Marching squares

In <a href="/facts/Computer_graphics/lapBE8wv">computer graphics</a>, marching squares is an <a href="/facts/Algorithm/fnl5NmRt">algorithm</a> that generates <a href="/facts/Contour_lines/35Qten5r">contours</a> for a two-dimensional <a href="/facts/Scalar_field/8MtPTGob">scalar field</a> (rectangular <a href="/facts/Array_data_structure/BKGvF8AM">array</a> of individual numerical values). A similar method can be used to contour 2D <a href="/facts/Triangulated_irregular_network/1ryhn22v">triangle meshes</a>.
The contours can be of two kinds:

<ul><li>Isolines – lines following a single data level, or isovalue.</li>
<li>Isobands – filled areas between isolines.</li></ul>
Typical applications include the contour lines on <a href="/facts/Topographic_map/sUxP398u">topographic maps</a> or the generation of isobars for <a href="/facts/Weather_map/rlRyVys2">weather maps</a>.
Marching squares takes a similar approach to the 3D <a href="/facts/Marching_cubes/mYbQyPYD">marching cubes</a> algorithm:

<ul><li>Process each cell in the grid independently.</li>
<li>Calculate a cell index using comparisons of the contour level(s) with the data values at the cell corners.</li>
<li>Use a pre-built <a href="/facts/Lookup_table/ULPEAGTJ">lookup table</a>, keyed on the cell index, to describe the output geometry for the cell.</li>
<li>Apply <a href="/facts/Linear_interpolation/galkvRGy">linear interpolation</a> along the boundaries of the cell to calculate the exact contour position.</li></ul>

Marching squares open-in-new

Marching squares