PolyData is one of the most versatile and commonly used data structures in the PyVista library, which is the Python interface to the visualization Toolkit(VTK). PolyData can be used to represent and manipulate the polygonal data, which includes the vertices, lines, polygons and triangle strips. It is ideal for representing the complex geometries like surfaces and volumes and it is commonly used in computer graphics, computational geometry and scientific visualization.

Key Features

• Points: It can be represents the vertices of the geometry.
• Cells: It can be represents the connections between the points to form lines, polygons, or other higher-dimensional constructs.
• Attributes: Additional data such as scalars, vectors and texture coordinates that can be associated with the points or cells.

Use Cases

• Visualization of the 3D surfaces and meshes.
• Scientific computing and simulations.
• Geometric modeling and computer graphics.
• Finite elements analysis and other enginerring applications.

Creating the PolyData Objects

Creating the PolyData object can involves defining the points (vertices) and the cells (connections between points). PyVista can provides the several methods for creating the PolyData objects, from basic shapes to the complex structures.

Creating from Points and Faces

import pyvista as pv
import numpy as np

# Define points
points = np.array([
    [0, 0, 0],
    [1, 0, 0],
    [1, 1, 0],
    [0, 1, 0],
    [0, 0, 1]
])

# Define faces (each face starts with the number of points it has)
faces = np.hstack([
    [3, 0, 1, 2],  # Triangle
    [4, 0, 1, 2, 3]  # Quadrilateral
])

# Create the PolyData object
mesh = pv.PolyData(points, faces)

Creating from Built-in Shapes

PyVista offers the serveral built-in methods for creating common geometric shapes.

# Create a sphere
sphere = pv.Sphere(radius=1.0, center=(0, 0, 0))

# Create a plane
plane = pv.Plane(center=(0, 0, 0), direction=(0, 0, 1), i_size=1, j_size=1)

Manipulating the PloyData

Once created, PolyData objects can be manipulated using the various methods provided by the PyVista.

Adding the Points and Cells

# Add a point
new_point = [2, 2, 2]
mesh.points = np.vstack([mesh.points, new_point])

# Add a new cell (triangle)
new_face = [3, len(mesh.points) - 1, 1, 2]
mesh.faces = np.hstack([mesh.faces, new_face])

Modifying the Attributes

# Add scalar data to points
scalars = np.random.rand(mesh.n_points)
mesh.point_data['scalars'] = scalars

# Add vector data to cells
vectors = np.random.rand(mesh.n_cells, 3)
mesh.cell_data['vectors'] = vectors

Applying the Transformations

# Translate the mesh
mesh.translate([1, 1, 1], inplace=True)

# Rotate the mesh
mesh.rotate_x(45, inplace=True)

# Scale the mesh
mesh.scale([2, 2, 2], inplace=True)

Example code:

import pyvista as pv
import numpy as np

# Define points and faces
points = np.array([
    [0, 0, 0],
    [1, 0, 0],
    [1, 1, 0],
    [0, 1, 0],
    [0, 0, 1]
])
faces = np.hstack([
    [3, 0, 1, 2],  # Triangle
    [4, 0, 1, 2, 3]  # Quadrilateral
])

# Create PolyData
mesh = pv.PolyData(points, faces)

# Add scalar data
scalars = np.array([1, 2, 3, 4, 5])
mesh.point_data['scalars'] = scalars

# Translate mesh
mesh.translate([1, 0, 0], inplace=True)

# Visualize the mesh
plotter = pv.Plotter()
plotter.add_mesh(mesh, scalars='scalars', show_edges=True)
plotter.show()

Output

Applications of PyVista PolyData

PolyData can be widely used in the various fields due to its versatility and ability to handle the complex geometric data.

Visualization

• It can be used in 3D modeling and rendering.
• Scientific visualization of the simulations and experimental data.

Engineering

• It can be used in Finite element analysis.
• It can be used in CAD/CAM and design verification.

Medical Imaging

• Reconstruction of the anatomical structures from imaging data.
• Visualization of the MRI and CT scans.

Computer Grpahics

• It can be used in Game development.
• It can be used in the Animation and visual effects.

Conclusion

PolyData in PyVista is the powerful and flexible tool for the handling and visualizing the 3D geometric data. Its comprehensive feature set allows the users to create, manipulate, and render the complex shapes and surfaces efficiently. Whether used for the scientific research engineering, or graphics. PolyData can provides the robust foundation for the 3D data representation and processing.