Project points to a plane and Tessellate

Using pyvista and numpy, generate a 3D point cloud, project it to a plane, and tessellate it.

This demonstrates how to use pyvista.UnstructuredGridFilters.delaunay_2d and a simple numpy function that projects points to a plane.

from __future__ import annotations

import numpy as np

import pyvista as pv

Project Points

Create a point cloud and project it to a plane.

num_points = 100
rng = np.random.default_rng(seed=0)  # Seed rng for reproducibility
point_cloud = rng.random((num_points, 3))

# Define a plane
origin = [0, 0, 0]
normal = [0, 0, 1]
plane = pv.Plane(center=origin, direction=normal)


def project_points_to_plane(points, plane_origin, plane_normal):
    """Project points to a plane."""
    vec = points - plane_origin
    dist = np.dot(vec, plane_normal)
    return points - np.outer(dist, plane_normal)


projected_points = project_points_to_plane(point_cloud, origin, normal)

# Create a polydata object with projected points
polydata = pv.PolyData(projected_points)

# Mesh using delaunay_2d and pyvista
mesh = polydata.delaunay_2d()

Visualize the Result

# Create a plane for visualization
plane_vis = pv.Plane(
    center=origin,
    direction=normal,
    i_size=2,
    j_size=2,
    i_resolution=10,
    j_resolution=10,
)

# plot it
pl = pv.Plotter()
pl.add_mesh(mesh, show_edges=True, color='white', opacity=0.5, label='Tessellated mesh')
pl.add_mesh(
    pv.PolyData(point_cloud),
    color='red',
    render_points_as_spheres=True,
    point_size=10,
    label='Points to project',
)
pl.add_mesh(plane_vis, color='blue', opacity=0.1, label='Projection Plane')
pl.add_legend()
pl.show()

Static Scene

Interactive Scene