Just to illustrate the geometry — here's an example from a CAD tool like AutoCAD.

The surface starts at a single vertex (top of the rod) and curves inward. This is the kind of shape I'm trying to build in PyVista.

But when I use delaunay_2d() or connect the points manually, the mesh curves upward, forming a convex shape.

The CAD version shows the intended concave behavior — maybe this clarifies what I'm trying to build?

Just to illustrate the geometry — here's an example from a CAD tool like AutoCAD.

The surface starts at a single vertex (top of the rod) and curves inward. This is the kind of shape I'm trying to build in PyVista.

But when I use delaunay_2d() or connect the points manually, the mesh curves upward, forming a convex shape.

This isn't caused by delaunay_2d. The points themselves have the wrong shape to begin with:

import pyvista as pv
import numpy as np

# Parameters
R = 20
h_top = 20
segments = 80
rings = 40

# Generate points on concentric rings
points = []
for r in np.linspace(0, R, rings):
    for i in range(segments):
        angle = 2 * np.pi * i / segments
        x = r * np.cos(angle)
        y = r * np.sin(angle)
        z = - (x**2 + y**2) / R + h_top  # Concave surface formula
        points.append([x, y, z])

# Create PolyData and apply delaunay_2d
points = np.array(points)
mesh = pv.PolyData(points)

# Visualize
plotter = pv.Plotter(off_screen=False)
plotter.add_mesh(points, color='black')
plotter.show()

Thanks for replying! I'm still quite new to PyVista and Python in general, so I'm trying to wrap my head around all this.

What confused me was that the points follow a downward shape based on the formula (like a bowl), but when I use delaunay_2d() to create the surface, it ends up looking like a dome that curves upward instead. I'm not really sure why it's connecting the points like that — maybe it's projecting them onto a flat plane?

I'd love to understand how to build a surface that matches the actual depth of the points, so it bends inward properly. Should I be using a different method or structure?

Thanks again for the help — I appreciate it!

This works beautifully — thank you so much! 🙏
The surface is exactly what I was trying to build. Using StructuredGrid made all the difference.

I really appreciate your help! I'm just getting started with PyVista and was stuck on this for a while — really grateful for the guidance!

Hi there.

I’m working with your curved surface formula to simulate lightning protection zones as spherical segments. To verify its geometric accuracy, I set up a controlled test:

I used a surface height of 10 meters

I set the sphere radius to 10 meters

Under these conditions, the curve should match exactly with a spherical arc—since the point lies on the sphere’s topmost segment.

However, when I compare the generated curve against an actual sphere (both with radius 10m), I notice a clear mismatch in curvature. The profile deviates slightly, suggesting the arc length or sag isn’t quite spherical.

Here’s a visual result from the test — you’ll see that the curve falls short of the actual sphere in terms of curvature.

❓My question: Is there a way to refine the formula (or use a parametric correction) so that the surface precisely matches the curvature of a sphere with radius R? I'd appreciate any insight or ideas to achieve a more accurate spherical segment.

Thanks in advance!

❓My question: Is there a way to refine the formula (or use a parametric correction) so that the surface precisely matches the curvature of a sphere with radius R? I'd appreciate any insight or ideas to achieve a more accurate spherical segment.

Yes the key line to modify is the definition of z. I used the reciprocal function (1/r) to model the curve, so you'll want to redefine this to model your desired curve. (This was also the main change that was made compared to your initial post where you had a concave surface).

As a completely different alternative, you can also consider defining an arc and extruding it with extrude_rotate