Marching squares

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In computer graphics, marching squares is an algorithm that generates contours for a two-dimensional scalar field (rectangular array of individual numerical values). A similar method can be used to contour 2D triangle meshes.

The contours can be of two kinds:

• Isolines – lines following a single data level, or isovalue.
• Isobands – filled areas between isolines.

Typical applications include the contour lines on topographic maps or the generation of isobars for weather maps.

Marching squares takes a similar approach to the 3D marching cubes algorithm:

• Process each cell in the grid independently.
• Calculate a cell index using comparisons of the contour level(s) with the data values at the cell corners.
• Use a pre-built lookup table, keyed on the cell index, to describe the output geometry for the cell.
• Apply linear interpolation along the boundaries of the cell to calculate the exact contour position.