Distance Between Two Surfaces

Compute the average thickness between two surfaces.

For example, you might have two surfaces that represent the boundaries of lithological layers in a subsurface geological model and you want to know the average thickness of a unit between those boundaries.

We can compute the thickness between the two surfaces using a few different methods. First, we will demo a method where we compute the normals of the bottom surface, and then project a ray to the top surface to compute the distance along the surface normals. Second, we will use a KDTree to compute the distance from every point in the bottom mesh to it’s closest point in the top mesh.

import pyvista as pv
import numpy as np

# A helper to make a random surface
def hill(seed):
    mesh = pv.ParametricRandomHills(randomseed=seed, u_res=50, v_res=50,
                                    hillamplitude=0.5)
    mesh.rotate_y(-10) # give the surfaces some tilt

    return mesh

h0 = hill(1).elevation()
h1 = hill(10)
# Shift one surface
h1.points[:,-1] += 5
h1 = h1.elevation()

p = pv.Plotter()
p.add_mesh(h0, smooth_shading=True)
p.add_mesh(h1, smooth_shading=True)
p.show_grid()
p.show()

Ray Tracing Distance

Compute normals of lower surface

h0n = h0.compute_normals(point_normals=True, cell_normals=False,
                         auto_orient_normals=True)

Travel along normals to the other surface and compute the thickness on each vector.

h0n["distances"] = np.empty(h0.n_points)
for i in range(h0n.n_points):
    p = h0n.points[i]
    vec = h0n["Normals"][i] * h0n.length
    p0 = p - vec
    p1 = p + vec
    ip, ic = h1.ray_trace(p0, p1, first_point=True)
    dist = np.sqrt(np.sum((ip - p)**2))
    h0n["distances"][i] = dist

# Replace zeros with nans
mask = h0n["distances"] == 0
h0n["distances"][mask] = np.nan
np.nanmean(h0n["distances"])

Out:

5.144072866943829

p = pv.Plotter()
p.add_mesh(h0n, scalars="distances", smooth_shading=True)
p.add_mesh(h1, color=True, opacity=0.75, smooth_shading=True)
p.show()

Nearest Neighbor Distance

You could also use a KDTree to compare the distance between each point of the upper surface and the nearest neighbor of the lower surface. This won’t be the exact surface to surface distance, but it will be noticeably faster than a ray trace, especially for large surfaces.

from scipy.spatial import KDTree

tree = KDTree(h1.points)
d, idx = tree.query(h0.points )
h0["distances"] = d
np.mean(d)

Out:

4.843639430073732

p = pv.Plotter()
p.add_mesh(h0, scalars="distances", smooth_shading=True)
p.add_mesh(h1, color=True, opacity=0.75, smooth_shading=True)
p.show()