Classes

Textile objects

class polytex.textile.Textile(name='textile')[source]

Bases: object

Initialize the textile object.

Attributes

bounds: Bounding box of the textile.
items: Return tow names as a list.
n_tows: Number of tows in the textile.

Methods

`add_group`([name, tow])	Groups of the tows in the textile.
`add_tow`(tow[, group])	Add a tow to the textile.
`case_prepare`([path])	Prepare a case for OpenFOAM simulation.
`cell_labeling`([surface_mesh, intersection, ...])	Label the cells of the background mesh with tow id.
`decimate`()	Decimate the mesh.
`export_as_inp`([fp, scale, orientation])	Export the textile mesh as inp file for Abaqus simulation.
`export_as_openfoam`(fp[, scale, ...])	Export the textile mesh as polyMesh folder for OpenFOAM simulation.
`export_as_vtu`(fp[, binary])	Export the textile mesh as a vtu file.
`from_file`(path)	Load a textile object from a file.
`meshing`(bbox[, voxel_size, show, labeling, ...])	Generate a mesh for the textile.
`reconstruct`()	Reconstruct the textile object from the saved file.
`remove`(tow)	Remove a tow from the textile.
`save`([path, filename, data_size])	Save the textile object to a file.
`triangulate`()	Hexahedral mesh to tetrahedral mesh.

add_group(name='group1', tow=None)[source]

Groups of the tows in the textile. Each is a group of Tow objects. if tow is None, then the group is empty.

Parameters

namestr: Name of the group.
towTow object: Tow to be added to the group. If tow is None, then the group is empty. If tow is not None, then tow is added to the group. Besides, if tow is not in the self.__tows__ yet, it will be added to self.__tows__.

Returns

None.

add_tow(tow, group=None)[source]

Add a tow to the textile. If tow is already in the textile, then raise a ValueError.

Parameters

towTow object: Tow to be added to the textile. Stored in self.__tows__ as a dictionary. Tow.name is the key, and tow is the value.
groupstr: Group name of the tow. If group is None, then the tow is not added to any group. Stored in self.groups.

Returns

None.

case_prepare(path=None)[source]

Prepare a case for OpenFOAM simulation.

Parameters

pathstr: Path of the case to be prepared. The default is None. If path is None, it is set to the root directory of the OpenFOAM mesh generated by Textile.export_as_openfoam().

Returns

None.

noindex

cell_labeling(surface_mesh=None, intersection=False, check_surface=False, yarn_permeability='Gebart', threshold=1, verbose=False)[source]

Label the cells of the background mesh with tow id.

Parameters

surface_meshpyvista mesh object (PolyData): Surface mesh of fiber tows. If None, then the surface meshes is selected user interactively. Otherwise, the surface mesh is loaded from the path specified by surface_mesh.
intersectionbool, optional: Whether to detect the intersection of the tows. The default is False.
check_surfacebool, optional: Whether to check if the surface mesh is watertight. The default is False.
yarn_permeabilitystr, optional: The permeability model used to calculate the permeability tensor of the fiber tow. The default is “Gebart”. The available permeability models are “Gebart”, “CaiBerdichevsky”, and “DrummondTahir”.
thresholdfloat, optional: The tolerance for the fiber tow section detection. The default is 1. A wavy fiber tow may have several intersections with the plane of a cross-section. The threshold is used to determine if the cells is correctly labelled.
verbosebool, optional: Whether to print the information. The default is False.

Returns

None.

Notes

Please make sure that the name of the tow (tow.name) is in the format of towType_towNumber.

decimate()[source]: Decimate the mesh.

export_as_inp(fp='./mesh-C3D8R.inp', scale=1, orientation=True)[source]

Export the textile mesh as inp file for Abaqus simulation.

Parameters

fpstr: The file path and filename of the output mesh. The default is “./mesh-C3D8R.inp”.
scalefloat, optional: The scale factor of the mesh. To convert the mesh from mm to m, the scale factor should be 0.001. The default is 1.
orientationbool, optional: Whether to export the orientation of the yarns. The default is True.

Returns

None.

export_as_openfoam(fp, scale=1, boundary_type=None, cell_data=['yarnIndex', 'D'])[source]

Export the textile mesh as polyMesh folder for OpenFOAM simulation.

The structure of the output case folder is:

 fp/ textile.name/
├── 0          
│   ├── D
│   ├── yarnIndex
│   └── ...       
└── constant          
      ├── polyMesh
      │   ├── boundary
      │   ├── faces
      │   ├── neighbour
      │   ├── owner 
      │   ├── points
      │   ├── ... 
      └── ...     

Parameters

fpstr: The file path of the output mesh.
scalefloat, optional: The scale factor of the mesh. To convert the mesh from mm to m, the scale factor should be 0.001. The default is 1.
boundary_typedict, optional: The boundary type of the mesh. The default is None. If None, the boundary type will be set as “wall” for all boundaries.
cell_datalist, optional: The cell data to be written into the mesh. The default is [“yarnIndex”, “D”].

Returns

None.

export_as_vtu(fp, binary=True)[source]

Export the textile mesh as a vtu file.

Parameters

fpstr: The file path of the output mesh.
binarybool, optional: Whether to save the mesh in binary format. The default is True.

Returns

None.

classmethod from_file(path)[source]

Load a textile object from a file.

Parameters

pathstr: Path of the file to be loaded.

Returns

Textile object.

meshing(bbox, voxel_size=None, show=False, labeling=False, yarn_permeability='Gebart', surface_mesh=None, verbose=False)[source]

Generate a mesh for the textile.

Parameters

bboxnumpy.ndarray: bounding box of the background mesh specified through a numpy array contains the minimum and maximum coordinates of the bounding box [xmin, xmax, ymin, ymax, zmin, zmax]
voxel_sizefloat, or numpy.ndarray: voxel size of the background mesh. if None, the voxel size is set to the 1/20 of the diagonal length of the bounding box; if float, the voxel size is set to the float value in x, y, z directions; if list, set, or tuple of size 3, the voxel size is set to the values for the x-, y- and z- directions.
showbool, optional: Whether to show the mesh. The default is False.
labelingbool, optional: Whether to label the background mesh cells with tow id. The default is True.
yarn_permeabilitystr, optional: The permeability model used to calculate the permeability tensor of the fiber tow. The default is “Gebart”. The available permeability models are “Gebart”, “CaiBerdichevsky”, and “DrummondTahir”.
surface_meshstr, optional: Path of the surface meshes of fiber tows. The default is None. If labeling=True, then the surface meshes are loaded from the path specified by surface_mesh. The surface meshes are used to label the background mesh cells with tow id. If surface_mesh is None, then the surface meshes are selected by the user interactively. TODO : Use the surface mesh generated by the tow object.

Returns

None.

reconstruct()[source]

Reconstruct the textile object from the saved file. The saved file must be in the format of “.tex” and loaded by the pk_load function.

Parameters

None.

Returns

None.

noindex

remove(tow)[source]

Remove a tow from the textile.

Parameters

towstr or Tow object: The tow to be removed.

Returns

None.

save(path=None, filename=None, data_size='minimal')[source]

Save the textile object to a file.

