Domains

Domains are mainly used when creating nets. There are different types that all inherit from the Domain class, for example

• EmptyDomain

• SmoothDomain

• DiscreteDomain

• SmoothInterval

• DiscreteInterval

or domains specified by their shape, for example

• SmoothRectangularDomain

• DiscreteRectangularDomain

• DiscreteTriangularDomain

• DiscreteDiagonalDomain

These classes are located in ddg.datastructures.nets.domain.

Creating a smooth domain

A smooth domain is given by an interval for each of its direction.

>>> import ddg
>>> import numpy as np

>>> domain = ddg.nets.SmoothDomain([[0,4],[-np.pi, np.pi]])
>>> domain.bounded
True
>>> domain.intervals
[[0.0, 4.0], [-3.141592653589793, 3.141592653589793]]
>>> domain.periodicity
set()

Note that SmoothDomain always expects a list of intervals to be passed to it, even if the domain is supposed to be 1-dimensional. To circumvent this, use SmoothInterval instead:

>>> import ddg

>>> domain = ddg.nets.SmoothInterval([0.0, 4.0])
>>> domain.interval
[0.0, 4.0]

You can also create both unbounded and periodic domains.

>>> import ddg
>>> import numpy as np

>>> domain = ddg.nets.SmoothDomain([[-np.inf, 0], [0, 2]])
>>> domain.bounded
False
>>> domain.unbounded_directions
[0]

To mark a direction as periodic, simply add True as the third entry of its interval:

>>> import ddg

>>> domain = ddg.nets.SmoothDomain([[0, 3], [0, 2*np.pi, True]])
>>> domain.periodicity
{1}

Creating a discrete domain

A DiscreteDomain behaves very much the same as a smooth one. They have all properties of a smooth domain, but additionally contain the combinatorial information of themselves, i.e. their edge and face data. These are used primarily in the conversion to a blender mesh.

>>> import ddg

>>> domain = ddg.nets.DiscreteDomain([[0,4], [-1,10]])
>>> domain.intervals
[[0, 4], [-1, 10]]

Moreover we can iterate over all points inside of a discrete domain with the help of its traverser:

>>> import ddg

>>> domain = ddg.nets.DiscreteDomain([[0,1],[0,1]])
>>> for i in domain.traverser:
...     print(i)
(0, 0)
(0, 1)
(1, 0)
(1, 1)

>>> for i in domain.traverser:
...     print(domain.traverser.idx(*i))
0
1
2
3

>>> for i in domain.edge_data:
...     print(i)
(0, 2)
(0, 1)
(1, 3)
(2, 3)

>>> for i in domain.face_data:
...     print(i)
(0, 2, 3, 1)

Modifying a domain

A domain can be modifyied by utility functions located at ddg.datastructures.nets.utils. Possibilities are

• shrink_domain()

• bound_domain()

• create_subdomain()

• delete_direction()

• modify_direction()

Converting a domain

Bounded discrete domains of dimension 2 or less can be converted to a The half-edge data structure object using the function ddg.conversion.halfedge.nets.discrete_domain_to_halfedge(). The vertices of the resulting halfedge object will have an attribute co containing the value from domain.traverser and the order will be the same.

>>> from ddg.conversion.halfedge.nets import discrete_domain_to_halfedge
>>> domain = ddg.nets.DiscreteDomain([[0,1],[0,1]])
>>> surface = discrete_domain_to_halfedge(domain)

>>> for c in domain.traverser:
...     print(c)
(0, 0)
(0, 1)
(1, 0)
(1, 1)

>>> for v in surface.verts:
...     print(v.co)
(0, 0)
(0, 1)
(1, 0)
(1, 1)

The name of the coordinate attribute can be changed using the co_attr argument of the conversion function.