OOF2: The Manual

Details

Description

EdgeFromNodes is a BoundaryConstructor, used as the constructor argument of the OOF.Skeleton.Boundary.Construct command when building Skeleton boundaries. It creates Edge Boundaries from the currently selected Skeleton Nodes or from a group of Nodes. The Nodes are specified by the group parameter, which must be either the name of a Node group or the special placeholder object, selection.

Edge boundaries must be constructed from a single contiguous non-branching set of Segments. To create an edge boundary, therefore, OOF2 must be able to find a unique path from Node to Node along the Segments joining them, passing through all of the selected Nodes exactly once. This is a version of the Hamiltonian path problem, which is NP-complete. That means that solving it is computationally expensive when the number of Nodes is large. However, if the selected set is not too large and is more or less linear (i.e, it defines a reasonable boundary) then OOF2 will be able to find the path quickly.

Not all sets of Nodes define a set of Segments, and some sets of Nodes can define more than one set of Segments. In those cases, EdgeFromNodes will fail and no boundary will be defined. In the GUI, the OK button in the dialog box will be disabled if the Nodes don't define exactly one linearly connected set of Segments. See Figure 6.74 to Figure 6.78 for some examples of configurations that do and do not define edge boundaries.

Edge boundaries must be directed. Boundary conditions use the direction to determine the boundary normal and the direction of applied Fields and Fluxes. The direction parameter specifies the direction of the boundary being created. The legal values for direction depend on the topology of the boundary being constructed. When the Segments form a closed loop, the legal values are 'Clockwise' and 'CounterClockwise'. When the Segments form an open line or curve, the values are 'Left to right', 'Right to left', 'Top to bottom', and 'Bottom to top'. OOF2 compares the positions of only the first and last Nodes when determining the direction of an open boundary.

EdgeFromNodes will always create a closed boundary if the set of Nodes allows it. To create an open boundary from a set of Nodes that also defines a closed boundary, first create the closed boundary and then use OOF.Skeleton.Boundary.Modify to remove one or more Segments from it.

Figure 6.74. Constructing a Closed Edge Boundary from Nodes

(a) Some selected Nodes (blue dots) in a Skeleton.

(b) Because the nodes can be connected by a loop of Segments, the choices for direction in the New Boundary dialog box are 'Clockwise' and 'Counterclockwise'.

(c) The clockwise boundary (orange lines and arrows) constructed from the selected Nodes.

Figure 6.75. Constructing an Open Edge Boundary from Nodes

(a) The selected Nodes do not form a closed loop, but they can be linked into an open path …

(b) … so the choices for direction are 'Left to right', etc.

(c) The boundary that would be constructed by choosing 'Left to right' or 'Buttom to top' in (b).

Figure 6.76. Failing to Construct an Edge Boundary

Adding a single Node to the selection in Figure 6.74 makes it impossible to connect the Nodes with a non-branching set of Segments. No boundary can be constructed. The dialog box says “No edge sequence” and the OK button is disabled.

Figure 6.77. Constructing an Edge Boundary Again

Adding yet another Node to the selection in Figure 6.76 makes it possible to construct a path through all the Nodes again.

Figure 6.78. More Failed Configurations

(a) There is more than one possible path through the set of Nodes, so it cannot be used to form an edge boundary.

(b) There is no path that joins the upper Nodes to the lower Nodes, so this set cannot be used to form a boundary either.

See Also