Parameters

pathstr, optional: Path of the file to be saved. The default is None. If path is None, then the user is asked to select the directory to save the file.
filenamestr, optional: Filename of the file to be saved. The default is None. If filename is None, then the filename is set to the textile name with extension “.tex”.
data_sizestr, optional: Size of the data to be saved. The default is “minimal”. If data_size is “minimal”, then only the minimal information of the textile that can be used to reconstruct the textile object is saved. If data_size is “full”, then all information of the textile is saved.

Returns

None.

Notes

TODOmore storage can be saved. The Textile and Tow classes should be designed carefully: at next version.

triangulate()[source]: Hexahedral mesh to tetrahedral mesh. Conformal meshing.

property bounds: Bounding box of the textile.

property items: Return tow names as a list. The tow names are reordered by the tow number if the tow name is in the format of “towType_towNumber”. Otherwise, the tow names are ordered according to the order of adding the tows to the textile.

property n_tows: Number of tows in the textile.

class polytex.tow.Tow(surf_points, order, rho_fiber, radius_fiber, length_scale, tex, name='Tow', packing_fiber='Hex', sort=True, resolution=None, **kwargs)[source]

Bases: object

Parameters

surf_pointsstr, ndarray or DataFrame

The surface points of the tow should be an array of shape (n, 3) where n is the number of points. The points are extracted from volumetric images slice by slice. Please always put the column that indicates the slice number as the last column. It serves as the label for differentiate the points from different slices.

If surf_points is a string, it should be the path to the file that stores the surface points. The file should be a .pcd file as defined in the PolyTex library.

If surf_points is a numpy array, it should be an array of shape (n, 3) where n is the number of points.

If surf_points is a pandas DataFrame, it should be a DataFrame with 3 columns and n rows where n is the number of points.

orderstr

It is preferred to set the last column of the surf_points as the coordinate in the direction that is perpendicular to the image slices for geometry analysis, parametrization and kriging resampling. Hence, you may have reordered the columns. Here, you can specify the order of the columns in the reordered points. Default is “xyz”. The other options are “xzy”, “yxz”, “yzx”, “zxy”, “zyx”. This function will recover the original order of the columns when generating the surface mesh.

rho_fiberfloat, optional

The density of the fiber in kg/m^3.

radius_fiberfloat, optional

The radius of the fiber in m.

length_scalestr, optional

The length scale of the coordinates. Default is “mm”. The other options are “m”, “cm”, “um”.

texfloat, optional

The linear density of the tow in tex.

namestr, optional

The name or type of the tow. Default is “Tow”.

packing_fiberstr, optional

The packing pattern of the fiber. Default is “Hex”. The other option is “Square”.

sortbool, optional

Whether to sort the points according to the slice number. Default is True.

resolutionfloat, optional

The resolution of the MicroCT image used to generate the tow dataset. Default is None. This is only stored as an attribute for future use. It is not used in the current version.

kwargsdict

The keyword arguments for the PolyTex Tow class. The user can specify any keyword arguments for the Tow class. The keyword arguments will be stored as attributes of the Tow class. The user can access the attributes by tow.attribute_name.

Attributes

attribute_names: Get the attribute names of the Tow class.

Methods

`axial_lines`([save_path, plot])	Generate the axial line of the fiber tow surface.
`from_file`(path)	Initialize the tow from a saved tow file.
`kde`([bw, save_path])	Generate the kernel density estimation of the radial normalized distance for point cloud decomposition.
`normal_cross_section`([algorithm, save_path, ...])	Generate the normal cross section of the fiber tow surface.
`radial_lines`([save_path, plot, type])	Generate the radial line of the fiber tow surface.
`resampling`([krig_config, skip, ...])	Kriging the cross-sections of the tow to obtain the parametric equations for each cross-section (which is a closed curve).
`save`(save_path)	Save the fiber tow data.
`smooth_window`(size, h_res[, extend])	The window size of smoothing operation.
`smoothing`([name_drift, name_cov, ...])	Smooth the tow using parametric surface kriging.
`surf_mesh`([plot, save_path, end_closed])	Generate the surface mesh of the tow.
`trajectory`([krig_config, smooth, plot, ...])	Generate the trajectory of the tow and smooth it using kriging.
`unit_vector`(vector[, ax])	Returns the unit vector of the input vector along the given axis.

mw_kde

axial_lines(save_path=None, plot=True)[source]

Generate the axial line of the fiber tow surface.

Parameters

save_pathstr, optional: The path to save the axial line data as a vtk mesh file.
plotbool, optional: Whether to plot the axial line. Default is True.

Returns

axial_linevtkPolyData: The axial lines of the fiber tow.

classmethod from_file(path)[source]

Initialize the tow from a saved tow file.

Parameters

pathstr: The path to the saved tow file. The file format is .tow.

Returns

towTow: The Tow object.

kde(bw=None, save_path=None)[source]

Generate the kernel density estimation of the radial normalized distance for point cloud decomposition.

Parameters

bwfloat, optional: The bandwidth of the kernel density estimation. Default is None and the bandwidth will be estimated using the Scott’s rule of thumb (one-fifth of the estimated value).
save_pathstr, optional: The path to save the kernel density estimation. Default is None. If None, the kernel density estimation will not be saved. The file format is .stat and can be loaded by the function polytex.pk_load.

Returns

clustersdict

normal_cross_section(algorithm='kriging', save_path=None, plot=True, i_size=0.7, j_size=1, skip=10, max_dist=2)[source]

Generate the normal cross section of the fiber tow surface.

Parameters

algorithmstr, optional: The algorithm to generate the cross section. Default is “kriging”. The other option is “pyvista” which uses pyvista’s mesh clip function (Polydata.clip_surface()).
save_pathstr, optional: The path to save the normal cross sections as a vtk mesh file.
plotbool, optional: Whether to plot the normal cross sections. Default is True.
i_sizefloat, optional: The size of the i direction of the noraml plane. Default is 0.7.
j_sizefloat, optional: The size of the j direction of the noraml plane. Default is 1.
skipint, optional: The number of cross sections to skip in plot. Default is 10. If skip is 1, all cross sections will be plotted.

Returns

cross_sectionpyvista.PolyData: The normal cross section of the fiber tows stored in a pyvista.PolyData object. Note that only the cross sections that are plotted are stored. If one wants to save all the cross sections, set skip=1.
planespyvista.PolyData: The corresponding planes that the cross sections are generated from. Note that only the planes that are plotted are stored. If one wants to save all the planes, set skip=1.

radial_lines(save_path=None, plot=True, type='resampled')[source]

Generate the radial line of the fiber tow surface.

Parameters

save_pathstr, optional: The path to save the radial line data as a vtk mesh file.
plotbool, optional: Whether to plot the radial line. Default is True.
typestr, optional: The type of radial line. Default is “resampled”. The other option is “original”.

Returns

radial_linevtkPolyData: The radial lines of the fiber tow.

resampling(krig_config=('lin', 'cub'), skip=5, sample_position=[], smooth=0, type='distance')[source]

Kriging the cross-sections of the tow to obtain the parametric equations for each cross-section (which is a closed curve).

