marchingsquares

Marching squares is a computer graphics and visualization algorithm used to extract isocontours, or lines of constant scalar value, from a two-dimensional scalar field defined on a grid. It serves as the 2D counterpart to marching cubes and is widely used for visualizing level sets in images and related data.

The method processes each square cell formed by four neighboring grid points. For each cell, the scalar values at the corners are compared to a chosen isovalue, producing a 4-bit index (0–15) that encodes which corners are above the isovalue. A precomputed lookup table assigns a set of line segments within the cell for that index. The intersection points along the cell edges are located by linear interpolation, and the corresponding segments are drawn. Collecting segments from all cells yields polylines that approximate the isocontour.

There are 16 basic configurations, reflecting the possible corner states, with some symmetric duplicates. Some configurations are ambiguous (notably cases 5 and 10), which can create topological artifacts such as diagonal connections. Variants and refinements, such as the asymptotic decider, address these ambiguities by evaluating the field more carefully to determine the correct connectivity.

Applications of marching squares include medical image visualization (CT or MRI slices), geographic information systems, meteorological data analysis, and general computer graphics where fast, local isocontour extraction is desirable. The algorithm is fast, simple to implement, and scales with grid size, producing a piecewise-linear approximation of level sets.

Implementation notes: it typically iterates over grid cells, performs edge interpolation to locate contour intersections, and uses a 16-entry lookup table to define cell segments. Special care may be taken to avoid duplicating vertices on shared edges.