Skirting subsets of the plane, with application to marginal stability curves

G. D. McBain

Abstract


An easily implemented algorithm is described for tracing the margin of a plane region defined by a predicate. Given a point inside and one outside, a sequence of marginal points is produced. The algorithm is a modified specialization of the `simplicial decomposition' method for n equations in n+1 dimensions. The case n=1 has special properties and its importance motivates their present exploitation. It is directly applicable to finding level curves. It does not require differentiability and copes well with cusps. Two questions of accuracy are the proximity of the outputs to the margin and the proximity of the margin to the output set. The first is answered precisely. The second is complicated and predicate-dependent, but is addressed in practical terms by adaptivity, which also improves the scheme's efficiency.

Full Text:

PDF BibTeX


DOI: http://dx.doi.org/10.21914/anziamj.v45i0.874



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.