Parameters

krig_configtuple, optional: The kriging configuration. The first element is the kriging model for the drift and the second is the name of covariance. Default is (“lin”, “cub”).
skipint, optional: The number of cross-sections to be skipped for resampling to accelerate the operation. Default is 5. Namely, 1 of every 5 cross-sections will be resampled. If skip is 1, all the cross-sections will be kriged.
sample_positionarray_like, optional: The resampling positions of each cross-sections specified by the normalized distance in radial direction of each cross-section. Default is [].
smoothfloat, optional: The smoothing parameter for the kriging resampling. Default is 0. Also known as the nugget effect in geo-statistics and kriging theory.
typestr, optional: The type of the kriging resampling. Default is “distance”. The other option is “angular”. If “distance”, the resampling positions are specified by the normalized distance (between 0 and 1) in radial direction of each cross-section. If “angular”, the resampling positions are specified by angular position (between 0 and 360) of control points in radial direction of each cross-section.

Returns

_Tow__kriged_verticesndarray

The kriged points for each cross-section of the tow. It is an array of shape (n, 3) where n is the number of points. The kriged points is obtained according to the kriging configuration and the resampling positions. If the resampling positions are not specified, the kriged points are obtained by evenly sampling the cross-sections with a sampling interval of 0.05, namely, 20 points per cross- section.

exprdict

The kriging expression for each cross-section. It contains two sub-dictionaries that: use the cross-section number as the key and the kriging expression as the value for the first two components of user input.

save(save_path)[source]

Save the fiber tow data.

Parameters

save_pathstr: The path to save the fiber tow data.

smooth_window(size, h_res, extend=2)[source]

The window size of smoothing operation. The window size is the number of slices in the axial direction of fiber tow that are smoothed per iteration.

A smaller window size will significantly decrease the computation time of smoothing operation.

Parameters

sizeint: The window size.
h_resint: The number of slices in the axial direction of fiber tow.
extendint, optional: The number of slices that are extended to the left and right of the smoothing window to ensure the smoothness of the surface at the boundary of the windows.

Returns

wins_interpndarray: The window size for interpolation (with extensions at the two ends).
wins_resultndarray: The index of effective smoothing results (without extensions).

smoothing(name_drift=['lin', 'lin'], name_cov=['cub', 'cub'], smooth_factor=[0, 0], size=25, save_path=None, plot=False)[source]

Smooth the tow using parametric surface kriging. Anisotropic smoothing is applied to the tow by using different smoothing factors for the two directions.

Parameters

name_driftlist, optional: The drift function for the parametric surface kriging. Default is [‘lin’, ‘lin’].
name_covlist, optional: The covariance function for the parametric surface kriging. Default is [‘cub’, ‘cub’].
smooth_factorlist, optional: The smoothing factor for the parametric surface kriging. Default is [0, 0]. Also known as the nugget effect in geo-statistics and kriging theory. The smoothing factor is applied to the two directions separately. The first element is the smoothing factor for the radial direction and the second element is the smoothing factor for the axial direction.
sizeint, optional: # TODO : improve the description The size of the window for the moving average filter. Default is 25.
save_pathstr, optional: The path to save the smoothed tow. Default is None. If None, the smoothed tow will not be saved. The file format is .ply.
plotbool, optional: Whether to plot the smoothed tow. Default is False.

Returns

verticesndarray: The smoothed tow vertices.

surf_mesh(plot=False, save_path=None, end_closed=False)[source]

Generate the surface mesh of the tow.

Parameters

plotbool, optional: Whether to plot the surface mesh. Default is False.
save_pathstr, optional: The path to save the surface mesh. Default is None and the surface mesh will not be saved. The file format can be .ply or .vtk.
Returns
——-
surf_mesh: The surface mesh of the tow.

trajectory(krig_config=('lin', 'cub'), smooth=0.0, plot=False, save_path=None, orientation=False)[source]

Generate the trajectory of the tow and smooth it using kriging.

Parameters

krig_configtuple, optional: The kriging configuration for the trajectory. It is a tuple of two strings that specify the drift and covariance function. Default is (“lin”, “cub”).
smoothfloat, optional: The smoothing parameter for the parametric curve kriging. Default is 0. Also known as the nugget effect in geo-statistics and kriging theory.
plotbool, optional: Whether to plot the trajectory. Default is False.
save_pathstr, optional: The path to save the trajectory as vtk file. Default is None and the trajectory will not be saved.
orientationbool, optional: Whether to calculate the orientation of the tow. Default is False. The orientation is the tangent vector of the trajectory.

Returns

trajnp.ndarray: The trajectory of the tow in the form of (n, 3) where n is the number of points.

unit_vector(vector, ax=1)[source]

Returns the unit vector of the input vector along the given axis.

Parameters

vectorndarray: The input vector.
axint, optional: The axis along which the unit vector is calculated. Default is 1 (column).

Returns

unit_vectorndarray: The unit vector of the input vector along the given axis.

property attribute_names

Get the attribute names of the Tow class.

Returns

attribute_nameslist: The attribute names of the Tow class.

Primitive geometries

class polytex.geometry.basic.Point(orig_3d=(0, 0, 0))[source]

Bases: ndarray

Default constructor. If no arguments are given, the point is initialized to (0, 0, 0).

Parameters

clsclass: The class of the object.
orig_3dtuple, list, or array_like: Defaults to 3d origin (0, 0, 0).

Returns

objPoint: The origin point of 3d space.

Examples

>>> p1 = Point()
>>> p1
Point([0, 0, 0])

Attributes

T: The transposed array.
base: Base object if memory is from some other object.
bounds: Returns ——- bounds : array_like The bounding box of the point.
ctypes: An object to simplify the interaction of the array with the ctypes module.
data: Python buffer object pointing to the start of the array’s data.
dtype: Data-type of the array’s elements.
flags: Information about the memory layout of the array.
flat: A 1-D iterator over the array.
imag: The imaginary part of the array.
itemsize: Length of one array element in bytes.
nbytes: Total bytes consumed by the elements of the array.
ndim: Number of array dimensions.
real: The real part of the array.
shape: Tuple of array dimensions.
size: Number of elements in the array.
strides: Tuple of bytes to step in each dimension when traversing an array.
x
xyz
y
z: Return —— z : float 3rd dimension element.

