Q:

What is an isosurface?

I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it?
Thanks.

A:

Isosurface is another way to call a surface defined by the implicit equation
$$F(x,y,z)=f$$ where $F$ is a function of space and $f$ a constant, often $0$. The prefix iso- indicates that the function $F$ takes the same value ($f$) all over the surface.
The marching cube algorithm is able to construct the iso-surfaces (decomposed in triangles) for a given $F$, by sampling over a regular grid.
Just knowing the function values at the vertices of many tiny cubes allows you to estimate the intersections of the faces with the surface by interpolation, giving you skewed polygons that approximates the surface inside each cube, in a way that ensures continuity across the cubes.
As there are 8 values to be considered, hence 8 signs/zero, there are 6561 possible configurations per cube. Fortunately, this number can be reduced by means of symmetries.

