marchingsquaresmarchingcubes

Marching squares and marching cubes are related algorithms used to extract contour lines and surfaces from scalar fields defined on regular grids. Marching squares is the two dimensional predecessor that operates on each square cell formed by four neighboring samples. Each corner is classified as above or below a chosen isovalue. The resulting 4-bit index selects a polygonal configuration from a compact lookup table. Linear interpolation along the cell edges locates the points where the isovalue crosses the edges, and the segments connect to form an iso-contour across the grid.

Marching cubes extends the idea to three dimensions. It processes each cube formed by eight corner samples and uses an 8-bit index to select a triangulation from a larger lookup table. The resulting triangles approximate the isosurface inside the cube, and adjacent cells’ triangles connect to form a continuous mesh over the volume. Both methods assume a regularly sampled grid and produce polygonal geometry suitable for rendering or further analysis.

Applications span medical imaging, scientific visualization, geology, and computer graphics, where iso-surfaces or contours reveal structure in volumetric data. They are valued for their simplicity and efficiency, but can produce topological ambiguities or aliasing in certain configurations, and the accuracy depends on grid resolution and interpolation. Various refinements address these issues, including alternative tables, edge-aware interpolation, and adaptive refinement, while preserving the basic marching principle.

The term marching squares marching cubes is sometimes used to refer collectively to the two related iso-contouring methods.