| Abstract Parallel Morphing of Trees and Cycles ∗ (2008) | |||||||||||||||
Abstract | |||||||||||||||
| We prove that for any two simple chains [more generally, trees] in R d with corresponding edges parallel, there is a parallel morph between them—i.e. a morph in which all intermediate chains [trees] remain simple and parallel to the original. A similar result had been proved by Guibas et al. [8] for simple cycles in R 2. We prove that the result for cycles does not extend to R 3 by giving two simple cycles, with corresponding edges parallel, that represent the same knot, and yet have no parallel morph. 1 | |||||||||||||||
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