Methods

`all`([axis, out, keepdims, where])	Returns True if all elements evaluate to True.
`any`([axis, out, keepdims, where])	Returns True if any of the elements of a evaluate to True.
`argmax`([axis, out, keepdims])	Return indices of the maximum values along the given axis.
`argmin`([axis, out, keepdims])	Return indices of the minimum values along the given axis.
`argpartition`(kth[, axis, kind, order])	Returns the indices that would partition this array.
`argsort`([axis, kind, order])	Returns the indices that would sort this array.
`astype`(dtype[, order, casting, subok, copy])	Copy of the array, cast to a specified type.
`byteswap`([inplace])	Swap the bytes of the array elements
`choose`(choices[, out, mode])	Use an index array to construct a new array from a set of choices.
`clip`([min, max, out])	Return an array whose values are limited to `[min, max]`.
`compress`(condition[, axis, out])	Return selected slices of this array along given axis.
`conj`()	Complex-conjugate all elements.
`conjugate`()	Return the complex conjugate, element-wise.
`copy`([order])	Return a copy of the array.
`cumprod`([axis, dtype, out])	Return the cumulative product of the elements along the given axis.
`cumsum`([axis, dtype, out])	Return the cumulative sum of the elements along the given axis.
`diagonal`([offset, axis1, axis2])	Return specified diagonals.
`direction_ratio`(other)	Gives the direction ratio between 2 points.
`dist`(other)	Both points must have the same dimensions :return: Euclidean distance
`dump`(file)	Dump a pickle of the array to the specified file.
`dumps`()	Returns the pickle of the array as a string.
`fill`(value)	Fill the array with a scalar value.
`flatten`([order])	Return a copy of the array collapsed into one dimension.
`getfield`(dtype[, offset])	Returns a field of the given array as a certain type.
`item`(*args)	Copy an element of an array to a standard Python scalar and return it.
`itemset`(*args)	Insert scalar into an array (scalar is cast to array's dtype, if possible)
`max`([axis, out, keepdims, initial, where])	Return the maximum along a given axis.
`mean`([axis, dtype, out, keepdims, where])	Returns the average of the array elements along given axis.
`min`([axis, out, keepdims, initial, where])	Return the minimum along a given axis.
`newbyteorder`([new_order])	Return the array with the same data viewed with a different byte order.
`nonzero`()	Return the indices of the elements that are non-zero.
`partition`(kth[, axis, kind, order])	Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array.
`prod`([axis, dtype, out, keepdims, initial, ...])	Return the product of the array elements over the given axis
`ptp`([axis, out, keepdims])	Peak to peak (maximum - minimum) value along a given axis.
`put`(indices, values[, mode])	Set `a.flat[n] = values[n]` for all n in indices.
`ravel`([order])	Return a flattened array.
`repeat`(repeats[, axis])	Repeat elements of an array.
`reshape`(shape[, order])	Returns an array containing the same data with a new shape.
`resize`(new_shape[, refcheck])	Change shape and size of array in-place.
`round`([decimals, out])	Return a with each element rounded to the given number of decimals.
`save_as_vtk`(filename[, color])	Save the point as a vtk file.
`searchsorted`(v[, side, sorter])	Find indices where elements of v should be inserted in a to maintain order.
`setfield`(val, dtype[, offset])	Put a value into a specified place in a field defined by a data-type.
`setflags`([write, align, uic])	Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.
`sort`([axis, kind, order])	Sort an array in-place.
`squeeze`([axis])	Remove axes of length one from a.
`std`([axis, dtype, out, ddof, keepdims, where])	Returns the standard deviation of the array elements along given axis.
`sum`([axis, dtype, out, keepdims, initial, where])	Return the sum of the array elements over the given axis.
`swapaxes`(axis1, axis2)	Return a view of the array with axis1 and axis2 interchanged.
`take`(indices[, axis, out, mode])	Return an array formed from the elements of a at the given indices.
`tobytes`([order])	Construct Python bytes containing the raw data bytes in the array.
`tofile`(fid[, sep, format])	Write array to a file as text or binary (default).
`tolist`()	Return the array as an `a.ndim`-levels deep nested list of Python scalars.
`tostring`([order])	A compatibility alias for tobytes, with exactly the same behavior.
`trace`([offset, axis1, axis2, dtype, out])	Return the sum along diagonals of the array.
`transpose`(*axes)	Returns a view of the array with axes transposed.
`var`([axis, dtype, out, ddof, keepdims, where])	Returns the variance of the array elements, along given axis.
`view`([dtype][, type])	New view of array with the same data.

dot
set_x
set_y
set_z

direction_ratio(other)[source]

Gives the direction ratio between 2 points.

Parameters

otherPoint object: The other point to which the direction ratio is calculated.

Returns

direction_ratiolist: The direction ratio between the 2 points.

Examples

>>> from polytex.geometry import Point
>>> p1 = Point(1, 2, 3)
>>> p1.direction_ratio(Point(2, 3, 5))
[1, 1, 2]

dist(other)[source]: Both points must have the same dimensions :return: Euclidean distance

save_as_vtk(filename, color=None)[source]: Save the point as a vtk file.

property bounds

Returns

boundsarray_like: The bounding box of the point. The first row is the minimum values and the second row is the maximum values for each dimension.

property size

Number of elements in the array.

Equal to np.prod(a.shape), i.e., the product of the array’s dimensions.

Notes

a.size returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggested np.prod(a.shape), which returns an instance of np.int_), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.

Examples

>>> x = np.zeros((3, 5, 2), dtype=np.complex128)
>>> x.size
30
>>> np.prod(x.shape)
30

property z

class polytex.geometry.basic.Vector(orig_3d=(0, 0, 0))[source]

Bases: Point

Default constructor. If no arguments are given, the point is initialized to (0, 0, 0).

Parameters

clsclass: The class of the object.
orig_3dtuple, list, or array_like: Defaults to 3d origin (0, 0, 0).

Returns

objPoint: The origin point of 3d space.

Examples

>>> p1 = Point()
>>> p1
Point([0, 0, 0])

Attributes

T: The transposed array.
add
base: Base object if memory is from some other object.
bounds: Returns ——- bounds : array_like The bounding box of the point.
ctypes: An object to simplify the interaction of the array with the ctypes module.
data: Python buffer object pointing to the start of the array’s data.
dtype: Data-type of the array’s elements.
flags: Information about the memory layout of the array.
flat: A 1-D iterator over the array.
imag: The imaginary part of the array.
itemsize: Length of one array element in bytes.
nbytes: Total bytes consumed by the elements of the array.
ndim: Number of array dimensions.
norm: Return —— norm : float The norm of the vector.
real: The real part of the array.
shape: Tuple of array dimensions.
size: Number of elements in the array.
strides: Tuple of bytes to step in each dimension when traversing an array.
sub
x
xyz
y
z: Return —— z : float 3rd dimension element.

