discretize.base.BaseRectangularMesh

class discretize.base.BaseRectangularMesh(*args, **kwargs)[source]

Bases: discretize.base.base_mesh.BaseMesh

BaseRectangularMesh

Required Properties:

  • axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X

  • axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y

  • axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z

  • origin (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

  • reference_system (String): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesian

Attributes
axis_u

axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X

axis_v

axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y

axis_w

axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z

dim

The dimension of the mesh (1, 2, or 3).

edge_tangents

Edge Tangents

face_normals

Face Normals

nCx

Number of cells in the x direction

nCy

Number of cells in the y direction

nCz

Number of cells in the z direction

nNx

Number of nodes in the x-direction

nNy

Number of nodes in the y-direction

nNz

Number of nodes in the z-direction

n_cells

Total number of cells in the mesh.

n_edges

Total number of edges.

n_edges_per_direction

The number of edges in each direction

n_edges_x

Number of x-edges

n_edges_y

Number of y-edges

n_edges_z

Number of z-edges

n_faces

Total number of faces.

n_faces_per_direction

The number of faces in each direction

n_faces_x

Number of x-faces

n_faces_y

Number of y-faces

n_faces_z

Number of z-faces

n_nodes

Total number of nodes

normals

normals has been deprecated. See face_normals for documentation

origin

origin (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

reference_is_rotated

True if the axes are rotated from the traditional <X,Y,Z> system

reference_system

reference_system (String): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesian

rotation_matrix

Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system.

shape_cells

The number of cells in each direction

shape_edges_x

Number of x-edges in each direction

shape_edges_y

Number of y-edges in each direction

shape_edges_z

Number of z-edges in each direction

shape_faces_x

Number of x-faces in each direction

shape_faces_y

Number of y-faces in each direction

shape_faces_z

Number of z-faces in each direction

shape_nodes

Number of nodes in each direction

tangents

tangents has been deprecated. See edge_tangents for documentation

x0

Methods

copy()

Make a copy of the current mesh

deserialize(value, **kwargs)

Creates HasProperties instance from serialized dictionary

equal(other)

Determine if two HasProperties instances are equivalent

from_omf(element)

Convert an OMF element to it’s proper discretize type.

plotGrid(*args, **kwargs)

plotGrid has been deprecated.

plotImage(*args, **kwargs)

plotImage has been deprecated.

plotSlice(*args, **kwargs)

plotSlice has been deprecated.

plot_3d_slicer(v[, xslice, yslice, zslice, …])

Plot slices of a 3D volume, interactively (scroll wheel).

plot_grid([ax, nodes, faces, centers, …])

Plot the nodal, cell-centered and staggered grids.

plot_image(v[, v_type, grid, view, ax, …])

Plots fields on the given mesh.

plot_slice(v[, v_type, normal, ind, …])

Plots slice of fields on the given 3D mesh.

projectEdgeVector(*args, **kwargs)

projectEdgeVector has been deprecated.

projectFaceVector(*args, **kwargs)

projectFaceVector has been deprecated.

project_edge_vector(edge_vector)

Project vectors onto the edges of the mesh

project_face_vector(face_vector)

Project vectors onto the faces of the mesh.

r(*args, **kwargs)

r has been deprecated.

reshape(x[, x_type, out_type, format])

A quick reshape command that will do the best it can at giving you what you want.

save([file_name, verbose])

Save the mesh to json :param str file: file_name for saving the casing properties :param str directory: working directory for saving the file

serialize([include_class, save_dynamic])

Serializes a HasProperties instance to dictionary

toVTK([models])

Convert this mesh object to it’s proper VTK or pyvista data object with the given model dictionary as the cell data of that dataset.

to_omf([models])

Convert this mesh object to it’s proper omf data object with the given model dictionary as the cell data of that dataset.

to_vtk([models])

Convert this mesh object to it’s proper VTK or pyvista data object with the given model dictionary as the cell data of that dataset.

validate()

Call all registered class validator methods

writeVTK(file_name[, models, directory])

Makes and saves a VTK object from this mesh and given models

write_vtk(file_name[, models, directory])

Makes and saves a VTK object from this mesh and given models

Attributes

BaseRectangularMesh.axis_u

axis_u (Vector3): Vector orientation of u-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: X

BaseRectangularMesh.axis_v

axis_v (Vector3): Vector orientation of v-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Y

BaseRectangularMesh.axis_w

axis_w (Vector3): Vector orientation of w-direction. For more details see the docs for the rotation_matrix property., a 3D Vector of <class ‘float’> with shape (3), Default: Z

BaseRectangularMesh.dim

The dimension of the mesh (1, 2, or 3).

