openalea.cellcomplex.property_topomesh.property_topomesh_optimization.property_topomesh_vertices_deformation

openalea.cellcomplex.property_topomesh.property_topomesh_optimization.property_topomesh_vertices_deformation(topomesh, iterations=1, omega_forces={'taubin_smoothing': 0.65}, sigma_deformation=0.1, gradient_derivatives=None, gaussian_sigma=10.0, resolution=(1.0, 1.0, 1.0), target_normal=None, target_areas=None, fix_borders=False)

Optimize the positions of the mesh vertices along multiple criteria.

The ‘barycenter’ property of the elements of degree 0 is updated following a different “force” vector for each vertex. This vector is computed as the opposite of the gradient of a composite energy functional defined over the mesh. The weights of the energy terms are to be specified in the function arguments. The deformation is constrained to a possibly small range around each vertex.

The function can for instance be used to apply a smoothing to the mesh (laplacian, curvature flow, taubin), or for more complex optimization such as planarization of interfaces, or triangle quality enhancement.

Parameters:

• topomesh (openalea.cellcomplex.property_topomesh.PropertyTopomesh) – The structure on which to apply the optimization.
• iterations (int) – The number of times the deformation is repeated.
• omega_forces (dict) –

  The weights (float) associated to each energy term:

  • regularization: energy optimizing triangle eccentricity
  • area: energy optimizing triangle size homogeneity
  • gradient: energy pushing vertices towards local maxima of a gradient field
  • laplacian: energy regularizing cell edges towards straight lines
  • planarization: energy regularizing cell interfaces towards planar surfaces
  • epidermis_planarization: energy regularizing outer cell surfaces towards planar surfaces
  • convexity: energy regularizing outer cell surfaces towards spherical surfaces
  • laplacian_smoothing: energy regularizing the mesh using a Laplacian operator
  • gaussian_smoothing: energy regularizing the mesh using a Gaussian operator
  • curvature_flow_smoothing: energy regularizing the mesh using a Cotangent Laplacian operator
  • taubin_smoothing: energy regularizing the mesh using two-pass Gaussian operator

• sigma_deformation (float) – The maximal allowed amplitude of a deformation of a vertex at each iteration.
• gaussian_sigma (float) – The standard deviation used to compute gaussian weights in gaussian/taubin smoothing.
• gradient_derivatives (openalea.image.SpatialImage) – The 3 derivatives of the gradient field (x, y, z) used for gradient optimization.
• target_normal (numpy.array, optional) – The normal of the desired plane for the interface planarization optimization. If None, the direction linking cell centers is chosen.
• target_areas (numpy.array, optional) – The values of areas to which the mesh triangles should tend in the area optimization. If None, the average area value is chosen.
• fix_borders (bool) – Whether the border vertices should be fixed or not (in the case of open surfaces).

Returns:

None

Note

The PropertyTopomesh passed as argument is updated.