ddg.optimize.ifs.functionals module

Module for functionals defined on IndexedFaceSets.

The general form of a functional f is f(ifs, *attributes), where ifs is the IndexedFaceSet and attributes are the names of the attributes to be used.

It is assumed that a functional ‘knows’ on what kind of cell it is defined.

Note that we also call vector-valued maps functionals.

ddg.optimize.ifs.functionals.flat_cubic_quad(ifs, attr_name)

Flatness energy of 4-gonal indexed face set calculated on each face as the distance of its diagonals.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

numpy.ndarray

ddg.optimize.ifs.functionals.g_flat_cubic_quad(ifs, attr_name)

Jacobian for flat_cubic_quad.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

scipy.sparse.csr_matrix

ddg.optimize.ifs.functionals.flat_cubic_n_quad(ifs, attr_name)

Flatness energy of 4-gonal indexed face set calculated on each face as the distance of its diagonals divided by the average lengths of the diagonals.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

numpy.ndarray

ddg.optimize.ifs.functionals.g_flat_cubic_n_quad(ifs, attr_name)

Jacobian for flat_cubic_n_quad.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

scipy.sparse.csr_matrix

ddg.optimize.ifs.functionals.flat_cubic_n2_quad(ifs, attr_name)

Flatness energy of 4-gonal indexed face set calculated on each face as the distance of its diagonals d1, d2 mutliplied by (1/d1**2+1/d2**2).

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

numpy.ndarray

ddg.optimize.ifs.functionals.g_flat_cubic_n2_quad(ifs, attr_name)

Jacobian for flat_cubic_n2_quad.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

scipy.sparse.csr_matrix

ddg.optimize.ifs.functionals.flat_det_quad(ifs, attr_name)

Flatness energy of 4-gonal indexed face set calculated on each face as the determinant of the matrix given by its horizontal, vertical and the corresponding diagonal vector.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

numpy.ndarray

ddg.optimize.ifs.functionals.g_flat_det_quad(ifs, attr_name)

Jacobian for flat_det_quad.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

scipy.sparse.csr_matrix

ddg.optimize.ifs.functionals.circ_angle_quad(ifs, attr_name)

Circularity energy of 4-gonal indexed face set calculated by the angles of its faces.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

numpy.ndarray

ddg.optimize.ifs.functionals.g_circ_angle_quad(ifs, attr_name)

Jacobian for flat_det_quad.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 3-dim. vertex attribute to use

Returns:

scipy.sparse.csr_matrix

ddg.optimize.ifs.functionals.dirichlet(ifs, attr_name)

Dirichlet energy for indexed face sets.

Parameters:

ifsddg.datastructures.indexedfaceset.ifs.IndexedFaceSet

4-gonal indexed face set to calculate the energy on

attr_namestr

Name of the 1-dim. vertex attribute to use

Returns:

numpy.ndarray