces.

Some of the surfaces, in particular Crixxi, require multiple input ranges to provide sufficient detail. These can be determined by examining each individual surface with this supplementary presentation. Some of the surfaces still exhibit ragged or incomplete edges at cusps and could stand improvement.

Mousing over the frame around each graphic gives a tooltip with the name and equation of the surface. Clicking on the frame opens the surface in a new window.

Uploaded 2019.08.23 analyticphysics.com