It seems that both piecewise-linear continuation and marching squares are methods to produce iso-contours of a scalar function given the function's values on a grid. It seems that piecwise-linear continuation works for any triangular mesh, not just a grid. Marching squares also has a variation which works on triangles.
What is the connection between these methods? They both seem to use linear interpolation to position the contour at the edges of the grid. Are the two methods equivalent under some conditions?