Volume Free-form Deformation

class VFFD(triangles, fixval, n_control_points=None, ffd_mask=None)[source]

Bases: CFFD

Class that handles the Volumetric Free Form Deformation on the mesh points.

Parameters:

  • n_control_points (list) – number of control points in the x, y, and z direction. Default is [2, 2, 2].

  • mode (string) – it can be affine or triaffine. The first option is for the F that are affine in all the coordinates of the points. The second one is for functions that are F in the coordinates of the points. The first option implies the second, but is optimal for that class of functions.

Variables:

  • box_length (numpy.ndarray) – dimension of the FFD bounding box, in the x, y and z direction (local coordinate system).

  • box_origin (numpy.ndarray) – the x, y and z coordinates of the origin of the FFD bounding box.

  • n_control_points (numpy.ndarray) – the number of control points in the x, y, and z direction.

  • array_mu_x (numpy.ndarray) – collects the displacements (weights) along x, normalized with the box length x.

  • array_mu_y (numpy.ndarray) – collects the displacements (weights) along y, normalized with the box length y.

  • array_mu_z (numpy.ndarray) – collects the displacements (weights) along z, normalized with the box length z.

  • fun (callable) – it defines the F of the constraint F(x)=c. Default is the constant 1 function.

  • fixval (numpy.ndarray) – it defines the c of the constraint F(x)=c. Default is 1.

  • ffd_mask (numpy.ndarray) – a boolean tensor that tells to the class which control points can be moved, and in what direction, to enforce the constraint. The tensor has shape (n_x,n_y,n_z,3), where the last dimension indicates movement on x,y,z respectively. Default is all true.

  • fun_mask (numpy.ndarray) – a boolean tensor that tells to the class on which axis which constraint depends on. The tensor has shape (n_cons,3), where the last dimension indicates dependency on on x,y,z respectively. Default is all true. It used only in the triaffine mode.

Example:
>>> from pygem import VFFD
>>> import numpy as np
>>> import meshio
>>> mesh = meshio.read('tests/test_datasets/test_sphere_cffd.stl')
>>> original_mesh_points = mesh.points
>>> triangles = mesh.cells_dict["triangle"]
>>> b = np.random.rand(1)
>>> vffd = VFFD(triangles, b, [2, 2, 2])
>>> vffd.read_parameters('tests/test_datasets/parameters_test_cffd.prm')
>>> vffd.adjust_control_points(original_mesh_points)
>>> new_mesh_points = vffd(original_mesh_points)
>>> assert np.isclose(np.linalg.norm(vffd.fun(new_mesh_points) - b), np.array([0.]), atol=1e-07)