Returns
int

dimension of the mesh

BaseRectangularMesh.edge_tangents

Edge Tangents

Returns
numpy.ndarray

normals, (n_edges, dim)

BaseRectangularMesh.face_normals

Face Normals

Returns
numpy.ndarray

normals, (n_faces, dim)

BaseRectangularMesh.nCx

Number of cells in the x direction

Returns
int

Deprecated since version 0.5.0: nCx will be removed in discretize 1.0.0, it is replaced by mesh.shape_cells[0] to reduce namespace clutter.

BaseRectangularMesh.nCy

Number of cells in the y direction

Returns
int or None

None if dim < 2

Deprecated since version 0.5.0: nCy will be removed in discretize 1.0.0, it is replaced by mesh.shape_cells[1] to reduce namespace clutter.

BaseRectangularMesh.nCz

Number of cells in the z direction

Returns
int or None

None if dim < 3

Deprecated since version 0.5.0: nCz will be removed in discretize 1.0.0, it is replaced by mesh.shape_cells[2] to reduce namespace clutter.

BaseRectangularMesh.nNx

Number of nodes in the x-direction

Returns
int

Deprecated since version 0.5.0: nNx will be removed in discretize 1.0.0, it is replaced by mesh.shape_nodes[0] to reduce namespace clutter.

BaseRectangularMesh.nNy

Number of nodes in the y-direction

Returns
int or None

None if dim < 2

Deprecated since version 0.5.0: nNy will be removed in discretize 1.0.0, it is replaced by mesh.shape_nodes[1] to reduce namespace clutter.

BaseRectangularMesh.nNz

Number of nodes in the z-direction

Returns
int or None

None if dim < 3

Deprecated since version 0.5.0: nNz will be removed in discretize 1.0.0, it is replaced by mesh.shape_nodes[2] to reduce namespace clutter.

BaseRectangularMesh.n_cells
BaseRectangularMesh.n_edges

Total number of edges.

Returns
int

sum([n_edges_x, n_edges_y, n_edges_z])

Notes

Also accessible as nE.

BaseRectangularMesh.n_edges_per_direction

The number of edges in each direction

Returns
n_edges_per_directiontuple

[n_edges_x, n_edges_y, n_edges_z], (dim, )

Notes

Also accessible as vnE.

Examples

>>> import discretize
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> M = discretize.TensorMesh([np.ones(n) for n in [2,3]])
>>> M.plot_grid(edges=True, show_it=True)

(Source code, png, pdf)

../../_images/discretize-base-BaseRectangularMesh-1.png
BaseRectangularMesh.n_edges_x
BaseRectangularMesh.n_edges_y
BaseRectangularMesh.n_edges_z
BaseRectangularMesh.n_faces

Total number of faces.

Returns
int

sum([n_faces_x, n_faces_y, n_faces_z])

Notes

Also accessible as nF.

BaseRectangularMesh.n_faces_per_direction

The number of faces in each direction

Returns
n_faces_per_directiontuple

[n_faces_x, n_faces_y, n_faces_z], (dim, )

Notes

Also accessible as vnF.

Examples

>>> import discretize
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> M = discretize.TensorMesh([np.ones(n) for n in [2,3]])
>>> M.plot_grid(faces=True, show_it=True)

(Source code, png, pdf)

../../_images/discretize-base-BaseRectangularMesh-2.png
BaseRectangularMesh.n_faces_x
BaseRectangularMesh.n_faces_y
BaseRectangularMesh.n_faces_z
BaseRectangularMesh.n_nodes
BaseRectangularMesh.normals

normals has been deprecated. See face_normals for documentation

BaseRectangularMesh.origin

origin (Array): origin of the mesh (dim, ), a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

BaseRectangularMesh.reference_is_rotated

True if the axes are rotated from the traditional <X,Y,Z> system with vectors of \((1,0,0)\), \((0,1,0)\), and \((0,0,1)\)

