Tow class example

This example shows how to use the Tow class in PolyTex package. It is designed to handle the parametrization and geometrical analysis of a fiber tow. A Tow instance is created by passing the point cloud of a tow, which consists only the points on the tow surface, to the constructor.

Example dataset

import polytex as ptx
import numpy as np

# Load the surface points of fiber tow
path = ptx.example("surface points")
surf_points = ptx.read_explicit_data(path)

resolution = 0.022  # mm/pixel
surf_points = surf_points * resolution  # convert to millimeters

We clip the coordinates to discard the part of the tow that is necessary for the modeling of the tow. Optional.

mask = (surf_points[:, 0] > 1.1 - 0.2) & (surf_points[:, 0] < 11.55 + 0.2)
surf_points_clip = surf_points[mask]

Exchange the first and last column for geometry analysis. Note that the last column is deemed as the label column. Namely, the points with the same label are considered as belonging to the same slice and are parametrized in the radial direction (theta). This data reorder is necessary for the users.

coordinates = surf_points_clip[:, [0, 1, 2]]

We can filtering the points to remove noise or the points that are not necessary: mask = abs(coordinates[:, -1] - 9.196) > 0.09 coordinates = coordinates[mask]

Create a Tow instance with PolyTex Tow class

tow = ptx.Tow(
        surf_points=coordinates,
        order="xyz",
        rho_fiber=2550,
        radius_fiber=6.5e-6,
        length_scale="mm", tex=1100,
        name="weft_0")

Get the parametric coordinates of the tow: The points on the same slice are parametrized in the radial direction (theta) and stored in the normalized distance column of the attribute, tow.coordinates, a pandas DataFrame.

df_coord = tow.coordinates  # parametric coordinates of the tow

Get the geometrical features of the tow: The geometrical features of the tow are stored in the attribute, tow.geom_features, a pandas DataFrame. For straight fiber tows, the geometrical features can be used as an approximation of the actual tow geometry. But for wavy tows, such as binder, the geometrical features are not accurate enough. We need to redo the geometrical analysis after identifying the normal cross-sections of the tow.

df_geom = tow.geom_features  # geometrical features of the tow

Resampling

Resampling the control points of the tow with a uniform spacing in the normalized distance direction. The resampling is necessary to create a parametric representation based on dual kriging.

# Equidistant resampling of the tow control points in the radial direction.
theta_res = 40  # number of control points in the radial direction
sample_position = np.linspace(0, 1, theta_res, endpoint=True)  # equal spaced points (normalized distance)

# # Resampling according to distribution density
# cluster = tow.kde(bw=0.004)
# sample_position = cluster["cluster centers"]

pts_krig, expr_krig = tow.resampling(krig_config=("lin", "cub"),
                                     skip=5, sample_position=sample_position,
                                     smooth=0.00001)

Save and reload the tow instance

tow.save(“./tow/weft_0.tow”)

Plot the tow

mesh = tow.surf_mesh(plot=True, save_path="./test_data/weft_0.ply", end_closed=True)

Smooth the tow trajectory with Kriging

trajectory_sm = tow.trajectory(smooth=0.0015, plot=False,
                               save_path="./test_data/trajectory.ply", orientation=True)

Axial and radial lines

Get the axial lines of the tow (the lines connecting the parametrized control points in the axial direction)

line_axi = tow.axial_lines(plot=True)

# Get the radial lines of the tow (the lines connecting the parametrized control points in
# the radial direction)
line_rad = tow.radial_lines(plot=True)

Get the normal cross-sections of the tow

So far, we provide two methods to get the normal cross-sections of the tow. The first method wraps the intersection function of plane and surface mesh in the pyvista package. The second method is based on the intersection of a parametric curve and an implicit plane.

cross_section, planes, clipped = tow.normal_cross_section(algorithm="pyvista")

Update the geometrical features of the tow

The geometrical features of the tow are stored in the attribute, tow.geom_features, a pandas DataFrame. You have this information once the tow instance is created. However, that is calculated based on the vertical cross-sections of the tow. A more accurate geometrical analysis can be done during the identification of the normal cross-sections with the class method, Tow.normal_cross_section. Acess the updated geometry features according to the normal cross-sections.

df_geom_pv = tow.geom_features.copy()

Get the normal cross-sections of the tow

The kriging method is based on the intersection of a parametric curve and an implicit plane.

cross_section, plane, clipped = tow.normal_cross_section(algorithm="kriging", plot=True,
                                                             i_size=2, j_size=3, skip=15)
# Acess the updated geometry features according to the normal cross-sections.
df_geom_krig = tow.geom_features

Geometry features

as shwon above, the tow geometry features can be updated after the normal cross-sections are identified using both method. However, the accuracy are different. The pyvista method is faster but less accurate. In the kriging method, we transform the identified cross-sections to a 2d plane. The geometry features are then calculated based on the 2d coordinates. Thus, the geometry features are more accurate than the pyvista method. However, this also makes the kriging method less efficient. The kriging method is recommended for wavy tows, such as binder.