Abstract
We explore the possibility of reconfiguring, or “morphing”, one simple polygon to another, maintaining simplicity, and preserving some properties of angles and edge lengths. In linkage reconfiguration, edge lengths must be preserved. By contrast, a monotone morph preserves edge directions and changes edge lengths monotonically. A monotone morph is only possible for parallel polygons—ones with corresponding edges parallel. Our main results are that monotone morphs exist for parallel pairs of polygons that are: (1) convex; or (2) orthogonally convex. Our morphs either move vertices in straight lines, or change few edge lengths at once. On the negative side, we show that it is NP-hard to decide if two simple parallel orthogonal polygons have a monotone morph. We also establish which of these results extend to 3-dimensional polyhedra.
Research partially supported by NSERC.
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Biedl, T., Lubiw, A., Spriggs, M.J. (2004). Angles and Lengths in Reconfigurations of Polygons and Polyhedra. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_58
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DOI: https://doi.org/10.1007/978-3-540-28629-5_58
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