%matplotlib inline from pyvista import set_plot_theme set_plot_theme('document')
Create Triangulated Surface¶
Create a surface from a set of points through a Delaunay triangulation.
# sphinx_gallery_thumbnail_number = 2 import pyvista as pv import numpy as np
First, create some points for the surface.
# Define a simple Gaussian surface n = 20 x = np.linspace(-200, 200, num=n) + np.random.uniform(-5, 5, size=n) y = np.linspace(-200, 200, num=n) + np.random.uniform(-5, 5, size=n) xx, yy = np.meshgrid(x, y) A, b = 100, 100 zz = A * np.exp(-0.5 * ((xx / b) ** 2.0 + (yy / b) ** 2.0)) # Get the points as a 2D NumPy array (N by 3) points = np.c_[xx.reshape(-1), yy.reshape(-1), zz.reshape(-1)] points[0:5, :]
array([[-197.58765542, -198.28684883, 1.98822521], [-175.84882467, -198.28684883, 2.9836459 ], [-161.80819309, -198.28684883, 3.78176903], [-136.67169993, -198.28684883, 5.50319475], [-112.29205961, -198.28684883, 7.45444972]])
Now use those points to create a point cloud PyVista data object. This will
be encompassed in a :class:
# simply pass the numpy points to the PolyData constructor cloud = pv.PolyData(points) cloud.plot(point_size=15)
Now that we have a PyVista data structure of the points, we can perform a triangulation to turn those boring discrete points into a connected surface.
surf = cloud.delaunay_2d() surf.plot(show_edges=True)
x = np.arange(10, dtype=float) xx, yy, zz = np.meshgrid(x, x, ) points = np.column_stack((xx.ravel(order="F"), yy.ravel(order="F"), zz.ravel(order="F"))) # Perturb the points points[:, 0] += np.random.rand(len(points)) * 0.3 points[:, 1] += np.random.rand(len(points)) * 0.3 # Create the point cloud mesh to triangulate from the coordinates cloud = pv.PolyData(points) cloud
Run the triangulation on these points
surf = cloud.delaunay_2d() surf.plot(cpos="xy", show_edges=True)
Note that some of the outer edges are unconstrained and the triangulation
added unwanted triangles. We can mitigate that with the
surf = cloud.delaunay_2d(alpha=1.0) surf.plot(cpos="xy", show_edges=True)
We could also add a polygon to ignore during the triangulation via the
# Define a polygonal hole with a clockwise polygon ids = [22, 23, 24, 25, 35, 45, 44, 43, 42, 32] # Create a polydata to store the boundary polygon = pv.PolyData() # Make sure it has the same points as the mesh being triangulated polygon.points = points # But only has faces in regions to ignore polygon.faces = np.array([len(ids),] + ids) surf = cloud.delaunay_2d(alpha=1.0, edge_source=polygon) p = pv.Plotter() p.add_mesh(surf, show_edges=True) p.add_mesh(polygon, color="red", opacity=0.5) p.show(cpos="xy")