Question

Given a grid map where each cell can be described by a pair (x, y), and a vector of such cells, how can I (nicely) check if the cells in that vector form a ‘tunnel’, ie. they are all lined up either vertically or horizontally? But what if I only want to see if most of them are lined up (and not all)?

All are lines up             Most are lined up      Not lined up

                             C                       C C C
 C C C C C C C C             C C C C C C C C         C   C C C
                                 C                   C C C C
                                                         C C

Answer 1

You could calculate the standard deviation of both the X and Y coordinates. The more ‘tunnelled’ your cells are, the lower the std deviation will be for either X or Y.

For example, in Python:

import numpy

def is_tunnelled(cells):
    # given cells=[(x,y), (x,y),...]
    x_values, y_values = zip(*cells)
    lowest_std_dev = min(numpy.std(x_values), numpy.std(y_values))
    return lowest_std_dev < STD_DEVIATION_THRESHOLD

It’s up to you to determine what the value of STD_DEVIATION_THRESHOLD should be.