example of differential geometry tools in slam

# Authors: Guillaume Auzias <guillaume.auzias@univ-amu.fr>

# License: MIT
# sphinx_gallery_thumbnail_number = 2

importation of slam modules

import slam.io as sio
import slam.differential_geometry as sdg
import numpy as np

loading an examplar mesh and corresponding texture

mesh_file = "../examples/data/example_mesh.gii"
texture_file = "../examples/data/example_texture.gii"
mesh = sio.load_mesh(mesh_file)
tex = sio.load_texture(texture_file)

compute various types of Laplacian of the mesh

lap, lap_b = sdg.compute_mesh_laplacian(mesh, lap_type="fem")
print(mesh.vertices.shape)
print(lap.shape)
lap, lap_b = sdg.compute_mesh_laplacian(mesh, lap_type="conformal")
lap, lap_b = sdg.compute_mesh_laplacian(mesh, lap_type="meanvalue")
lap, lap_b = sdg.compute_mesh_laplacian(mesh, lap_type="authalic")

  Computing Laplacian
    Computing mesh weights of type fem
    -edge length threshold needed for  0  values =  0.0  %
    -number of Nan in weights:  0  =  0.0  %
    -number of Negative values in weights:  936  =  6.706792777300086  %
    -nb Nan in Laplacian :  0
    -nb Inf in Laplacian :  0
(2328, 3)
(2328, 2328)
  Computing Laplacian
    Computing mesh weights of type conformal
    -edge length threshold needed for  0  values =  0.0  %
    -number of Nan in weights:  0  =  0.0  %
    -number of Negative values in weights:  936  =  6.706792777300086  %
    -nb Nan in Laplacian :  0
    -nb Inf in Laplacian :  0
  Computing Laplacian
    Computing mesh weights of type meanvalue
    -number of Nan in weights:  0  =  0.0  %
    -number of Negative values in weights:  0  =  0.0  %
    -nb Nan in Laplacian :  0
    -nb Inf in Laplacian :  0
  Computing Laplacian
    Computing mesh weights of type authalic
    -number of Nan in weights:  0  =  0.0  %
    -number of Negative values in weights:  0  =  0.0  %
    -nb Nan in Laplacian :  0
    -nb Inf in Laplacian :  0

smooth the mesh using Laplacian

s_mesh = sdg.laplacian_mesh_smoothing(mesh, nb_iter=100, dt=0.1)

    Smoothing mesh
  Computing Laplacian
    Computing mesh weights of type fem
    -edge length threshold needed for  0  values =  0.0  %
    -number of Nan in weights:  0  =  0.0  %
    -number of Negative values in weights:  936  =  6.706792777300086  %
    -nb Nan in Laplacian :  0
    -nb Inf in Laplacian :  0
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    OK

compute the gradient of texture tex

triangle_grad = sdg.triangle_gradient(mesh, tex.darray[0])
print(triangle_grad)
grad = sdg.gradient(mesh, tex.darray[0])
print(grad)
norm_grad = sdg.norm_gradient(mesh, tex.darray[0])
print(norm_grad)

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[[ 0.00434682  0.00094788 -0.01505408]
 [ 0.00294091  0.00038984 -0.00959341]
 [-0.0190667  -0.010571   -0.01175931]
 ...
 [ 0.0021132   0.00327109  0.01139427]
 [ 0.00167353  0.00282758  0.01242133]
 [ 0.00175571  0.00266182  0.01337094]]
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[[-7.56323397e-03 -3.16016138e-03 -1.21617037e-02]
 [-7.34847031e-03  6.37035386e-05 -1.23221759e-02]
 [ 2.32632728e-03  1.88016554e-03 -3.03642984e-03]
 ...
 [ 4.04642855e-03  2.24089885e-03  1.09245023e-02]
 [ 1.60189335e-03 -1.08939493e-04  4.64315729e-03]
 [-1.52567188e-03 -5.57641899e-04  6.48352716e-04]]
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[0.01466616 0.01434713 0.00426224 ... 0.01186339 0.00491293 0.001749  ]

VISUALIZATION USING INTERNAL TOOLS

import slam.plot as splt

# Plot Original Mesh
display_settings = {}
display_settings['colorbar_label'] = 'Curvature'
mesh_data = {}
mesh_data['vertices'] = mesh.vertices
mesh_data['faces'] = mesh.faces
mesh_data['title'] = 'Mean Curvature'
intensity_data = {}
intensity_data['values'] = tex.darray[0]
intensity_data["mode"] = "vertex"
fig1 = splt.plot_mesh(
    mesh_data=mesh_data,
    intensity_data=intensity_data,
    display_settings=display_settings)
fig1.show()

# Show the Norm of the Gradient of the Curvature

display_settings['colorbar_label'] = 'Gradient Magnitude'
mesh_data['title'] = 'Norm of the Gradient of Curvature'
intensity_data['values'] = norm_grad
intensity_data["mode"] = "vertex"
fig2 = splt.plot_mesh(
    mesh_data=mesh_data,
    intensity_data=intensity_data,
    display_settings=display_settings)
fig2.show()
fig2