Chapter 4 Vortex detection - Computer Graphics and Visualization

Chapter 5. Deformable surfaces
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Figure 5.9: Rivara’s method: first bisects the marked face ABC, then face ABD, and
finally face ABQ. The longest edges are dashed.
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Figure 5.10: Mitchell’s method only refines pairs of triangles that are ‘compatibly divisible’,
to prevent inconsistent triangles from occurring.
When we implemented these schemes in GARIS, the problem of cycles occurred. In
recursively marking the adjacent triangles, the algorithm encountered the same triangle
where it started, which resulted in an infinite recursion. This was probably caused
by equilateral triangles; in accordance with the original algorithm, the longest edge
was chosen as the refinement edge, which is of course ambiguous in equilateral triangles.
A solution to this ambiguity problem does not seem trivial.
Another refinement mechanism we have implemented is the one described by
[Miller, 1990], and illustrated in Figure 5.11. A marked face (hatched in the figure) is
refined into four triangles, and the adjacent faces, where hanging nodes would occur,
are bisected into two triangles.
Care must be taken when faces are adjacent to more than one marked face, as
shown in Figure 5.12. Here, the two faces would cause different bisection directions in
their respective adjacent faces. This is solved by not bisecting such a face, but refining
it into four faces as well, as if it had also been marked.
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