def voxelize(source, dx=0.25, xlo=None, xhi=None, ylo=None, yhi=None, zlo=None, zhi=None, n_soma_step=100):
"""
Generates a cartesian mesh of the volume of a neuron.
Parameters
----------
source : :func:`list`, ``nrn.SectionList``, or ``nrn.Import3D``
The geometry to mesh.
dx : double, optional
Mesh step size.
xlo : double, optional
Minimum x value. If omitted or None, uses minimum x value in the geometry.
xhi : double, optional
Maximum x value. If omitted or None, uses maximum x value in the geometry.
ylo : double, optional
Minimum y value. If omitted or None, uses minimum y value in the geometry.
yhi : double, optional
Maximum y value. If omitted or None, uses maximum y value in the geometry.
zlo : double, optional
Minimum z value. If omitted or None, uses minimum z value in the geometry.
zhi : double, optional
Maximum z value. If omitted or None, uses maximum z value in the geometry.
n_soma_step : integer, optional
Number of pieces to slice a soma outline into.
Returns
-------
result : :class:`ScalarField`
The mesh. Values are scalars, but may be used as True inside the
geometry and False outside.
Examples
--------
Basic usage:
>>> mesh = geometry3d.voxelize(h.allsec())
Full example, using :mod:`pyplot`:
>>> s1, s2, s3 = [h.Section() for i in xrange(3)]
>>> for sec in [s2, s3]: ignore_return = sec.connect(s1)
...
>>> for sec in h.allsec():
... sec.diam = 1
... sec.L = 5
...
>>> mesh = geometry3d.voxelize(h.allsec(), dx=.1)
>>> for i in xrange(10):
... ignore_return = pyplot.subplot(2, 5, i + 1)
... ignore_return = pyplot.imshow(mesh.values[:, :, i])
... ignore_return = pyplot.xticks([])
... ignore_return = pyplot.yticks([])
...
>>> pyplot.show()
.. plot::
from neuron import h
from matplotlib import pyplot
import geometry3d
s1, s2, s3 = [h.Section() for i in xrange(3)]
for sec in [s2, s3]: ignore_return = sec.connect(s1)
for sec in h.allsec():
sec.diam = 1
sec.L = 5
mesh = geometry3d.voxelize(h.allsec(), dx=.1)
for i in xrange(10):
ignore_return = pyplot.subplot(2, 5, i + 1)
ignore_return = pyplot.imshow(mesh.values[:, :, i])
ignore_return = pyplot.xticks([])
ignore_return = pyplot.yticks([])
pyplot.show()
.. note::
The use of Import3D objects is recommended over lists of sections
because the former preserves the soma outline information while
the later does not. Up to one soma outline is currently supported.
"""
objects = ctng.constructive_neuronal_geometry(source, n_soma_step, dx)
if xlo is None: xlo = min(obj.xlo for obj in objects)
if ylo is None: ylo = min(obj.ylo for obj in objects)
if zlo is None: zlo = min(obj.zlo for obj in objects)
if xhi is None: xhi = max(obj.xhi for obj in objects)
if yhi is None: yhi = max(obj.yhi for obj in objects)
if zhi is None: zhi = max(obj.zhi for obj in objects)
mesh = scalarField.ScalarField(xlo, xhi, ylo, yhi, zlo, zhi, dx, dtype='B')
grid = mesh.values
# figure out which objects go with which x/y/z values
x_objs = {x: [obj for obj in objects if obj.xlo < x < obj.xhi] for x in mesh.xs}
y_objs = {y: [obj for obj in objects if obj.ylo < y < obj.yhi] for y in mesh.ys}
z_objs = {z: [obj for obj in objects if obj.zlo < z < obj.zhi] for z in mesh.zs}
for i, x in enumerate(mesh.xs):
x_obj = set(x_objs[x])
for j, y in enumerate(mesh.ys):
xy_obj = x_obj.intersection(y_objs[y])
for k, z in enumerate(mesh.zs):
grid[i, j, k] = is_inside(x, y, z, xy_obj.intersection(z_objs[z]))
return mesh
def surface(source, dx=0.25, internal_membranes=False, n_soma_step=100):
"""
Generates a triangularized mesh of the surface of a neuron.