Methods

`all`([axis, out, keepdims, where])	Returns True if all elements evaluate to True.
`angle_between`(other[, radian])	Return the angle between 2 vectors.
`any`([axis, out, keepdims, where])	Returns True if any of the elements of a evaluate to True.
`argmax`([axis, out, keepdims])	Return indices of the maximum values along the given axis.
`argmin`([axis, out, keepdims])	Return indices of the minimum values along the given axis.
`argpartition`(kth[, axis, kind, order])	Returns the indices that would partition this array.
`argsort`([axis, kind, order])	Returns the indices that would sort this array.
`astype`(dtype[, order, casting, subok, copy])	Copy of the array, cast to a specified type.
`byteswap`([inplace])	Swap the bytes of the array elements
`choose`(choices[, out, mode])	Use an index array to construct a new array from a set of choices.
`clip`([min, max, out])	Return an array whose values are limited to `[min, max]`.
`compress`(condition[, axis, out])	Return selected slices of this array along given axis.
`conj`()	Complex-conjugate all elements.
`conjugate`()	Return the complex conjugate, element-wise.
`copy`([order])	Return a copy of the array.
`cumprod`([axis, dtype, out])	Return the cumulative product of the elements along the given axis.
`cumsum`([axis, dtype, out])	Return the cumulative sum of the elements along the given axis.
`diagonal`([offset, axis1, axis2])	Return specified diagonals.
`direction_ratio`(other)	Gives the direction ratio between 2 points.
`dist`(other)	Both points must have the same dimensions :return: Euclidean distance
`dump`(file)	Dump a pickle of the array to the specified file.
`dumps`()	Returns the pickle of the array as a string.
`fill`(value)	Fill the array with a scalar value.
`flatten`([order])	Return a copy of the array collapsed into one dimension.
`getfield`(dtype[, offset])	Returns a field of the given array as a certain type.
`item`(*args)	Copy an element of an array to a standard Python scalar and return it.
`itemset`(*args)	Insert scalar into an array (scalar is cast to array's dtype, if possible)
`max`([axis, out, keepdims, initial, where])	Return the maximum along a given axis.
`mean`([axis, dtype, out, keepdims, where])	Returns the average of the array elements along given axis.
`min`([axis, out, keepdims, initial, where])	Return the minimum along a given axis.
`newbyteorder`([new_order])	Return the array with the same data viewed with a different byte order.
`nonzero`()	Return the indices of the elements that are non-zero.
`partition`(kth[, axis, kind, order])	Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array.
`prod`([axis, dtype, out, keepdims, initial, ...])	Return the product of the array elements over the given axis
`ptp`([axis, out, keepdims])	Peak to peak (maximum - minimum) value along a given axis.
`put`(indices, values[, mode])	Set `a.flat[n] = values[n]` for all n in indices.
`ravel`([order])	Return a flattened array.
`repeat`(repeats[, axis])	Repeat elements of an array.
`reshape`(shape[, order])	Returns an array containing the same data with a new shape.
`resize`(new_shape[, refcheck])	Change shape and size of array in-place.
`round`([decimals, out])	Return a with each element rounded to the given number of decimals.
`save_as_vtk`(filename[, color])	Save the point as a vtk file.
`searchsorted`(v[, side, sorter])	Find indices where elements of v should be inserted in a to maintain order.
`setfield`(val, dtype[, offset])	Put a value into a specified place in a field defined by a data-type.
`setflags`([write, align, uic])	Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.
`sort`([axis, kind, order])	Sort an array in-place.
`squeeze`([axis])	Remove axes of length one from a.
`std`([axis, dtype, out, ddof, keepdims, where])	Returns the standard deviation of the array elements along given axis.
`sum`([axis, dtype, out, keepdims, initial, where])	Return the sum of the array elements over the given axis.
`swapaxes`(axis1, axis2)	Return a view of the array with axis1 and axis2 interchanged.
`take`(indices[, axis, out, mode])	Return an array formed from the elements of a at the given indices.
`tobytes`([order])	Construct Python bytes containing the raw data bytes in the array.
`tofile`(fid[, sep, format])	Write array to a file as text or binary (default).
`tolist`()	Return the array as an `a.ndim`-levels deep nested list of Python scalars.
`tostring`([order])	A compatibility alias for tobytes, with exactly the same behavior.
`trace`([offset, axis1, axis2, dtype, out])	Return the sum along diagonals of the array.
`transpose`(*axes)	Returns a view of the array with axes transposed.
`var`([axis, dtype, out, ddof, keepdims, where])	Returns the variance of the array elements, along given axis.
`view`([dtype][, type])	New view of array with the same data.

cross
dot
set_x
set_y
set_z

angle_between(other, radian=False)[source]

Return the angle between 2 vectors.

\[\theta = \arccos \frac{v_1 \cdot v_2}{\|v_1\| \|v_2\|}\]

Parameters

otherVector object: The other vector to which the angle is calculated.
radianbool, optional: If True, return the angle in radians. The default is False.

Returns

anglefloat: The angle between the 2 vectors. If radian is True, the angle is in radians. Otherwise, the angle is in degrees.

property norm

class polytex.geometry.basic.Line(p1, p2=None, **kwargs)[source]

Bases: Line

Parameters

p1Point object: The first point of the line.
p2Point object: The second point of the line.

Attributes

ambient_dimension: A property method that returns the dimension of LinearEntity object.
args: Returns a tuple of arguments of ‘self’.
assumptions0: Return object type assumptions.
boundary: The boundary or frontier of a set.
bounds: Return a tuple (xmin, ymin, xmax, ymax) representing the bounding rectangle for the geometric figure.
canonical_variables: Return a dictionary mapping any variable defined in self.bound_symbols to Symbols that do not clash with any free symbols in the expression.
closure: Property method which returns the closure of a set.
direction: The direction vector of the LinearEntity.
expr_free_symbols
free_symbols: Return from the atoms of self those which are free symbols.
func: The top-level function in an expression.
inf: The infimum of self.
interior: Property method which returns the interior of a set.
is_Complement
is_EmptySet
is_Intersection
is_UniversalSet
is_algebraic
is_antihermitian
is_closed: A property method to check whether a set is closed.
is_commutative
is_comparable: Return True if self can be computed to a real number (or already is a real number) with precision, else False.
is_complex
is_composite
is_empty
is_even
is_extended_negative
is_extended_nonnegative
is_extended_nonpositive
is_extended_nonzero
is_extended_positive
is_extended_real
is_finite
is_finite_set
is_hermitian
is_imaginary
is_infinite
is_integer
is_irrational
is_negative
is_noninteger
is_nonnegative
is_nonpositive
is_nonzero
is_odd
is_open: Property method to check whether a set is open.
is_polar
is_positive
is_prime
is_rational
is_real
is_transcendental
is_zero
kind: The kind of a Set
length: The length of the line.
measure: The (Lebesgue) measure of self.
p1: The first defining point of a linear entity.
p2: The second defining point of a linear entity.
points: The two points used to define this linear entity.
sup: The supremum of self.

