Load SPHARM Coefficients#

ktch can read spherical harmonic coefficients from SPHARM-PDM .coef files, the output of the ParaToSPHARMMesh step of SPHARM-PDM. This guide reads a sample .coef file and reconstructs the 3D shape encoded by its coefficients.

Read SPHARM-PDM coefficients#

from ktch.datasets import fetch
from ktch.io import read_spharmpdm_coef

coef_path = fetch("danshaku_08_allSegments_SPHARM.coef")
data = read_spharmpdm_coef(coef_path)

print(f"specimen={data.specimen_name}, l_max={data.l_max}, "
      f"shape={data.to_numpy().shape}")

specimen=danshaku_08_allSegments_SPHARM, l_max=25, shape=(676, 3)

data.coeffs[l] holds the complex coefficients of degree l with shape (2*l+1, 3). See Harmonic-based Morphometrics for the convention.

Reconstruct the surface#

Convert the SPHARM-PDM coefficients to the real basis used by SphericalHarmonicAnalysis, then call inverse_transform to evaluate the reconstructed surface on a (theta, phi) grid.

from ktch.harmonic import SphericalHarmonicAnalysis
from ktch.io import spharmpdm_to_sha_coeffs

coeffs = spharmpdm_to_sha_coeffs(data)

sha = SphericalHarmonicAnalysis(n_harmonics=data.l_max)
X_coords = sha.inverse_transform(coeffs)
print(f"surface grid shape: {X_coords.shape}")  # (1, n_theta, n_phi, 3)

surface grid shape: (1, 90, 180, 3)

To use a different angular resolution, pass theta_range and phi_range to inverse_transform.

Plot the 3D shape#

import plotly.graph_objects as go

x, y, z = X_coords[0].T

fig = go.Figure(
    data=[
        go.Surface(x=x, y=y, z=z, opacity=0.8, showscale=False),
    ]
)

fig.update_layout(
    width=700,
    height=700,
    autosize=False,
    scene=dict(
        camera=dict(
            up=dict(x=0, y=0, z=1),
            eye=dict(x=1.1, y=1.1, z=1.1),
        ),
        aspectmode="data",
    ),
)

fig.show()