Parameters
----------
source : :func:`list`, ``nrn.SectionList``, or ``nrn.Import3D``
The geometry to mesh.
dx : double, optional
Underlying mesh used to generate the triangles.
internal_membranes : [``True`` | ``False``], optional
Set to True to not remove internal membranes.
n_soma_step : integer, optional
Number of pieces to slice a soma outline into.
Returns
-------
result : :class:`TriangularMesh`
The mesh.
Examples
--------
A simple meshing of the entire NEURON morphology.
>>> tri_mesh = geometry3d.surface(h.allsec()) #doctest: +SKIP
Importing from Neurolucida with a coarser grid.
>>> h.load_file('stdlib.hoc')
1.0
>>> h.load_file('import3d.hoc')
1.0
>>> cell = h.Import3d_Neurolucida3()
>>> cell.input(filename_dot_asc)
>>> tri_mesh = geometry3d.surface(cell, dx=0.5)
Removal of the internal membranes is not necessary if the only
goal is to plot the surface; here we use :mod:`mayavi.mlab`.
>>> tri_mesh = geometry3d.surface([sec1, sec2, sec3],
... internal_membranes=True)
>>> mlab.triangular_mesh(tri_mesh.x, tri_mesh.y, tri_mesh.z,
... tri_mesh.faces, color=(1, 0, 0))
>>> mlab.show()
.. note::
The use of Import3D objects is recommended over lists of sections
because the former preserves the soma outline information while
the later does not. Up to one soma outline is currently supported.
"""
objects = ctng.constructive_neuronal_geometry(source, n_soma_step, dx)
xlo = min(obj.xlo for obj in objects)
ylo = min(obj.ylo for obj in objects)
zlo = min(obj.zlo for obj in objects)
xhi = max(obj.xhi for obj in objects)
yhi = max(obj.yhi for obj in objects)
zhi = max(obj.zhi for obj in objects)
# I'm implicitly taking dx = dy = dz here
# NOTE: triangulate_surface requires consistent discretization
xs = numpy.arange(xlo - 3 * dx, xhi + 3 * dx, dx)
ys = numpy.arange(ylo - 3 * dx, yhi + 3 * dx, dx)
zs = numpy.arange(zlo - 3 * dx, zhi + 3 * dx, dx)
return triangularMesh.TriangularMesh(
surfaces.triangulate_surface(objects, xs, ys, zs, internal_membranes))
def surface(source, dx=0.25, internal_membranes=False, n_soma_step=100):
"""
Generates a triangularized mesh of the surface of a neuron.
Parameters
----------
source : :func:`list`, ``nrn.SectionList``, or ``nrn.Import3D``
The geometry to mesh.
dx : double, optional
Underlying mesh used to generate the triangles.
internal_membranes : [``True`` | ``False``], optional
Set to True to not remove internal membranes.
n_soma_step : integer, optional
Number of pieces to slice a soma outline into.
Returns
-------
result : :class:`TriangularMesh`
The mesh.
Examples
--------
A simple meshing of the entire NEURON morphology.
>>> tri_mesh = geometry3d.surface(h.allsec()) #doctest: +SKIP
Importing from Neurolucida with a coarser grid.
>>> h.load_file('stdlib.hoc')
1.0
>>> h.load_file('import3d.hoc')
1.0
>>> cell = h.Import3d_Neurolucida3()
>>> cell.input(filename_dot_asc)
>>> tri_mesh = geometry3d.surface(cell, dx=0.5)
Removal of the internal membranes is not necessary if the only
goal is to plot the surface; here we use :mod:`mayavi.mlab`.
>>> tri_mesh = geometry3d.surface([sec1, sec2, sec3],
... internal_membranes=True)
>>> mlab.triangular_mesh(tri_mesh.x, tri_mesh.y, tri_mesh.z,
... tri_mesh.faces, color=(1, 0, 0))
>>> mlab.show()
.. note::
The use of Import3D objects is recommended over lists of sections
because the former preserves the soma outline information while
the later does not. Up to one soma outline is currently supported.
