Marching squares

Marching squares is a computer graphics 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:

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:

Here are the steps of the algorithm:

Apply a threshold to the 2D field to make a binary image containing:

Every 2x2 block of pixels in the binary image forms a contouring cell, so the whole image is represented by a grid of such cells (shown in green in the picture below). Note that this contouring grid is one cell smaller in each direction than the original 2D field.

For each cell in the contouring grid:

The contour is ambiguous at saddle points. It is possible to resolve the ambiguity by using the average data value for the center of the cell to choose between different connections of the interpolated points. Here is another summary of the method showing options for the saddle:

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