Methods

`angle_between`(l2)	Return the non-reflex angle formed by rays emanating from the origin with directions the same as the direction vectors of the linear entities.
`arbitrary_point`([parameter])	A parameterized point on the Line.
`are_concurrent`(*lines)	Is a sequence of linear entities concurrent?
`as_content_primitive`([radical, clear])	A stub to allow Basic args (like Tuple) to be skipped when computing the content and primitive components of an expression.
`as_dummy`()	Return the expression with any objects having structurally bound symbols replaced with unique, canonical symbols within the object in which they appear and having only the default assumption for commutativity being True.
`atoms`(*types)	Returns the atoms that form the current object.
`bisectors`(other)	Returns the perpendicular lines which pass through the intersections of self and other that are in the same plane.
`class_key`()	Nice order of classes.
`compare`(other)	Return -1, 0, 1 if the object is less than, equal, or greater than other in a canonical sense.
`complement`(universe)	The complement of 'self' w.r.t the given universe.
`contains`(other)	Return True if other is on this Line, or False otherwise.
`count`(query)	Count the number of matching subexpressions.
`count_ops`([visual])	Wrapper for count_ops that returns the operation count.
`distance`(other)	Finds the shortest distance between a line and a point.
`doit`(**hints)	Evaluate objects that are not evaluated by default like limits, integrals, sums and products.
`dummy_eq`(other[, symbol])	Compare two expressions and handle dummy symbols.
`encloses`(o)	Return True if o is inside (not on or outside) the boundaries of self.
`equals`(other)	Returns True if self and other are the same mathematical entities
`evalf`([n, subs, maxn, chop, strict, quad, ...])	Evaluate the given formula to an accuracy of n digits.
`find`(query[, group])	Find all subexpressions matching a query.
`fromiter`(args, **assumptions)	Create a new object from an iterable.
`has`(*patterns)	Test whether any subexpression matches any of the patterns.
`has_free`(*patterns)	Return True if self has object(s) `x` as a free expression else False.
`has_xfree`(s)	Return True if self has any of the patterns in s as a free argument, else False.
`intersect`(other)	Returns the intersection of 'self' and 'other'.
`intersection`(other)	The intersection with another geometrical entity.
`is_disjoint`(other)	Returns True if `self` and `other` are disjoint.
`is_parallel`(l2)	Are two linear entities parallel?
`is_perpendicular`(l2)	Are two linear entities perpendicular?
`is_proper_subset`(other)	Returns True if `self` is a proper subset of `other`.
`is_proper_superset`(other)	Returns True if `self` is a proper superset of `other`.
`is_same`(b[, approx])	Return True if a and b are structurally the same, else False.
`is_similar`(other)	Return True if self and other are contained in the same line.
`is_subset`(other)	Returns True if `self` is a subset of `other`.
`is_superset`(other)	Returns True if `self` is a superset of `other`.
`isdisjoint`(other)	Alias for `is_disjoint()`
`issubset`(other)	Alias for `is_subset()`
`issuperset`(other)	Alias for `is_superset()`
`match`(pattern[, old])	Pattern matching.
`matches`(expr[, repl_dict, old])	Helper method for match() that looks for a match between Wild symbols in self and expressions in expr.
`n`([n, subs, maxn, chop, strict, quad, verbose])	Evaluate the given formula to an accuracy of n digits.
`parallel_line`(p)	Create a new Line parallel to this linear entity which passes through the point p.
`parameter_value`(other, t)	Return the parameter corresponding to the given point.
`perpendicular_line`(p)	Create a new Line perpendicular to this linear entity which passes through the point p.
`perpendicular_segment`(p)	Create a perpendicular line segment from p to this line.
`plot_interval`([parameter])	The plot interval for the default geometric plot of line.
`powerset`()	Find the Power set of `self`.
`projection`(other)	Project a point, line, ray, or segment onto this linear entity.
`random_point`([seed])	A random point on a LinearEntity.
`rcall`(*args)	Apply on the argument recursively through the expression tree.
`refine`([assumption])	See the refine function in sympy.assumptions
`reflect`(line)	Reflects an object across a line.
`replace`(query, value[, map, simultaneous, exact])	Replace matching subexpressions of `self` with `value`.
`rewrite`(*args[, deep])	Rewrite self using a defined rule.
`rotate`(angle[, pt])	Rotate `angle` radians counterclockwise about Point `pt`.
`scale`([x, y, pt])	Scale the object by multiplying the x,y-coordinates by x and y.
`simplify`(**kwargs)	See the simplify function in sympy.simplify
`smallest_angle_between`(l2)	Return the smallest angle formed at the intersection of the lines containing the linear entities.
`sort_key`([order])	Return a sort key.
`subs`(args, *kwargs)	Substitutes old for new in an expression after sympifying args.
`symmetric_difference`(other)	Returns symmetric difference of `self` and `other`.
`translate`([x, y])	Shift the object by adding to the x,y-coordinates the values x and y.
`union`(other)	Returns the union of `self` and `other`.
`xreplace`(rule)	Replace occurrences of objects within the expression.

copy
could_extract_minus_sign
is_hypergeometric

class polytex.geometry.basic.Curve(points)[source]

Bases: object

A partial inheritance of polytex.geometry.Point class.

Parameters

pointslist, tuple or array_like: A list of Point objects.

Attributes

ambient_dimension: Return the dimension of the curve.
bounds: Return the bounds of the curve.
curvature: Return the curvature of the curve.
length: Return the length of the curve.
tangent: Return the tangent vector of the curve at each point.

Methods

`plot`()	Plot the curve.
`save`([save_path])	Save the curve to a vtk file.
`to_polygon`()	Convert the curve to a polygon.

plot()[source]

Plot the curve.

Returns

None

save(save_path=None)[source]

Save the curve to a vtk file.

Parameters

save_pathstr: The path to save the vtk file.

Returns

None

to_polygon()[source]

Convert the curve to a polygon.

Returns

polygonPolygon object

property ambient_dimension

Return the dimension of the curve.

Returns

ambient_dimensionint

property bounds

Return the bounds of the curve.

Returns

boundstuple

property curvature

Return the curvature of the curve.

TODO: curvature of a curve

Returns

curvaturefloat

property length

Return the length of the curve.

Returns

lengthfloat

property tangent

Return the tangent vector of the curve at each point.

Returns

tangentVector object

class polytex.geometry.basic.Polygon(points)[source]

Bases: Curve

A partial inheritance of polytex.geometry.Point class.

Parameters

pointslist, tuple or array_like: A list of Point objects.

Attributes

ambient_dimension: Return the dimension of the curve.
area: Return the area of the polygon.
bounds: Return the bounds of the curve.
centroid: Return the centroid of the polygon.
curvature: Return the curvature of the curve.
length: Return the length of the curve.
perimeter: Return the perimeter of the polygon.
tangent: Return the tangent vector of the curve at each point.

Methods

`plot`()	Plot the curve.
`save`([save_path])	Save the curve to a vtk file.
`to_curve`()	Convert the polygon to a curve.
`to_polygon`()	Convert the curve to a polygon.

to_curve()[source]

Convert the polygon to a curve.

Returns

curveCurve object

property area

Return the area of the polygon.

Returns

areafloat

property centroid

Return the centroid of the polygon.

Returns

centroidPoint object

property perimeter

Return the perimeter of the polygon.

Returns

perimeterfloat

class polytex.geometry.basic.Plane(p1, a=None, b=None, **kwargs)[source]

Bases: object

Create a plane from 3 points or a point and a normal vector.

Parameters

p1Point object: A point on the plane.
aPoint object, optional: A point on the plane. The default is None.
bPoint object, optional: A point on the plane. The default is None.
**kwargsdict, optional: normal_vector can be passed as a keyword argument when leaving a and b as None. If both a and b are not None, normal_vector will be ignored.

Returns

planePlane object

Methods

`distance`(point)	Return the signed distance between a point and the plane.
`function`()	Return the equation of the plane as a function of x, y and z.
`intersection`(obj, max_dist)	Return the intersection of the plane with a curve or a polygon.
`show`()	Plot the plane.

distance(point)[source]

Return the signed distance between a point and the plane.

Parameters

pointPoint object: The point to calculate the distance. shape = (n, 3), where n is the number of points.

