Explanation of the Marching Squares saddle points resolution I was reading the Wikipedia entry on Marching Squares, and was confused by the explanation of the saddle point disambiguation:

Ambiguous Case:



Basically, given the saddle points, the ambiguity is resolved by using the average data value for the center of the cell. I don't understand why this would help resolve the ambiguity. It seems to just select the longer pair of lines over the shorter pair. Is there any reason for this approach?

https://en.wikipedia.org/wiki/Marching_squares#Disambiguation_of_saddle_points
Imagine that a black dot represents a value of -1 whereas a white dot represents a value of +1. You are looking for the iso-line(s) where each point upon the line is 0.

For this example you could either place the iso-lines like on the left or the right:

 or 

The difference between the solutions is the value in the center. In the left case we assume 1s whereas in the right solution we assume -1s. So we check the center value and based on that value decide which solution fits best. If the center value is 1, we pick the left solution. If the center value is -1, we choose the right solution.