CAD shape to signed-distance field

A tessellated CAD part drives a signed-distance volume directly through PyVista’s compute_implicit_distance. The result is a volumetric scalar field useful for collision queries, mesh morphing, implicit modeling, or feeding marching-cubes-style reconstructions.

The part is a real STEP solid, the NIST AM Bench 2022 LPBF bridge specimen (public domain, https://doi.org/10.18434/mds2-2607). Its multi-leg structure gives the SDF interior real shape to slice through.

import numpy as np
import pandas as pd
import pyvista as pv

import pyvista_cad
from pyvista_cad.examples import downloads

Load the real STEP part as a surface.

part = pyvista_cad.read_step(downloads.step_part_path()).combine().extract_surface()
part

/home/runner/work/pyvista-cad/pyvista-cad/examples/05_workflows/cad_to_signed_distance.py:28: PyVistaFutureWarning: The default value of `algorithm` for the filter
`UnstructuredGrid.extract_surface` will change in the future. It currently defaults to
`'dataset_surface'`, but will change to `None`. Explicitly set the `algorithm` keyword to
silence this warning.
  part = pyvista_cad.read_step(downloads.step_part_path()).combine().extract_surface()

PolyData (0x7f6faa75c7c0)
  N Cells:    436
  N Points:   690
  N Strips:   0
  X Bounds:   0.000e+00, 7.500e+01
  Y Bounds:   -2.446e-13, 5.000e+00
  Z Bounds:   0.000e+00, 1.225e+01
  N Arrays:   8

PolyData 690 points 436 cells 48 KiB

Bounds⧉X [0.000e+00, 7.500e+01]Y [-2.446e-13, 5.000e+00]Z [0.000e+00, 1.225e+01]

Cellsfaces 436

• Point Data: (1)
  • vtkOriginalPointIds⧉
    scalar
    int64
    [0.000e+00, 6.890e+02]
• Cell Data: (1)
  • vtkOriginalCellIds⧉
    scalar
    int64
    [0.000e+00, 4.350e+02]
• Field Data: (6)
  • cad.color⧉
    (4,)
    float64
  • cad.label⧉
    (1,)
    <U23
  • cad.source_format⧉
    (1,)
    <U4
  • cad.reader⧉
    (1,)
    <U21
  • cad.backend⧉
    (1,)
    <U9
  • cad.units⧉
    (1,)
    <U2

Build a uniform grid wrapping the part with a small margin.

bounds = np.array(part.bounds).reshape(3, 2)
margin = 4.0
dims = np.array((90, 30, 40))
origin = bounds[:, 0] - margin
spacing = (bounds[:, 1] - bounds[:, 0] + 2 * margin) / (dims - 1)
grid = pv.ImageData(dimensions=dims, origin=origin, spacing=spacing)

Sample the signed distance into the volume.

grid = grid.compute_implicit_distance(part)
sdf = grid['implicit_distance']

pd.DataFrame(
    {
        'metric': ['SDF min', 'SDF max', 'inside-mass fraction'],
        'value': [sdf.min(), sdf.max(), float((sdf < 0).mean())],
    }
)

	metric	value
0	SDF min	-2.275862
1	SDF max	8.554969
2	inside-mass fraction	0.165463

Slice the SDF through two orthogonal planes to expose the interior field.

mid = bounds.mean(axis=1)
slc_z = grid.slice(normal='z', origin=mid)
slc_x = grid.slice(normal='x', origin=mid)
clim = (-float(np.percentile(np.abs(sdf), 95)), float(np.percentile(np.abs(sdf), 95)))

pl = pv.Plotter()
pl.add_mesh(part, color='lightgray', opacity=0.2)
pl.add_mesh(
    slc_z,
    scalars='implicit_distance',
    cmap='RdBu',
    clim=clim,
    scalar_bar_args={'title': 'signed dist [mm]'},
)
pl.add_mesh(slc_x, scalars='implicit_distance', cmap='RdBu', clim=clim, show_scalar_bar=False)
pl.show()

Static Scene

Interactive Scene