Basic neighboorhood
jrpotter
parent
cfb43944d3
commit
0113ee34ae
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@ -2,36 +2,7 @@
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"""
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import enum
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class Cells(enum.Enum):
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"""
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Allows for specification of which cells should be considered in a 2D or 3D matrix.
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For example, to specify the CENTER and NORTH cells, we consider CENTER | NORTH. It
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does not make sense to use FORWARD and BACKWARD in a 2D matrix, as that specifies
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looking up and down a bitplane for further cells.
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For higher level dimensions, forgo use of this enumeration entirely, as described in
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the Neighborhood class.
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"""
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# 2D & 3D
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CENTER = 1 << 0
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NORTH = 1 << 1
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NORTHEAST = 1 << 2
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EAST = 1 << 3
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SOUTHEAST = 1 << 4
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SOUTH = 1 << 5
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SOUTHWEST = 1 << 6
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WEST = 1 << 7
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NORTHWEST = 1 << 8
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NORTH = 1 << 9
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# 3D
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FORWARD = 1 << 10
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BACKWARD = 1 << 11
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import itertools
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class Neighborhood:
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@ -42,13 +13,136 @@ class Neighborhood:
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the basic Moore neighborhood comprises of the 8 cells surrounding the center, but what if we wanted
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these 8 and include the cell north of north? The following enables this:
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...
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m_neighborhood = Neighborhood.moore(2)
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m_neighborhood.extend({(-2, 0): True})
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This allows indexing at levels beyond 3D, which the Cells enumeration does not allow, though visualization
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at this point isn't possible.
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"""
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def __init__(self, grid):
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pass
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class NeighborhoodKey:
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"""
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Allows proper sorting of neighborhoods.
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Lists should be returned in order, where cell's with smaller indices (in most significant axis first)
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are listed before cell's with larger ones. For example, in a 3D grid, the neighbors corresponding to:
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offsets = (-1, -1, -1), (-1, 1, 0), (-1, 0, -1), and (1, 0, -1)
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are returned in the following order:
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offsets = (-1, -1, -1), (-1, 0, -1), (1, 0, -1), (-1, 1, 0)
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since the z-axis is most significant, followed by the y-axis, and lastly the x-axis.
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"""
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def __init__(self, obj, *args):
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self.obj = obj
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def __lt__(self, other):
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return self.compare(self.obj, other.obj) < 0
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def __gt__(self, other):
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return self.compare(self.obj, other.obj) > 0
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def __eq__(self, other):
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return self.compare(self.obj, other.obj) == 0
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def __le__(self, other):
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return self.compare(self.obj, other.obj) <= 0
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def __ge__(self, other):
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return self.compare(self.obj, other.obj) >= 0
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def __ne__(self, other):
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return self.compare(self.obj, other.obj) != 0
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def compare(self, other):
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for i in reversed(range(len(a))):
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if a[i] < b[i]:
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return -1
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elif a[i] > b[i]:
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return 1
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return 0
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def __init__(self):
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"""
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Sets up an empty neighborhood.
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Initially, no cells are included in a neighborhood. All neighborhoods must be extended.
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Note the offsets have a tuple as a key representing the position being offsetted by, and as a value,
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the current state the given cell at the offset is checked to be.
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"""
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self.offsets = {}
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def neighbors(self, bit, grid):
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"""
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Returns all bits in the given neighborhood.
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The returned cells are grouped with the value the cell is checked to be (a 2-tuple (Bit, value) pair).
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These are sorted based on the NeighborhoodKey comparison class defined above.
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"""
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bits = []
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for k in sorted(self.offsets.keys()):
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bits.append((k, self.offsets[k]))
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return bits
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def extend(self, offsets, strict=False):
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"""
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Adds new offsets to the instance member offsets.
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We complain if the strict flag is set to True and an offset has already been declared with a different value.
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"""
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if not strict:
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self.offsets.update(offsets)
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else:
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for k in offsets.keys():
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value = self.offsets.get(k, None)
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if value is None:
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self.offsets[k] = offsets[k]
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elif value != offsets[k]:
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raise KeyError
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@classmethod
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def moore(cls, dimen, value=True):
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"""
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Returns a neighborhood corresponding to the Moore neighborhood.
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The Moore neighborhood consists of all adjacent cells. In 2D, these correspond to the 8 touching cells
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N, NE, E, SE, S, SW, S, and NW. In 3D, this corresponds to all cells in the "backward" and "forward"
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layer that adjoin the nine cells in the "center" layer. This concept can be extended to N dimensions.
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Note the center cell is excluded, so the total number of offsets are 3^N - 1.
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"""
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offsets = {}
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variants = ([-1, 0, 1],) * dimen
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for current in itertools.product(*variants):
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if any(current):
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offsets[current] = value
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m_neighborhood = cls()
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m_neighborhood.extend(offsets)
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return m_neighborhood
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@classmethod
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def neumann(cls, dimen, value=True):
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"""
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Returns a neighborhood corresponding to the Von Neumann neighborhood.
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The Von Neumann neighborhood consists of adjacent cells that directly share a face with the current cell.
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In 2D, these correspond to the 4 touching cells N, S, E, W. In 3D, we include the "backward" and "forward"
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cell. This concept can be extended to N dimensions.
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Note the center cell is excluded, so the total number of offsets are 2N.
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"""
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offsets = {}
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variant = [0] * dimen
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for i in range(len(variant)):
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for j in [-1, 1]:
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variant[i] = j
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offsets[tuple(variant)] = value
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variant[i] = 0
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n_neighborhood = cls()
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n_neighborhood.extend(offsets)
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return n_neighborhood
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