import matplotlib.pyplot as plt
%matplotlib inline
import pandas as pd
import numpy as np


from tyssue import config
from tyssue.draw import sheet_view

Geometry classes

A Geometry class is a stateless class holding functions to compute geometrical aspects of an epithelium, such as the edge lengths or the cells volume. As they are classes, inheritance can be used to define more and more specialized geometries.

For the user, a geomtry class is expected to have an update_all method that takes an Epithelium instance as sole argument.

Planar Geometries

It’s simple to create hexagonal apical junction meshes with the Sheet class method planar_sheet_2d():

from tyssue import Sheet
from tyssue import PlanarGeometry
from tyssue.generation import generate_ring

sheet_2d = Sheet.planar_sheet_2d('planar', nx=6, ny=6,
                                 distx=1, disty=1)
sheet_2d.sanitize(trim_borders=True, order_edges=True)

PlanarGeometry.update_all(sheet_2d)

ring = generate_ring(24, 12, 14)
PlanarGeometry.update_all(ring)

fig, (ax, ax2) = plt.subplots(1, 2)
fig, ax = sheet_view(sheet_2d, ax=ax)
fig, ax2 = sheet_view(ring, ax=ax2)
fig.set_size_inches(12, 6)

Sheet geometry in 3D

from tyssue import SheetGeometry
from tyssue.geometry.sheet_geometry import EllipsoidGeometry
from tyssue.generation import ellipsoid_sheet

sheet_3d = Sheet.planar_sheet_3d('sheet', nx=6, ny=6,
                                 distx=1, disty=1)
sheet_3d.sanitize(trim_borders=True)

SheetGeometry.update_all(sheet_3d)

ellipso = ellipsoid_sheet(a=12, b=12, c=21, n_zs=12)
EllipsoidGeometry.update_all(ellipso)

sheet_3d.vert_df.head()

	y	is_active	x	z	rho	height	basal_shift
vert
0	2.625	1	0.5	0	0	-4.0	4.0
1	3.375	1	1.5	0	0	-4.0	4.0
2	2.625	1	2.5	0	0	-4.0	4.0
3	3.375	1	0.5	0	0	-4.0	4.0
4	3.625	1	1.0	0	0	-4.0	4.0

EllipsoidGeometry inherits from SheetGeometry through ClosedSheetGeometry:

import inspect
print(*(cls.__name__ for cls in
        inspect.getmro(EllipsoidGeometry)), sep="\n\t|_ ")

EllipsoidGeometry
        |_ ClosedSheetGeometry
        |_ SheetGeometry
        |_ PlanarGeometry
        |_ BaseGeometry
        |_ object

for i, cls in enumerate(inspect.getmro(EllipsoidGeometry)):
    print(cls.__name__, "which defines:")

    for method, _ in inspect.getmembers(cls, inspect.ismethod):
        print("\t", method)
    if cls.__name__ == "BaseGeometry":
        break
    print("inherits from", end=" ")

EllipsoidGeometry which defines:
         face_rotations
         get_phis
         reset_scafold
         update_all
inherits from ClosedSheetGeometry which defines:
         face_rotations
         get_phis
         reset_scafold
         update_all
         update_height
inherits from SheetGeometry which defines:
         face_rotations
         get_phis
         reset_scafold
         update_all
         update_height
inherits from PlanarGeometry which defines:
         get_phis
         update_all
inherits from BaseGeometry which defines:

fig, ax = sheet_view(sheet_3d, ["x", "y"],
                     mode="quick", edge={"color": 'k'})

from tyssue.draw.ipv_draw import view_ipv
import ipyvolume as ipv
ipv.clear()

fig, mesh = sheet_view(ellipso, mode="3D")
fig

Monolayer

from tyssue import Monolayer
from tyssue.generation import extrude

extruded = extrude(sheet_3d.datasets, method='translation')
specs = config.geometry.bulk_spec()
monolayer = Monolayer('mono', extruded, specs)

mono_ellipso = Monolayer('ell', extrude(ellipso.datasets, method='homotecy', scale=0.9))
mono_ellipso.vert_df['z'] += 5
from tyssue.draw.ipv_draw import view_ipv
import ipyvolume as ipv
ipv.clear()
fig2, mesh = sheet_view(monolayer, mode="3D")
fig2, mesh = sheet_view(mono_ellipso, mode="3D")

fig2

Bulk tissue

from tyssue import Epithelium, BulkGeometry
from tyssue.generation import from_3d_voronoi, hexa_grid3d
from tyssue.draw import highlight_cells
from scipy.spatial import Voronoi

cells = hexa_grid3d(4, 4, 6)
datasets = from_3d_voronoi(Voronoi(cells))
specs = config.geometry.bulk_spec()
bulk = Epithelium('bulk', datasets, specs)
bulk.reset_topo()
bulk.reset_index()
bulk.sanitize()
bulk.reset_topo()
bulk.reset_index()


BulkGeometry.update_all(bulk)

bulk.face_df['visible'] = False

highlight_cells(bulk, [12, 4])
ipv.clear()
fig2, mesh = sheet_view(bulk, mode="3D",
                        face={"visible":True})
fig2