"""
objects = ctng.constructive_neuronal_geometry(source, n_soma_step, dx)
xlo = min(obj.xlo for obj in objects)
ylo = min(obj.ylo for obj in objects)
zlo = min(obj.zlo for obj in objects)
xhi = max(obj.xhi for obj in objects)
yhi = max(obj.yhi for obj in objects)
zhi = max(obj.zhi for obj in objects)
# I'm implicitly taking dx = dy = dz here
# NOTE: triangulate_surface requires consistent discretization
xs = numpy.arange(xlo - 3 * dx, xhi + 3 * dx, dx)
ys = numpy.arange(ylo - 3 * dx, yhi + 3 * dx, dx)
zs = numpy.arange(zlo - 3 * dx, zhi + 3 * dx, dx)
return triangularMesh.TriangularMesh(surfaces.triangulate_surface(objects, xs, ys, zs, internal_membranes))
def voxelize2(source,
dx=0.25,
xlo=None,
xhi=None,
ylo=None,
yhi=None,
zlo=None,
zhi=None,
n_soma_step=100):
"""
Generates a cartesian mesh of the volume of a neuron, together with discretized information on
surface areas and volumes. This is more accurate than voxelize, which only checks the center
point of a voxel, but it is slower.
Parameters
----------
source : :func:`list`, ``nrn.SectionList``, or ``nrn.Import3D``
The geometry to mesh.
dx : double, optional
Mesh step size.
xlo : double, optional
Minimum x value. If omitted or None, uses minimum x value in the geometry.
xhi : double, optional
Maximum x value. If omitted or None, uses maximum x value in the geometry.
ylo : double, optional
Minimum y value. If omitted or None, uses minimum y value in the geometry.
yhi : double, optional
Maximum y value. If omitted or None, uses maximum y value in the geometry.
zlo : double, optional
Minimum z value. If omitted or None, uses minimum z value in the geometry.
zhi : double, optional
Maximum z value. If omitted or None, uses maximum z value in the geometry.
n_soma_step : integer, optional
Number of pieces to slice a soma outline into.
Returns
-------
mesh : :class:`ScalarField`
The mesh. Values are scalars, but may be used as True inside the
geometry and False outside.
surface_areas : :class:`ScalarField`
The total surface area passing through the node.
volumes : :class:`ScalarField`
The volume of the neuron contained in the given node.
Examples
--------
Basic usage:
>>> mesh, surface_areas, volumes = geometry3d.voxelize2(h.allsec())
Full example, using :mod:`pyplot`:
>>> s1, s2, s3 = [h.Section() for i in xrange(3)]
>>> for sec in [s2, s3]: ignore_return = sec.connect(s1)
...
>>> for sec in h.allsec():
... sec.diam = 1
... sec.L = 5
...
>>> mesh = geometry3d.voxelize2(h.allsec(), dx=.1)[0]
>>> for i in xrange(10):
... ignore_return = pyplot.subplot(2, 5, i + 1)
... ignore_return = pyplot.imshow(mesh.values[:, :, i])
... ignore_return = pyplot.xticks([])
... ignore_return = pyplot.yticks([])
...
>>> pyplot.show()
.. plot::
from neuron import h
from matplotlib import pyplot
import geometry3d
s1, s2, s3 = [h.Section() for i in xrange(3)]
for sec in [s2, s3]: ignore_return = sec.connect(s1)
for sec in h.allsec():
sec.diam = 1
sec.L = 5
mesh = geometry3d.voxelize2(h.allsec(), dx=.1)[0]
for i in xrange(10):
ignore_return = pyplot.subplot(2, 5, i + 1)
ignore_return = pyplot.imshow(mesh.values[:, :, i])
ignore_return = pyplot.xticks([])
ignore_return = pyplot.yticks([])
pyplot.show()
.. note::
The use of Import3D objects is recommended over lists of sections
because the former preserves the soma outline information while
the later does not. Up to one soma outline is currently supported.
"""
objects = ctng.constructive_neuronal_geometry(source, n_soma_step, dx)
if xlo is None: xlo = min(obj.xlo for obj in objects) - 3 * dx
if ylo is None: ylo = min(obj.ylo for obj in objects) - 3 * dx
if zlo is None: zlo = min(obj.zlo for obj in objects) - 3 * dx
if xhi is None: xhi = max(obj.xhi for obj in objects) + 3 * dx
if yhi is None: yhi = max(obj.yhi for obj in objects) + 3 * dx
if zhi is None: zhi = max(obj.zhi for obj in objects) + 3 * dx
mesh = scalarField.ScalarField(xlo, xhi, ylo, yhi, zlo, zhi, dx, dtype='B')
grid = mesh.values
xs, ys, zs = mesh.xs, mesh.ys, mesh.zs
# use chunks no smaller than 10 voxels across, but aim for max_chunks chunks
chunk_size = max(
10,
int((len(mesh.xs) * len(mesh.ys) * len(mesh.zs) / _max_chunks)**(1 /
3.)))
