eigen_compression.py

import igl
import numpy as np
import polyscope as ps
import scipy
from sklearn.preprocessing import normalize
import robust_laplacian 
from scipy.sparse import linalg as sla

path = "scan_007.obj"

# vertices and faces
V,F = igl.read_triangle_mesh(path)

max_eigenvectors = 500

# cotan laplacian and mass matrix
laplacian = igl.cotmatrix(V,F)
massmatrix = igl.massmatrix(V,F)

# eigenvectors of the laplacian
_, eigenvectors = scipy.sparse.linalg.eigsh(
  laplacian, max_eigenvectors, massmatrix, sigma=-1e-6
)

# reverse to order by descending eigenvalues
spectral_basis = eigenvectors[:, ::-1]

# the spectral representation of mesh coordinate functions
# very important to scale by the mass matrix when projecting into the eigenfunctions
spectral_coefficients = spectral_basis.T @ massmatrix @ V

ps.init()

# visualize the original mesh
original_mesh = ps.register_surface_mesh("mesh", V, F)

for k in [500,300, 100,50,10,5]:
  
  # reconstruct with basis truncated to k basis vectors
  # representing different levels of compression
  new_vertices = spectral_basis[:,:k] @ spectral_coefficients[:k,:]

  # visualize the reconstruction
  ps.register_surface_mesh(f"reconstructed_mesh_{k}", new_vertices.astype(np.float32), F)

ps.show()