Returns

distancefloat: The distance between the point and the plane.

Examples

>>> from polytex.geometry import Point, Plane
>>> p1 = Point([5, 0, 0])
>>> normal = Point([1, 0, 0])
>>> plane = Plane(p1, normal_vector=normal)
>>> plane.show()
>>> plane.distance([[0, 0, 0], [1, 0, 0], [2, 0, 0]])
array([-5., -4., -3.])

function()[source]

Return the equation of the plane as a function of x, y and z.

Parameters

normalarray-like: normal vector of the plane.
pointarray-like: point on the plane.

Returns

A lambda function of x, y and z.: function of plane.

Notes

normal = (a, b, c) point = (x0, y0, z0) Equation of a plane: a(x-x0) + b(y-y0) + c(z-z0) = 0

Examples

Create a plane from a point and a normal vector >>> from polytex.geometry import Point, Plane >>> p1 = Point([1, 1, 1]) >>> normal = Point([1, 4, 7]) >>> plane2 = Plane(p1, normal_vector=normal) >>> f = plane2.function() >>> f <function polytex.geometry.basic.Plane.function.<locals>.<lambda>(x, y, z)> >>> f(1, 1, 1) 0

intersection(obj, max_dist)[source]

Return the intersection of the plane with a curve or a polygon.

Parameters

objCurve or Polygon object: The object to intersect with the plane.
max_distfloat: The maximum distance of checked points from the plane.

Returns

intersectionlist or array: The intersection point of the plane with the obj in the shape of (1, 3). If the intersection is not found, none is returned.

show()[source]

Plot the plane.

Returns

None

class polytex.geometry.basic.Ellipse2D(n: int, a: float, b: float, center=[0, 0])[source]

Bases: object

Parameters

nint: The number of points to generate.
afloat: The length of the major axis.
bfloat: The length of the minor axis.
centerlist, tuple or array_like: The center of the ellipse.

Methods

elipse_2d()

Generate points on an ellipse.

elipse_2d() → ndarray[source]

Generate points on an ellipse.

Returns

xy: array-like: Points on the ellipse with shape (n, 2).

class polytex.geometry.basic.Tube(theta_res, h_res, vertices=None, **kwargs)[source]

Bases: GeometryEntity

Create a tubular surface.

Parameters

theta_resint: The number of points on each cross-section.
h_resint: The number of cross-sections.
verticesarray_like: The points on the cross-sections. The shape of the array should be (h_res * theta_res, 3). The points should be ordered in the following way: [p1, p2, …, p_theta_res, p1, p2, …, p_theta_res, …, p1, p2, …, p_theta_res] where p1, p2, …, p_theta_res are the points on each cross-section from the top to the bottom. The default value is None. If the value is None, the points will be generated automatically by assigning the height, major and minor radius to the tube.

Returns

tubeTube object

Examples

>>> from polytex.geometry import Tube
>>> tube = Tube(4, 10, major=2, minor=1, h=5)
>>> mesh = tube.mesh(plot=True)
>>> tube.save_as_mesh('tube.vtk')

Attributes

args: Returns a tuple of arguments of ‘self’.
assumptions0: Return object type assumptions.
bounds: Return a tuple (xmin, ymin, xmax, ymax) representing the bounding rectangle for the geometric figure.
canonical_variables: Return a dictionary mapping any variable defined in self.bound_symbols to Symbols that do not clash with any free symbols in the expression.
expr_free_symbols
free_symbols: Return from the atoms of self those which are free symbols.
func: The top-level function in an expression.
h_res
is_algebraic
is_antihermitian
is_commutative
is_comparable: Return True if self can be computed to a real number (or already is a real number) with precision, else False.
is_complex
is_composite
is_even
is_extended_negative
is_extended_nonnegative
is_extended_nonpositive
is_extended_nonzero
is_extended_positive
is_extended_real
is_finite
is_hermitian
is_imaginary
is_infinite
is_integer
is_irrational
is_negative
is_noninteger
is_nonnegative
is_nonpositive
is_nonzero
is_odd
is_polar
is_positive
is_prime
is_rational
is_real
is_transcendental
is_zero
points
theta_res

Methods

`as_content_primitive`([radical, clear])	A stub to allow Basic args (like Tuple) to be skipped when computing the content and primitive components of an expression.
`as_dummy`()	Return the expression with any objects having structurally bound symbols replaced with unique, canonical symbols within the object in which they appear and having only the default assumption for commutativity being True.
`atoms`(*types)	Returns the atoms that form the current object.
`class_key`()	Nice order of classes.
`compare`(other)	Return -1, 0, 1 if the object is less than, equal, or greater than other in a canonical sense.
`count`(query)	Count the number of matching subexpressions.
`count_ops`([visual])	Wrapper for count_ops that returns the operation count.
`doit`(**hints)	Evaluate objects that are not evaluated by default like limits, integrals, sums and products.
`dummy_eq`(other[, symbol])	Compare two expressions and handle dummy symbols.
`encloses`(o)	Return True if o is inside (not on or outside) the boundaries of self.
`evalf`([n, subs, maxn, chop, strict, quad, ...])	Evaluate the given formula to an accuracy of n digits.
`find`(query[, group])	Find all subexpressions matching a query.
`fromiter`(args, **assumptions)	Create a new object from an iterable.
`has`(*patterns)	Test whether any subexpression matches any of the patterns.
`has_free`(*patterns)	Return True if self has object(s) `x` as a free expression else False.
`has_xfree`(s)	Return True if self has any of the patterns in s as a free argument, else False.
`intersection`(o)	Returns a list of all of the intersections of self with o.
`is_same`(b[, approx])	Return True if a and b are structurally the same, else False.
`match`(pattern[, old])	Pattern matching.
`matches`(expr[, repl_dict, old])	Helper method for match() that looks for a match between Wild symbols in self and expressions in expr.
`mesh`([plot, show_edges])	TODO : raise TypeError("Given points must be a sequence or an array.")
`n`([n, subs, maxn, chop, strict, quad, verbose])	Evaluate the given formula to an accuracy of n digits.
`rcall`(*args)	Apply on the argument recursively through the expression tree.
`refine`([assumption])	See the refine function in sympy.assumptions
`replace`(query, value[, map, simultaneous, exact])	Replace matching subexpressions of `self` with `value`.
`rewrite`(*args[, deep])	Rewrite self using a defined rule.
`rotate`(angle[, pt])	Rotate `angle` radians counterclockwise about Point `pt`.
`save_as_mesh`(save_path[, end_closed])	Save the tubular mesh to a file.
`scale`([x, y, pt])	Scale the object by multiplying the x,y-coordinates by x and y.
`simplify`(**kwargs)	See the simplify function in sympy.simplify
`sort_key`([order])	Return a sort key.
`subs`(args, *kwargs)	Substitutes old for new in an expression after sympifying args.
`translate`([x, y])	Shift the object by adding to the x,y-coordinates the values x and y.
`xreplace`(rule)	Replace occurrences of objects within the expression.

copy
could_extract_minus_sign
is_hypergeometric

mesh(plot=False, show_edges=True)[source]

TODO : raise TypeError(“Given points must be a sequence or an array.”)