BaseRectangularMesh.reference_system

reference_system (String): The type of coordinate reference frame. Can take on the values cartesian, cylindrical, or spherical. Abbreviations of these are allowed., a unicode string, Default: cartesian

BaseRectangularMesh.rotation_matrix

Builds a rotation matrix to transform coordinates from their coordinate system into a conventional cartesian system. This is built off of the three axis_u, axis_v, and axis_w properties; these mapping coordinates use the letters U, V, and W (the three letters preceding X, Y, and Z in the alphabet) to define the projection of the X, Y, and Z durections. These UVW vectors describe the placement and transformation of the mesh’s coordinate sytem assuming at most 3 directions.

Why would you want to use these UVW mapping vectors the this rotation_matrix property? They allow us to define the realationship between local and global coordinate systems and provide a tool for switching between the two while still maintaing the connectivity of the mesh’s cells. For a visual example of this, please see the figure in the docs for the InterfaceVTK.

BaseRectangularMesh.shape_cells

The number of cells in each direction

Returns
tuple of ints

Notes

Also accessible as vnC.

BaseRectangularMesh.shape_edges_x

Number of x-edges in each direction

Returns
tuple of int

(nx_cells, ny_nodes, nz_nodes)

Notes

Also accessible as vnEx.

BaseRectangularMesh.shape_edges_y

Number of y-edges in each direction

Returns
tuple of int or None

(nx_nodes, ny_cells, nz_nodes), None if dim < 2

Notes

Also accessible as vnEy.

BaseRectangularMesh.shape_edges_z

Number of z-edges in each direction

Returns
tuple of int or None

(nx_nodes, ny_nodes, nz_cells), None if dim < 3

Notes

Also accessible as vnEz.

BaseRectangularMesh.shape_faces_x

Number of x-faces in each direction

Returns
tuple of int

(nx_nodes, ny_cells, nz_cells)

Notes

Also accessible as vnFx.

BaseRectangularMesh.shape_faces_y

Number of y-faces in each direction

Returns
tuple of int or None

(nx_cells, ny_nodes, nz_cells), None if dim < 2

Notes

Also accessible as vnFy.

BaseRectangularMesh.shape_faces_z

Number of z-faces in each direction

Returns
tuple of int or None

(nx_cells, ny_cells, nz_nodes), None if dim < 3

Notes

Also accessible as vnFz.

BaseRectangularMesh.shape_nodes

Number of nodes in each direction

Returns
tuple of int

Notes

Also accessible as vnN.

BaseRectangularMesh.tangents

tangents has been deprecated. See edge_tangents for documentation

BaseRectangularMesh.x0

Methods

BaseRectangularMesh.copy()

Make a copy of the current mesh

classmethod BaseRectangularMesh.deserialize(value, **kwargs)

Creates HasProperties instance from serialized dictionary

This uses the Property deserializers to deserialize all JSON-compatible dictionary values into their corresponding Property values on a new instance of a HasProperties class. Extra keys in the dictionary that do not correspond to Properties will be ignored.

Parameters:

  • value - Dictionary to deserialize new instance from.

  • trusted - If True (and if the input dictionary has '__class__' keyword and this class is in the registry), the new HasProperties class will come from the dictionary. If False (the default), only the HasProperties class this method is called on will be constructed.

  • strict - Requires '__class__', if present on the input dictionary, to match the deserialized instance’s class. Also disallows unused properties in the input dictionary. Default is False.

  • assert_valid - Require deserialized instance to be valid. Default is False.

  • Any other keyword arguments will be passed through to the Property deserializers.

BaseRectangularMesh.equal(other)

Determine if two HasProperties instances are equivalent

Equivalence is determined by checking if all Property values on two instances are equal, using Property.equal.

static BaseRectangularMesh.from_omf(element)

Convert an OMF element to it’s proper discretize type. Automatically determines the output type. Returns both the mesh and a dictionary of model arrays.

