How to create your own geometry

SME can work with any image format for 2D geometries, and with stacked tiff images for 3D geometries. You can create these in whatever way you feel comfortable with. Here, we are going to use Python to create example geometries. We will use the numpy and matplotlib libraries to create a 2D geometry and save it as a png image. For the 3D tiff image, we will use tifffile which allows us to save a 3D array to a tiff image.

Create a 2D Geometry

We first import the necessary models.

import numpy as np
import matplotlib.pyplot as plt

Next, we create a 2D numpy array that represents the geometry. We will use a simple example of a 2D geometry with a circle in the middle.

# create a 2D numpy array
size = 100
x0 = 40
y0 = 50
r = 10
geometry = np.zeros((size, size))
for i in range(size):
    for j in range(size):
        # make a circle around (40, 50) with radius 10
        if (i - x0 // 2) ** 2 + (j - y0 // 2) ** 2 < r ** 2:
            geometry[i, j] = 1

Finally, we plot the geometry and save it as a png image.

# plot the geometry
img = plt.imshow(geometry, cmap="gray")
plt.axis("off")
img.get_figure().savefig("2d_geometry.png", bbox_inches="tight", pad_inches=0)

The resulting 2D geometry image with a circle in the upper left.

Create a 3D Geometry

We follow the same steps as for the 2D geometry: We define the basic shape of the domain and then create functions that defines the various compartments in the domain. Here, we will create 2 spheres that intersect each other. This time, we use tifffile instead of matplotlib:

import tifffile as tiff
import numpy as np

Then, we create the 3D domain and the compartments.

arr = np.zeros((100, 100, 100))

def sphere(x,y,z, x0=50, y0=50, z0=50, r=25):
    return (x-x0)**2 + (y-y0)**2 + (z-z0)**2 < r**2

def compartment(x,y,z):
    return sphere(x, y, z, 40, 40, 40) or sphere(x, y, z, 60, 60, 60)

for i in range(100):
    for j in range(100):
        for k in range(100):
            arr[i,j,k] = compartment(x,y,z)

Finally, we save the 3D geometry as a tiff image.

tiff.imwrite('3d_skewed_hourglass.tiff', arr)

A slice at z=50 through the resulting 3D geometry created with the code above.

Create an image for initial conditions

You can use the same workflow to create images that can serve as initial conditions for a species in a certain compartment. To that end, we can add another function which computes the concentration field at each pixel of the image. The resulting array then can be stored as a png (2D) or tiff (3D) image and loaded into a model as described in the section on reactions in the ‘getting started’ page.

# same logic as before
arr_init = np.zeros((100, 100, 100))

def sphere(x,y,z, x0=50, y0=50, z0=50, r=25):
    return (x-x0)**2 + (y-y0)**2 + (z-z0)**2 < r**2

def compartment(x,y,z):
    return sphere(x, y, z, 40, 40, 40) or sphere(x, y, z, 60, 60, 60)

def init(x,y,z):
    return np.sin(np.pi*x/100) * np.sin(np.pi*y/100) + 1/100*z

# 'compartment' is zero outside the inner compartment
for i in range(100):
    for j in range(100):
        for k in range(100):
            arr_init[i,j,k] = compartment(x,y,z)*init(i,j,k)

tiff.imwrite('3d_skewed_hourglass_init.tiff', arr_init)

The initial condition at z=50 created with the code above.

In this code, we used the fact that the compartment function is zero outside the inner compartment and one inside. We then defined the initial condition as a function of the position in the compartment. This way, we can create an initial condition that is zero outside the compartment and has a certain shape inside. More complex initial conditions can be readily created in this way by providing more complex functions for the compartment or initial conditions.