Notes

theta_res should be 1 less then else where. To be fixed in the future.

save_as_mesh(save_path, end_closed=True)[source]

Save the tubular mesh to a file. The file format is determined by the extension of the filename. The possible file formats are: [“.ply”, “.stl”, “.vtk”, “.vtu”].

TODO : There seems to be a bug in correction option of the to_meshio_data() method of the tubular mesh.

Parameters

save_pathstr: The path and the name of the file to be saved with the extension.
end_closedbool: If True, the ends of the tube will be closed. The default value is True.

Returns

meshpyvista.UnstructuredGrid: The tubular mesh.

Examples

>>> from polytex.geometry import Tube
>>> tube = Tube(5,10,major=2, minor=1,h=5)
>>> tube.save_as_mesh('tube.vtu')

property bounds: Return a tuple (xmin, ymin, xmax, ymax) representing the bounding rectangle for the geometric figure.

Parametric geometries

class polytex.geometry.basic.ParamCurve(limits, function=[], dataset=None, krig_config=('lin', 'cub'), smooth=0.0, verbose=False)[source]

Bases: object

Parameters

limits3-tuple

Function parameter and lower and upper bounds.

functionlist

The function list for each coordinate component. The default value is [].

datasetarray_like

The dataset of the curve. The default value is None. The first column is the parameter and the other columns are the value of coordinate components.

One of the function or dataset must be given. Please note that both are given, the dataset will be ignored.

krig_configtuple

The kriging interpolation configuration. The default value is (“lin”, “cub”). The tuple should be in the form of (drift_name, covariance_name).

smoothfloat

The smoothing factor. The default value is 0.0.

verbosebool

If True, print the information of the kriging process. The default value is False.

Returns

curveParamCurve object

Methods

eval(t_value)

Evaluate the curve at a given parameter value.

bounds

eval(t_value)[source]

Evaluate the curve at a given parameter value. The parameter value should be within the limits. Otherwise, an error will be raised.

Parameters

t_valuefloat or array_like: The parameter value for evaluation.

Returns

curveCurve object: The evaluated curve.

class polytex.geometry.basic.ParamSurface(functions, limits, **kwargs)[source]

Bases: GeometryEntity

Parameters

functionslist of functions: Function argument should be (x(s, t), y(s, t), z(s, t)) for a 3D surface.
limits2-tuple: Function parameter and lower and upper bounds of the two parameters. For example, ((s, 0, 1), (t, 0, 1)) is valid. The parameter should be the same for all three functions.

Attributes

args: Returns a tuple of arguments of ‘self’.
assumptions0: Return object type assumptions.
bounds: Return a tuple (xmin, ymin, xmax, ymax) representing the bounding rectangle for the geometric figure.
canonical_variables: Return a dictionary mapping any variable defined in self.bound_symbols to Symbols that do not clash with any free symbols in the expression.
expr_free_symbols
free_symbols: Return from the atoms of self those which are free symbols.
func: The top-level function in an expression.
functions: The functions specifying the surface.
is_algebraic
is_antihermitian
is_commutative
is_comparable: Return True if self can be computed to a real number (or already is a real number) with precision, else False.
is_complex
is_composite
is_even
is_extended_negative
is_extended_nonnegative
is_extended_nonpositive
is_extended_nonzero
is_extended_positive
is_extended_real
is_finite
is_hermitian
is_imaginary
is_infinite
is_integer
is_irrational
is_negative
is_noninteger
is_nonnegative
is_nonpositive
is_nonzero
is_odd
is_polar
is_positive
is_prime
is_rational
is_real
is_transcendental
is_zero
limits: The limits of the two parameters specifying the surface.

Methods

`as_content_primitive`([radical, clear])	A stub to allow Basic args (like Tuple) to be skipped when computing the content and primitive components of an expression.
`as_dummy`()	Return the expression with any objects having structurally bound symbols replaced with unique, canonical symbols within the object in which they appear and having only the default assumption for commutativity being True.
`atoms`(*types)	Returns the atoms that form the current object.
`class_key`()	Nice order of classes.
`compare`(other)	Return -1, 0, 1 if the object is less than, equal, or greater than other in a canonical sense.
`count`(query)	Count the number of matching subexpressions.
`count_ops`([visual])	Wrapper for count_ops that returns the operation count.
`doit`(**hints)	Evaluate objects that are not evaluated by default like limits, integrals, sums and products.
`dummy_eq`(other[, symbol])	Compare two expressions and handle dummy symbols.
`encloses`(o)	Return True if o is inside (not on or outside) the boundaries of self.
`eval`(s_value, t_value)	Evaluate the surface at the given parameter values.
`evalf`([n, subs, maxn, chop, strict, quad, ...])	Evaluate the given formula to an accuracy of n digits.
`find`(query[, group])	Find all subexpressions matching a query.
`fromiter`(args, **assumptions)	Create a new object from an iterable.
`has`(*patterns)	Test whether any subexpression matches any of the patterns.
`has_free`(*patterns)	Return True if self has object(s) `x` as a free expression else False.
`has_xfree`(s)	Return True if self has any of the patterns in s as a free argument, else False.
`intersection`(o)	Returns a list of all of the intersections of self with o.
`is_same`(b[, approx])	Return True if a and b are structurally the same, else False.
`match`(pattern[, old])	Pattern matching.
`matches`(expr[, repl_dict, old])	Helper method for match() that looks for a match between Wild symbols in self and expressions in expr.
`n`([n, subs, maxn, chop, strict, quad, verbose])	Evaluate the given formula to an accuracy of n digits.
`rcall`(*args)	Apply on the argument recursively through the expression tree.
`refine`([assumption])	See the refine function in sympy.assumptions
`replace`(query, value[, map, simultaneous, exact])	Replace matching subexpressions of `self` with `value`.
`rewrite`(*args[, deep])	Rewrite self using a defined rule.
`rotate`(angle[, axis])	Rotate `angle` radians counterclockwise about Point `pt`.
`scale`([x, y, z])	Scale the object by multiplying the x,y-coordinates by x and y.
`simplify`(**kwargs)	See the simplify function in sympy.simplify
`sort_key`([order])	Return a sort key.
`subs`(args, *kwargs)	Substitutes old for new in an expression after sympifying args.
`translate`([x, y, z])	Shift the object by adding to the x,y-coordinates the values x and y.
`xreplace`(rule)	Replace occurrences of objects within the expression.

copy
could_extract_minus_sign
is_hypergeometric

eval(s_value, t_value)[source]

Evaluate the surface at the given parameter values.

Parameters

s_valuefloat or array_like: The parameter value for evaluation.
t_valuefloat or array_like: The parameter value for evaluation.

Returns

Surface: The surface evaluated at the given parameter values. the shape of the returned surface is (len(s) * len(t), 3). The first column is s values, the second column is t values, and the following columns are the coordinates of the surface at the given parameter values (x, y, z).

rotate(angle, axis='z')[source]

Rotate angle radians counterclockwise about Point pt.

The default pt is the origin, Point(0, 0)