BaseRectangularMesh.plotGrid(*args, **kwargs)

plotGrid has been deprecated. See plot_grid for documentation

BaseRectangularMesh.plotImage(*args, **kwargs)

plotImage has been deprecated. See plot_image for documentation

BaseRectangularMesh.plotSlice(*args, **kwargs)

plotSlice has been deprecated. See plot_slice for documentation

BaseRectangularMesh.plot_3d_slicer(v, xslice=None, yslice=None, zslice=None, v_type='CC', view='real', axis='xy', transparent=None, clim=None, xlim=None, ylim=None, zlim=None, aspect='auto', grid=[2, 2, 1], pcolor_opts=None, fig=None, **kwargs)

Plot slices of a 3D volume, interactively (scroll wheel).

If called from a notebook, make sure to set

%matplotlib notebook

See the class discretize.View.Slicer for more information.

It returns nothing. However, if you need the different figure handles you can get it via

fig = plt.gcf()

and subsequently its children via

fig.get_children()

and recursively deeper, e.g.,

fig.get_children()[0].get_children().

One can also provide an existing figure instance, which can be useful for interactive widgets in Notebooks. The provided figure is cleared first.

BaseRectangularMesh.plot_grid(ax=None, nodes=False, faces=False, centers=False, edges=False, lines=True, show_it=False, **kwargs)

Plot the nodal, cell-centered and staggered grids.

Parameters
axmatplotlib.axes.Axes or None, optional

The axes to draw on. None produces a new Axes.

nodes, faces, centers, edges, linesbool, optional

Whether to plot the corresponding item

show_itbool, optional

whether to call plt.show()

colorColor or str, optional

If lines=True, the color of the lines, defaults to first color.

linewidthfloat, optional

If lines=True, the linewidth for the lines.

Returns
matplotlib.axes.Axes

Axes handle for the plot

Other Parameters
edges_x, edges_y, edges_z, faces_x, faces_y, faces_zbool, optional

When plotting a TreeMesh, these are also options to plot the individual component items.

cell_linebool, optional

When plotting a TreeMesh, you can also plot a line through the cell centers in order.

slice{‘both’, ‘theta’, ‘z’}

When plotting a CylindricalMesh, which dimension to slice over.

Notes

Excess arguments are passed on to plot

Examples

Plotting a 2D TensorMesh grid

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> import numpy as np
>>> h1 = np.linspace(.1, .5, 3)
>>> h2 = np.linspace(.1, .5, 5)
>>> mesh = discretize.TensorMesh([h1, h2])
>>> mesh.plot_grid(nodes=True, faces=True, centers=True, lines=True)
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-base-BaseRectangularMesh-3_00_00.png

Plotting a 3D TensorMesh grid

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> import numpy as np
>>> h1 = np.linspace(.1, .5, 3)
>>> h2 = np.linspace(.1, .5, 5)
>>> h3 = np.linspace(.1, .5, 3)
>>> mesh = discretize.TensorMesh([h1, h2, h3])
>>> mesh.plot_grid(nodes=True, faces=True, centers=True, lines=True)
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseRectangularMesh-3_01_00.png

Plotting a 2D CurvilinearMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> X, Y = discretize.utils.exampleLrmGrid([10, 10], 'rotate')
>>> M = discretize.CurvilinearMesh([X, Y])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseRectangularMesh-3_02_00.png

Plotting a 3D CurvilinearMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> X, Y, Z = discretize.utils.exampleLrmGrid([5, 5, 5], 'rotate')
>>> M = discretize.CurvilinearMesh([X, Y, Z])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseRectangularMesh-3_03_00.png

Plotting a 2D TreeMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> M = discretize.TreeMesh([32, 32])
>>> M.insert_cells([[0.25, 0.25]], [4])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseRectangularMesh-3_04_00.png

Plotting a 3D TreeMesh

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> M = discretize.TreeMesh([32, 32, 32])
>>> M.insert_cells([[0.3, 0.75, 0.22]], [4])
>>> M.plot_grid()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseRectangularMesh-3_05_00.png
BaseRectangularMesh.plot_image(v, v_type='CC', grid=False, view='real', ax=None, clim=None, show_it=False, pcolor_opts=None, stream_opts=None, grid_opts=None, range_x=None, range_y=None, sample_grid=None, stream_thickness=None, stream_threshold=None, **kwargs)

Plots fields on the given mesh.