chunk_objs, nx, ny, nz = chunkify(objects, mesh.xs, mesh.ys, mesh.zs,
chunk_size, dx)
# this is the crude volumetric approach shared with voxelize
for i, x in enumerate(mesh.xs):
chunk_objsa = chunk_objs[i // chunk_size]
for j, y in enumerate(mesh.ys):
chunk_objsb = chunk_objsa[j // chunk_size]
for k, z in enumerate(mesh.zs):
grid[i, j, k] = is_inside(x, y, z,
chunk_objsb[k // chunk_size])
surface_areas = scalarField.ScalarField(xlo, xhi, ylo, yhi, zlo, zhi, dx)
sa_grid = surface_areas.values
# triangulate the surface
triangles = surfaces._triangulate_surface_given_chunks(
objects, xs, ys, zs, False, chunk_size, chunk_objs, nx, ny, nz, True,
sa_grid)
# for each triangle, compute the area. Add it to the appropriate spots in sa_grid
# TODO: move this to C? or at least cythonize it?
for tdata in triangles.reshape(len(triangles) / 9, 9):
v0, v1, v2 = tdata[0:3], tdata[3:6], tdata[6:9]
centerx, centery, centerz = (v0 + v1 + v2) / 3
i, j, k = (centerx - xlo) / dx, (centery - ylo) / dx, (centerz -
zlo) / dx
sa_grid[i, j, k] += 0.5 * norm(numpy.cross(v1 - v0, v2 - v0))
# now ensure that any grid containing surface is included in the voxelization
# TODO: change this when supporting multiple non-overlapping regions in one 3d Domain
grid[sa_grid.nonzero()] = 1
volumes = scalarField.ScalarField(xlo, xhi, ylo, yhi, zlo, zhi, dx)
volume_values = volumes.values
# TODO: compute the correct partial volumes for nodes on the boundary
# start out with the full volumes for every place that contains volume
volume_values[grid.nonzero()] = dx**3
# correct the boundary node volumes
#surface_nodes = sa_grid.nonzero()
#for i, j, k in zip(*surface_nodes):
# volume_values[i, j, k] = surfaces.volume_inside_cell(i, j, k, chunk_objs[i // chunk_size][j // chunk_size][k // chunk_size], xs, ys, zs)
return mesh, surface_areas, volumes, triangles.reshape(
len(triangles) / 9, 9)
def voxelize2(source, dx=0.25, xlo=None, xhi=None, ylo=None, yhi=None, zlo=None, zhi=None, n_soma_step=100):
"""
Generates a cartesian mesh of the volume of a neuron, together with discretized information on
surface areas and volumes. This is more accurate than voxelize, which only checks the center
point of a voxel, but it is slower.
Parameters
----------
source : :func:`list`, ``nrn.SectionList``, or ``nrn.Import3D``
The geometry to mesh.
dx : double, optional
Mesh step size.
xlo : double, optional
Minimum x value. If omitted or None, uses minimum x value in the geometry.
xhi : double, optional
Maximum x value. If omitted or None, uses maximum x value in the geometry.
ylo : double, optional
Minimum y value. If omitted or None, uses minimum y value in the geometry.
yhi : double, optional
Maximum y value. If omitted or None, uses maximum y value in the geometry.
zlo : double, optional
Minimum z value. If omitted or None, uses minimum z value in the geometry.
zhi : double, optional
Maximum z value. If omitted or None, uses maximum z value in the geometry.
n_soma_step : integer, optional
Number of pieces to slice a soma outline into.
Returns
-------
mesh : :class:`ScalarField`
The mesh. Values are scalars, but may be used as True inside the
geometry and False outside.
surface_areas : :class:`ScalarField`
The total surface area passing through the node.
volumes : :class:`ScalarField`
The volume of the neuron contained in the given node.
Examples
--------
Basic usage:
>>> mesh, surface_areas, volumes = geometry3d.voxelize2(h.allsec())
Full example, using :mod:`pyplot`:
>>> s1, s2, s3 = [h.Section() for i in xrange(3)]
>>> for sec in [s2, s3]: ignore_return = sec.connect(s1)
...
>>> for sec in h.allsec():
... sec.diam = 1
... sec.L = 5
...
