OOF2: The Manual

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Description

FixIllegal is a SkeletonModifier that fixes illegal Skeleton Elements.

Excluding paranormal alien interventions, illegal elements are only generated by moving Nodes manually with the Move Nodes toolbox. Many algorithms used by OOF2 (including solving finite element equations and some Skeleton modifiers) assume that Elements are legal, so it prohibits almost all operations if illegal Elements exist.

FixIllegal fixes an Element by moving one or more of its Nodes to the average position of its neighboring Nodes In many cases, it is sufficient to fix an Element by applying this smoothing procedure to the offending Nodes, namely those Nodes located at corners that subtend interior angles greater than 180° or less than 0° (for quadrilaterals, illegal elements include those that have non-convex geometries). However, this smoothing procedure may not work when the corner angle is very close to zero. In this case, the Nodes at other corners should be moved as well. Each move is ultimately accepted or rejected solely by whether or not it reduces the number of illegal Elements in the vicinity of the Node.

Figure 6.80 illustrates the process of creating and fixing illegal Elements. Notice that in (c) the Nodes are not exactly in their initial positions. This is because FixIllegal is a brutal technique: it pays no attention to Element homogeneity or shape energy and does not attempt to optimize the positions of the Nodes that it moves. If it's necessary to return them to a particular legal configuration, it's better to undo the modification that created the illegal Elements.

Figure 6.80. Fixing Illegal Elements

(a) A section of a Skeleton. The highlighted Nodes will be moved as shown by the arrows to make the highlighted Elements illegal.

(b) The Nodes have been moved and the illegal Elements are automatically highlighted in red. For comparison, the original Element edges are displayed in pale green. The triangle has been inverted and the quadrilateral is no longer convex.

(c) After applying FixIllegal, the Elements are legal again, but the Nodes are not exactly where they started in (a).

On one pass through the Skeleton, FixIllegal attempts to move each Node of the troublesome elements once, choosing the Elements and Nodes in a random order. It may not be successful on the first pass, so it repeats the process until there are no more illegal Elements. If any one pass through the Skeleton fails to fix any Elements, or if it fails to remove all the illegal Elements after a fixed number of iterations,^[34] it will quit trying and notify the user.

See Also