# OOF2: The Manual

## Name

RuleSet — Refinement rule sets.

## Description

OOF2 provides two sets of refinement rules. When refining a `Skeleton`, the refinement rules determine how the interior of an element is subdivided after the subdivision of its edges has been determined. The rule set appears as an argument to the `degree` parameter of the Refine `Skeleton` modifier.

The rule sets are displayed in Table 6.8 and Table 6.9. The tables contain diagrams for each possible element geometry and all possible ways of subdividing the element's edges. Each diagram shows how the element will be subdivided (after appropriate rotations and distortions to bring it into alignment with the actual shape and position of the `Skeleton` element).

The two sets of rules are called conservative and liberal. The conservative rules never change the topology of an element: quadrilateral elements will beget little quadrilaterals, and triangular elements will beget little triangles.[40] The liberal rules, in some cases, will create triangles from quadrilaterals and vice versa. When using the liberal rule set, OOF2 will substitute the corresponding conservative rule if it would produce a configuration with lower effective energy.[41]

There are two distinct ways in which two segments can be marked for subdivision on a quadrilateral element. The column marked opposite in Table 6.8 contains the rules that apply when the marked edges are on opposite sides of the quadrilateral. The column marked adjacent contains the rules that apply when the marked edges are next to one another.

Table 6.8. Refinement Rules for Quadrilaterals

`degree` `rule_set` No. of Marked Segments
1 2 (opposite) 2 (adjacent) 3 4
Bisection Conservative N/A
N/A
Liberal
Trisection Conservative
Liberal

Table 6.9. Refinement Rules for Triangles

`degree` `rule_set` No. of Marked Segments
1 2 3
Bisection Conservative
Liberal
Trisection Conservative
Liberal

## Values

• `conservative`: Preserve topology: quads are refined into quads and triangles into triangles (whenever possible).
• `liberal`: If there's a choice, choose the refinement that minimizes E, without trying to preserve topology.

[40] It's not always possible to preserve topology when bisecting quadrilaterals. When using conservative bisection, OOF2 will try to preserve topology by bisecting unmarked segments. If this fails, the user will be notified, and OOF2 will proceed using the wrong kind of element.

[41] The effective energy is calculated with α=0.5. It may be adjustable by the user in some future version of OOF2.