Parameters
vnumpy.ndarray

values to plot

v_type{‘CC’,’CCV’, ‘N’, ‘F’, ‘Fx’, ‘Fy’, ‘Fz’, ‘E’, ‘Ex’, ‘Ey’, ‘Ez’}

Where the values of v are defined.

view{‘real’, ‘imag’, ‘abs’, ‘vec’}

How to view the array.

axmatplotlib.axes.Axes, optional

The axes to draw on. None produces a new Axes.

climtuple of float, optional

length 2 tuple of (vmin, vmax) for the color limits

range_x, range_ytuple of float, optional

length 2 tuple of (min, max) for the bounds of the plot axes.

pcolor_optsdict, optional

Arguments passed on to pcolormesh

gridbool, optional

Whether to plot the edges of the mesh cells.

grid_optsdict, optional

If grid is true, arguments passed on to plot for grid

sample_gridtuple of numpy.ndarray, optional

If view == ‘vec’, mesh cell widths (hx, hy) to interpolate onto for vector plotting

stream_optsdict, optional

If view == ‘vec’, arguments passed on to streamplot

stream_thicknessfloat, optional

If view == ‘vec’, linewidth for streamplot

stream_thresholdfloat, optional

If view == ‘vec’, only plots vectors with magnitude above this threshold

show_itbool, optional

Whether to call plt.show()

numberingbool, optional

For 3D TensorMesh only, show the numbering of the slices

annotation_colorColor or str, optional

For 3D TensorMesh only, color of the annotation

Examples

2D TensorMesh plotting

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> import numpy as np
>>> M = discretize.TensorMesh([20, 20])
>>> v = np.sin(M.gridCC[:, 0]*2*np.pi)*np.sin(M.gridCC[:, 1]*2*np.pi)
>>> M.plot_image(v)
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-base-BaseRectangularMesh-4_00_00.png

3D TensorMesh plotting

>>> import discretize
>>> import numpy as np
>>> M = discretize.TensorMesh([20, 20, 20])
>>> v = np.sin(M.gridCC[:, 0]*2*np.pi)*np.sin(M.gridCC[:, 1]*2*np.pi)*np.sin(M.gridCC[:, 2]*2*np.pi)
>>> M.plot_image(v, annotation_color='k')
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseRectangularMesh-4_01_00.png
BaseRectangularMesh.plot_slice(v, v_type='CC', normal='Z', ind=None, slice_loc=None, grid=False, view='real', ax=None, clim=None, show_it=False, pcolor_opts=None, stream_opts=None, grid_opts=None, range_x=None, range_y=None, sample_grid=None, stream_threshold=None, stream_thickness=None, **kwargs)

Plots slice of fields on the given 3D mesh.

Parameters
vnumpy.ndarray

values to plot

v_type{‘CC’,’CCV’, ‘N’, ‘F’, ‘Fx’, ‘Fy’, ‘Fz’, ‘E’, ‘Ex’, ‘Ey’, ‘Ez’}, or tuple of these options

Where the values of v are defined.

normal{‘Z’, ‘X’, ‘Y’}

Normal direction of slicing plane.

indNone, optional

index along dimension of slice. Defaults to the center index.

slice_locNone, optional

Value along dimension of slice. Defaults to the center of the mesh.

view{‘real’, ‘imag’, ‘abs’, ‘vec’}

How to view the array.

axmatplotlib.axes.Axes, optional

The axes to draw on. None produces a new Axes. Must be None if v_type is a tuple.

climtuple of float, optional

length 2 tuple of (vmin, vmax) for the color limits

range_x, range_ytuple of float, optional

length 2 tuple of (min, max) for the bounds of the plot axes.

pcolor_optsdict, optional

Arguments passed on to pcolormesh

gridbool, optional

Whether to plot the edges of the mesh cells.

grid_optsdict, optional

If grid is true, arguments passed on to plot for the edges

sample_gridtuple of numpy.ndarray, optional

If view == ‘vec’, mesh cell widths (hx, hy) to interpolate onto for vector plotting

stream_optsdict, optional

If view == ‘vec’, arguments passed on to streamplot

stream_thicknessfloat, optional

If view == ‘vec’, linewidth for streamplot

stream_thresholdfloat, optional

If view == ‘vec’, only plots vectors with magnitude above this threshold

show_itbool, optional

Whether to call plt.show()

Examples

Plot a slice of a 3D TensorMesh solution to a Laplace’s equaiton.

