2025-10-27

More progress on marching cubes approach to problem:

1. Fixed orientation
2. Generated tetrahedralization of unit cube that contains complex from marching cubes as a 2-chain

For 4D, I’m using the following isosurface:

$$f(x,y,z,w)={\left(\sqrt{x^2+y^2}-R\right)}^2+{\left(\sqrt{z^2+w^2}-R\right)}^2-r^2$$

Which looks like the following animation (animating $w$ from $-0.5$ to $0.5$):

Alternatively, we could do a 4D sphere:

$$f(x,y,z,w)=x^2+y^2+z^2+w^2-r^2$$

Or metaballs:

$$f(x,y,z,w)=\sum _i\frac{r_i^2}{(x-x_i{)}^2+(y-y_i{)}^2+(z-z_i{)}^2+(w-w_i{)}^2}-1$$