>>> mesh = geometry3d.voxelize2(h.allsec(), dx=.1)[0]
>>> for i in xrange(10):
... ignore_return = pyplot.subplot(2, 5, i + 1)
... ignore_return = pyplot.imshow(mesh.values[:, :, i])
... ignore_return = pyplot.xticks([])
... ignore_return = pyplot.yticks([])
...
>>> pyplot.show()
.. plot::
from neuron import h
from matplotlib import pyplot
import geometry3d
s1, s2, s3 = [h.Section() for i in xrange(3)]
for sec in [s2, s3]: ignore_return = sec.connect(s1)
for sec in h.allsec():
sec.diam = 1
sec.L = 5
mesh = geometry3d.voxelize2(h.allsec(), dx=.1)[0]
for i in xrange(10):
ignore_return = pyplot.subplot(2, 5, i + 1)
ignore_return = pyplot.imshow(mesh.values[:, :, i])
ignore_return = pyplot.xticks([])
ignore_return = pyplot.yticks([])
pyplot.show()
.. note::
The use of Import3D objects is recommended over lists of sections
because the former preserves the soma outline information while
the later does not. Up to one soma outline is currently supported.
"""
objects = ctng.constructive_neuronal_geometry(source, n_soma_step, dx)
if xlo is None: xlo = min(obj.xlo for obj in objects) - 3 * dx
if ylo is None: ylo = min(obj.ylo for obj in objects) - 3 * dx
if zlo is None: zlo = min(obj.zlo for obj in objects) - 3 * dx
if xhi is None: xhi = max(obj.xhi for obj in objects) + 3 * dx
if yhi is None: yhi = max(obj.yhi for obj in objects) + 3 * dx
if zhi is None: zhi = max(obj.zhi for obj in objects) + 3 * dx
mesh = scalarField.ScalarField(xlo, xhi, ylo, yhi, zlo, zhi, dx, dtype='B')
grid = mesh.values
xs, ys, zs = mesh.xs, mesh.ys, mesh.zs
# use chunks no smaller than 10 voxels across, but aim for max_chunks chunks
chunk_size = max(10, int((len(mesh.xs) * len(mesh.ys) * len(mesh.zs) / _max_chunks) ** (1 / 3.)))
chunk_objs, nx, ny, nz = chunkify(objects, mesh.xs, mesh.ys, mesh.zs, chunk_size, dx)
# this is the crude volumetric approach shared with voxelize
for i, x in enumerate(mesh.xs):
chunk_objsa = chunk_objs[i // chunk_size]
for j, y in enumerate(mesh.ys):
chunk_objsb = chunk_objsa[j // chunk_size]
for k, z in enumerate(mesh.zs):
grid[i, j, k] = is_inside(x, y, z, chunk_objsb[k // chunk_size])
surface_areas = scalarField.ScalarField(xlo, xhi, ylo, yhi, zlo, zhi, dx)
sa_grid = surface_areas.values
# triangulate the surface
triangles = surfaces._triangulate_surface_given_chunks(objects, xs, ys, zs, False, chunk_size, chunk_objs, nx, ny, nz, True, sa_grid)
# for each triangle, compute the area. Add it to the appropriate spots in sa_grid
# TODO: move this to C? or at least cythonize it?
for tdata in triangles.reshape(len(triangles) / 9, 9):
v0, v1, v2 = tdata[0 : 3], tdata[3 : 6], tdata[6 : 9]
centerx, centery, centerz = (v0 + v1 + v2) / 3
i, j, k = (centerx - xlo) / dx, (centery - ylo) / dx, (centerz - zlo) / dx
sa_grid[i, j, k] += 0.5 * norm(numpy.cross(v1 - v0, v2 - v0))
# now ensure that any grid containing surface is included in the voxelization
# TODO: change this when supporting multiple non-overlapping regions in one 3d Domain
grid[sa_grid.nonzero()] = 1
volumes = scalarField.ScalarField(xlo, xhi, ylo, yhi, zlo, zhi, dx)
volume_values = volumes.values
# TODO: compute the correct partial volumes for nodes on the boundary
# start out with the full volumes for every place that contains volume
volume_values[grid.nonzero()] = dx ** 3
# correct the boundary node volumes
#surface_nodes = sa_grid.nonzero()
#for i, j, k in zip(*surface_nodes):
# volume_values[i, j, k] = surfaces.volume_inside_cell(i, j, k, chunk_objs[i // chunk_size][j // chunk_size][k // chunk_size], xs, ys, zs)
return mesh, surface_areas, volumes, triangles.reshape(len(triangles) / 9, 9)
def voxelize(source, dx=0.25, xlo=None, xhi=None, ylo=None, yhi=None, zlo=None, zhi=None, n_soma_step=100):
"""
Generates a cartesian mesh of the volume of a neuron.
