Stencils

In this tutorial we will look at the Stencils in topoGenesis and the computational concept behind them.

import topogenesis as tg

Creation and basic properties

We can create a stencil based on well-known neighbourhood definitions: Von Neumann or Moore

von_neumann_stencil = tg.create_stencil("von_neumann", 1, 1)

print(type(von_neumann_stencil))
print(von_neumann_stencil)

<class 'topogenesis.datastructures.datastructures.stencil'>
[[[0 0 0]
  [0 1 0]
  [0 0 0]]

 [[0 1 0]
  [1 1 1]
  [0 1 0]]

 [[0 0 0]
  [0 1 0]
  [0 0 0]]]

We can also expand the stencil into the local addresses

print(von_neumann_stencil.expand())

[[ 0  0  0]
 [ 1  0  0]
 [ 0  1  0]
 [ 0  0  1]
 [ 0  0 -1]
 [ 0 -1  0]
 [-1  0  0]]

Neigbourhood type in stencils

Check the neighborhoud type and origin

print(von_neumann_stencil.ntype)
print(von_neumann_stencil.origin)

von_neumann
[1 1 1]

Create a moore neighbourhood stencil

moore_stencil = tg.create_stencil("moore", 1, 1)
print(moore_stencil)

[[[1 1 1]
  [1 1 1]
  [1 1 1]]

 [[1 1 1]
  [1 1 1]
  [1 1 1]]

 [[1 1 1]
  [1 1 1]
  [1 1 1]]]

Customizing stencils

Customizing the stencil with the help of global indicies: in this case removing the up-center cell

moore_stencil[1,0,1] = 0
print(moore_stencil)

[[[1 1 1]
  [1 1 1]
  [1 1 1]]

 [[1 0 1]
  [1 1 1]
  [1 1 1]]

 [[1 1 1]
  [1 1 1]
  [1 1 1]]]

Customizing the stencil with the help of local indicies: in this case removing the down-center cell.

moore_stencil.set_index([0,1,0], 0)
print(moore_stencil)

[[[1 1 1]
  [1 1 1]
  [1 1 1]]

 [[1 0 1]
  [1 1 1]
  [1 0 1]]

 [[1 1 1]
  [1 1 1]
  [1 1 1]]]

Stencils and Universal Functions

We can peform all universal functions(addition, subtraction, multiplication, etc) on stencils.

custom_stencil = moore_stencil - von_neumann_stencil

print(custom_stencil.ntype)
print(custom_stencil)

custom
[[[1 1 1]
  [1 0 1]
  [1 1 1]]

 [[1 0 1]
  [0 0 0]
  [1 0 1]]

 [[1 1 1]
  [1 0 1]
  [1 1 1]]]