# 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.

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isosurface is the locus of constant value of some function. – Sasha Aug 4 '11 at 16:26
Would it help if we replace "isosurfaces" by "contours"? In the same way that a usual contour map plots vertical two-dimensional "slices" of a three-dimensional surface, isosurfaces would be the three-dimensional slices of some higher-dimensional function. – J. M. Aug 4 '11 at 16:26

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.

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It's a 2d/3d function where a ouside surface is defined as everywhere in the graph where the value crosses a certain point for example from 0.999 to 1.0001, 1 is the isometric value... <1 is inside the surface and >1 is outside of it. if the surface is the formula surface = y+1; then it is a flat plane parralel to the y axis. Search for isosurface tutorial/guide on google to have illustrated learning pages.

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