Parameters
----------
source : :func:`list`, ``nrn.SectionList``, or ``nrn.Import3D``
The geometry to mesh.
dx : double, optional
Mesh step size.
xlo : double, optional
Minimum x value. If omitted or None, uses minimum x value in the geometry.
xhi : double, optional
Maximum x value. If omitted or None, uses maximum x value in the geometry.
ylo : double, optional
Minimum y value. If omitted or None, uses minimum y value in the geometry.
yhi : double, optional
Maximum y value. If omitted or None, uses maximum y value in the geometry.
zlo : double, optional
Minimum z value. If omitted or None, uses minimum z value in the geometry.
zhi : double, optional
Maximum z value. If omitted or None, uses maximum z value in the geometry.
n_soma_step : integer, optional
Number of pieces to slice a soma outline into.
Returns
-------
result : :class:`ScalarField`
The mesh. Values are scalars, but may be used as True inside the
geometry and False outside.
Examples
--------
Basic usage:
>>> mesh = geometry3d.voxelize(h.allsec())
Full example, using :mod:`pyplot`:
>>> s1, s2, s3 = [h.Section() for i in xrange(3)]
>>> for sec in [s2, s3]: ignore_return = sec.connect(s1)
...
>>> for sec in h.allsec():
... sec.diam = 1
... sec.L = 5
...
>>> mesh = geometry3d.voxelize(h.allsec(), dx=.1)
>>> for i in xrange(10):
... ignore_return = pyplot.subplot(2, 5, i + 1)
... ignore_return = pyplot.imshow(mesh.values[:, :, i])
... ignore_return = pyplot.xticks([])
... ignore_return = pyplot.yticks([])
...
>>> pyplot.show()
.. plot::
from neuron import h
from matplotlib import pyplot
import geometry3d
s1, s2, s3 = [h.Section() for i in xrange(3)]
for sec in [s2, s3]: ignore_return = sec.connect(s1)
for sec in h.allsec():
sec.diam = 1
sec.L = 5
mesh = geometry3d.voxelize(h.allsec(), dx=.1)
for i in xrange(10):
ignore_return = pyplot.subplot(2, 5, i + 1)
ignore_return = pyplot.imshow(mesh.values[:, :, i])
ignore_return = pyplot.xticks([])
ignore_return = pyplot.yticks([])
pyplot.show()
.. note::
The use of Import3D objects is recommended over lists of sections
because the former preserves the soma outline information while
the later does not. Up to one soma outline is currently supported.
"""
objects = ctng.constructive_neuronal_geometry(source, n_soma_step, dx)
if xlo is None: xlo = min(obj.xlo for obj in objects)
if ylo is None: ylo = min(obj.ylo for obj in objects)
if zlo is None: zlo = min(obj.zlo for obj in objects)
if xhi is None: xhi = max(obj.xhi for obj in objects)
if yhi is None: yhi = max(obj.yhi for obj in objects)
if zhi is None: zhi = max(obj.zhi for obj in objects)
mesh = scalarField.ScalarField(xlo, xhi, ylo, yhi, zlo, zhi, dx, dtype='B')
grid = mesh.values
# use chunks no smaller than 10 voxels across, but aim for max_chunks chunks
chunk_size = max(10, int((len(mesh.xs) * len(mesh.ys) * len(mesh.zs) / _max_chunks) ** (1 / 3.)))
chunk_objs, nx, ny, nz = chunkify(objects, mesh.xs, mesh.ys, mesh.zs, chunk_size, dx)
for i, x in enumerate(mesh.xs):
chunk_objsa = chunk_objs[i // chunk_size]
for j, y in enumerate(mesh.ys):
chunk_objsb = chunk_objsa[j // chunk_size]
for k, z in enumerate(mesh.zs):
grid[i, j, k] = is_inside(x, y, z, chunk_objsb[k // chunk_size])
return mesh