First build the mesh:

>>> from matplotlib import pyplot as plt
>>> import discretize
>>> from pymatsolver import Solver
>>> hx = [(5, 2, -1.3), (2, 4), (5, 2, 1.3)]
>>> hy = [(2, 2, -1.3), (2, 6), (2, 2, 1.3)]
>>> hz = [(2, 2, -1.3), (2, 6), (2, 2, 1.3)]
>>> M = discretize.TensorMesh([hx, hy, hz])

then build the necessary parts of the PDE:

>>> q = np.zeros(M.vnC)
>>> q[[4, 4], [4, 4], [2, 6]]=[-1, 1]
>>> q = discretize.utils.mkvc(q)
>>> A = M.face_divergence * M.cell_gradient
>>> b = Solver(A) * (q)

and finaly, plot the vector values of the result, which are defined on faces

>>> M.plot_slice(M.cell_gradient*b, 'F', view='vec', grid=True, pcolor_opts={'alpha':0.8})
>>> plt.show()

(Source code, png, pdf)

../../_images/discretize-base-BaseRectangularMesh-5_00_00.png

We can use the slice_loc kwarg to tell `plot_slice where to slice the mesh. Let’s create a mesh with a random model and plot slice of it. The slice_loc kwarg automatically determines the indices for slicing the mesh along a plane with the given normal.

>>> M = discretize.TensorMesh([32, 32, 32])
>>> v = discretize.utils.random_model(M.vnC, seed=789).reshape(-1, order='F')
>>> x_slice, y_slice, z_slice = 0.75, 0.25, 0.9
>>> plt.figure(figsize=(7.5, 3))
>>> ax = plt.subplot(131)
>>> M.plot_slice(v, normal='X', slice_loc=x_slice, ax=ax)
>>> ax = plt.subplot(132)
>>> M.plot_slice(v, normal='Y', slice_loc=y_slice, ax=ax)
>>> ax = plt.subplot(133)
>>> M.plot_slice(v, normal='Z', slice_loc=z_slice, ax=ax)
>>> plt.tight_layout()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseRectangularMesh-5_01_00.png

This also works for TreeMesh. We create a mesh here that is refined within three boxes, along with a base level of refinement.

>>> TM = discretize.TreeMesh([32, 32, 32])
>>> TM.refine(3, finalize=False)
>>> BSW = [[0.25, 0.25, 0.25], [0.15, 0.15, 0.15], [0.1, 0.1, 0.1]]
>>> TNE = [[0.75, 0.75, 0.75], [0.85, 0.85, 0.85], [0.9, 0.9, 0.9]]
>>> levels = [6, 5, 4]
>>> TM.refine_box(BSW, TNE, levels)
>>> v_TM = discretize.utils.volume_average(M, TM, v)
>>> plt.figure(figsize=(7.5, 3))
>>> ax = plt.subplot(131)
>>> TM.plot_slice(v_TM, normal='X', slice_loc=x_slice, ax=ax)
>>> ax = plt.subplot(132)
>>> TM.plot_slice(v_TM, normal='Y', slice_loc=y_slice, ax=ax)
>>> ax = plt.subplot(133)
>>> TM.plot_slice(v_TM, normal='Z', slice_loc=z_slice, ax=ax)
>>> plt.tight_layout()
>>> plt.show()

(png, pdf)

../../_images/discretize-base-BaseRectangularMesh-5_02_00.png
BaseRectangularMesh.projectEdgeVector(*args, **kwargs)

projectEdgeVector has been deprecated. See project_edge_vector for documentation

BaseRectangularMesh.projectFaceVector(*args, **kwargs)

projectFaceVector has been deprecated. See project_face_vector for documentation

BaseRectangularMesh.project_edge_vector(edge_vector)

Project vectors onto the edges of the mesh

Given a vector, edge_vector, in cartesian coordinates, this will project it onto the mesh using the tangents

Parameters
edge_vectornumpy.ndarray

edge vector with shape (n_edges, dim)

Returns
numpy.ndarray

projected edge vector, (n_edges, )

BaseRectangularMesh.project_face_vector(face_vector)

Project vectors onto the faces of the mesh.

