In computer graphics, marching squares is an algorithm that generates contours for a two-dimensional scalar field (rectangular array of individual numerical values).
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 (four images in bottom-right corner):
For example, a triangular mesh may represent a 2D data surface embedded in 3D space, where spatial positions of the vertices and interpolated points along a contour will all have 3 coordinates.
Note that the case of squares is ambiguous again, because a quadrilateral embedded in 3-dimensional space is not necessarily planar, so there is a choice of geometrical interpolation scheme to draw the banded surfaces in 3D.
It is easy to write a parallel algorithm assuming: A naive implementation of Marching Squares that processes every cell independently will perform every linear interpolation twice (isoline) or four times (isoband).