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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
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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.

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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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