Generating surfaces with procedural noise
The ProceduralSurfaceGeometry-class is a child of the Geometry class, and carves out a procedural surface of a already existing object. We will here present a basic example where we carve out a procedural surface from a block of beta-cristobalite.
First, we need to import necessary functionality:
from molecular_builder import create_bulk_crystal, carve_geometry, write
from molecular_builder.geometry import ProceduralSurfaceGeometry
Second, a block of beta-cristobalite is generated. We go with a block of dimensions (50Å, 200Å, 200Å).
atoms = create_bulk_crystal("beta_cristobalite", [200, 200, 50])
A block of \(\beta\)-cristobalite.
Basic example
To get a basic surface with structures generated by procedural noise, we need to define a point on the surface, its normal vector and the thickness of the noise:
geometry = ProceduralSurfaceGeometry(point=(100, 100, 40),
normal=(0, 0, 1),
thickness=20,
seed=97455
)
The result is
Surface with procedural structures generated using Perlin noise. Scale is 1, octaves is 1.
Noise parameters
There is a bunch of parameters associated with the procedural noise. The scale of the noise structures is given by the scale-parameters, and the number of octaves (levels of details) is given by octaves. To generate different surfaces with the same parameters, change seed. See <https://pypi.org/project/noise/>`_. for more options.
geometry = ProceduralSurfaceGeometry(point=(100, 100, 40),
normal=(0, 0, 1),
thickness=20,
method='simplex',
scale=3,
octaves=2,
seed=16591
)
num_carved = carve_geometry(atoms, geometry, side="out")
The result is
Surface with procedural structures generated using Simplex noise. Scale is 3, octaves is 2.
Two-level surface
Instead of having continuous surfaces, one may wants to set a threshold and create a two-level surface. As the expectation value of the noise is zero, setting threshold=0 gives a surface where the surface area of the two levels is approximately the same.
geometry = ProceduralSurfaceGeometry(point=(100, 100, 40),
normal=(0, 0, 1),
thickness=20,
method='simplex',
scale=3,
octaves=2,
seed=16591,
threshold=0
)
num_carved = carve_geometry(atoms, geometry, side="out")
The result is
Surface with two-level structures generated using Simplex noise. Scale is 3, octaves is 2.
Periodic structures
Often it is convenient to have periodic structures. By setting repeat=True, the structures are repeated once in each direction:
geometry = ProceduralSurfaceGeometry(point=(100, 100, 40),
normal=(0, 0, 1),
thickness=20,
method='simplex',
scale=3,
octaves=2,
seed=16591,
threshold=0,
repeat=True
)
num_carved = carve_geometry(atoms, geometry, side="out")
The result is
Surface with periodic two-level structures. Scale is 3, octaves is 2.
One can also set how often the structures should repeat. By setting repeat=(100, 200), the structures are repeated twice in x-direction and once in y-direction:
geometry = ProceduralSurfaceGeometry(point=(100, 100, 40),
normal=(0, 0, 1),
thickness=20,
method='simplex',
scale=3,
octaves=2,
seed=16591,
threshold=0,
repeat=(100, 200)
)
num_carved = carve_geometry(atoms, geometry, side="out")
The result is
Surface with periodic two-level structures. Scale is 3, octaves is 2.
Screwed noise
Another possibility is to make the noise screwed. This is done by setting the relative angle between the x-axis and the noise axis, which by default in 90 degrees. This can be useful when dealing with triclinic systems:
geometry = ProceduralSurfaceGeometry(point=(100, 100, 40),
normal=(0, 0, 1),
thickness=20,
method='simplex',
scale=3,
octaves=2,
seed=16591,
threshold=0,
repeat=True,
angle=45
)
num_carved = carve_geometry(atoms, geometry, side="out")
The result is
Surface with periodic, screwed two-level structures. Scale is 3, octaves is 2.
Add function
A function can be added to the noise. Here, we add a fucntion that is lineary increasing when x<100 and a lineary decreasing when x>100:
def f(x, y):
if x < 100:
return x/100
else:
return 1 - (x-100)/100
Then, we set f=f:
geometry = ProceduralSurfaceGeometry(point=(100, 100, 40),
normal=(0, 0, 1),
thickness=20,
method='simplex',
scale=3,
octaves=2,
seed=16591,
threshold=0,
repeat=True,
f=f
)
num_carved = carve_geometry(atoms, geometry, side="out")
The result is
Surface with periodic two-level structures and an added function. Scale is 3, octaves is 2.