Given a vector, face_vector, in cartesian coordinates, this will project it onto the mesh using the normals

Parameters
face_vectornumpy.ndarray

face vector with shape (n_faces, dim)

Returns
numpy.ndarray

projected face vector, (n_faces, )

BaseRectangularMesh.r(*args, **kwargs)

r has been deprecated. See reshape for documentation

BaseRectangularMesh.reshape(x, x_type='cell_centers', out_type='cell_centers', format='V', **kwargs)[source]

A quick reshape command that will do the best it can at giving you what you want.

For example, you have a face variable, and you want the x component of it reshaped to a 3D matrix.

reshape can fulfil your dreams:

mesh.reshape(V, 'F', 'Fx', 'M')
             |   |     |    |
             |   |     |    {
             |   |     |      How: 'M' or ['V'] for a matrix
             |   |     |      (ndgrid style) or a vector (n x dim)
             |   |     |    }
             |   |     {
             |   |       What you want: ['CC'], 'N',
             |   |                       'F', 'Fx', 'Fy', 'Fz',
             |   |                       'E', 'Ex', 'Ey', or 'Ez'
             |   |     }
             |   {
             |     What is it: ['CC'], 'N',
             |                  'F', 'Fx', 'Fy', 'Fz',
             |                  'E', 'Ex', 'Ey', or 'Ez'
             |   }
             {
               The input: as a list or ndarray
             }

For example:

# Separates each component of the Ex grid into 3 matrices
Xex, Yex, Zex = r(mesh.gridEx, 'Ex', 'Ex', 'M')

# Given an edge vector, return just the x edges as a vector
XedgeVector = r(edgeVector, 'E', 'Ex', 'V')

# Separates each component of the edgeVector into 3 vectors
eX, eY, eZ = r(edgeVector, 'E', 'E', 'V')
BaseRectangularMesh.save(file_name='mesh.json', verbose=False, **kwargs)

Save the mesh to json :param str file: file_name for saving the casing properties :param str directory: working directory for saving the file

BaseRectangularMesh.serialize(include_class=True, save_dynamic=False, **kwargs)

Serializes a HasProperties instance to dictionary

This uses the Property serializers to serialize all Property values to a JSON-compatible dictionary. Properties that are undefined are not included. If the HasProperties instance contains a reference to itself, a properties.SelfReferenceError will be raised.

Parameters:

  • include_class - If True (the default), the name of the class will also be saved to the serialized dictionary under key '__class__'

  • save_dynamic - If True, dynamic properties are written to the serialized dict (default: False).

  • Any other keyword arguments will be passed through to the Property serializers.

BaseRectangularMesh.toVTK(models=None)

Convert this mesh object to it’s proper VTK or pyvista data object with the given model dictionary as the cell data of that dataset.

Parameters
modelsdict(numpy.ndarray)

Name(‘s) and array(‘s). Match number of cells

BaseRectangularMesh.to_omf(models=None)

Convert this mesh object to it’s proper omf data object with the given model dictionary as the cell data of that dataset.

Parameters
modelsdict(numpy.ndarray)

Name(‘s) and array(‘s). Match number of cells

BaseRectangularMesh.to_vtk(models=None)

Convert this mesh object to it’s proper VTK or pyvista data object with the given model dictionary as the cell data of that dataset.

Parameters
modelsdict(numpy.ndarray)

Name(‘s) and array(‘s). Match number of cells

BaseRectangularMesh.validate()

Call all registered class validator methods

These are all methods decorated with @properties.validator. Validator methods are expected to raise a ValidationError if they fail.

BaseRectangularMesh.writeVTK(file_name, models=None, directory='')

Makes and saves a VTK object from this mesh and given models

Parameters
file_namestr

path to the output vtk file or just its name if directory is specified

modelsdict

dictionary of numpy.array - Name(‘s) and array(‘s). Match number of cells

directorystr

directory where the UBC GIF file lives

BaseRectangularMesh.write_vtk(file_name, models=None, directory='')

Makes and saves a VTK object from this mesh and given models

Parameters
file_namestr

path to the output vtk file or just its name if directory is specified

modelsdict

dictionary of numpy.array - Name(‘s) and array(‘s). Match number of cells

directorystr

directory where the UBC GIF file lives