OOF2: The Manual

Name

Geographic (GeographicQ2T) — Split a quad based on its neighbors.

Synopsis

GeographicQ2T()

Details

Description

GeographicQ2T is a SplitQuadMethod, used as the split_how parameter in when splitting quadrilateral Elements into triangles.

An interior quadrilateral has four neighboring Elements. If it has two neighbors of one type (defined by their dominant pixel category) and two of another, arranged as in Figure 6.82(a), and if the Element itself is inhomogeneous, then there's a chance that dividing it along the diagonal shown in Figure 6.82(b) will improve the homogeneity of the Skeleton.

Figure 6.82. Splitting Quads Geographically

Splitting Quads Geographically

(a) A central Element (marked by the '?') and its neighbors e0, e1, e2, and e3. The central element is a candidate for splitting with GeographicQ2T because e0 and e1 have the same category, and e2 and e3 have the same category. The category of the central element is not a factor in the decision to attempt to apply SplitQuads.

(b) New elements created by SplitQuads and GeographicQ2T.

Splitting Quads Geographically

(c) In this example GeographicQ2T fails to split the central element correctly, even though the e0 and e1 have the same pixel category (pink) and e2 and e3 have the same category (white).

(d) Dividing along the geographical boundary has created two inhomogeneous Elements. This modification will be rejected unless it was done with a very small alpha.


GeographicQ2T can be fast because it only examines quads with a high likelihood of being splittable. However, it can skip over splittable quads if the Skeleton is not already sufficiently refined and one of the neighbors has the wrong type. TrialAndErrorQ2T is slower but more thorough.