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If the transformation requires several steps, each resulting in an intermediate object, then each of these intermediate objects must also obey the same property. We show that in transforming one triangulation of a polygon into another, a parallel algorithm achieves a superlinear speedup. In the case where a convex decomposition of a set of points is to be transformed, the improvement in performance is unbounded, meaning that a parallel algorithm succeeds in solving the problem as posed, while all sequential algorithms fail. <\/jats:p>","DOI":"10.1142\/s0129626406002447","type":"journal-article","created":{"date-parts":[[2006,3,24]],"date-time":"2006-03-24T11:18:03Z","timestamp":1143199083000},"page":"19-37","source":"Crossref","is-referenced-by-count":3,"title":["INHERENTLY PARALLEL GEOMETRIC COMPUTATIONS"],"prefix":"10.1142","volume":"16","author":[{"given":"SELIM G.","family":"AKL","sequence":"first","affiliation":[{"name":"School of Computing, Queen's University, Kingston, Ontario, K7L 3N6, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(01)00042-6"},{"key":"rf3","volume-title":"Parallel Computation: Models And Methods","author":"Akl S. 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