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Star Unfolding from a Geodesic Curve Kiazyk, Stephen Lubiw, Anna unfolding convex polyhedra geodesic curve There are two known ways to unfold a convex polyhedron without overlap: the star unfolding and the source unfolding, both of which use shortest paths from vertices to a source point on the surface of the polyhedron. Non-overlap of the source unfolding is straightforward; non-overlap of the star unfolding was proved by Aronov and O'Rourke in 1992. Our first contribution is a much simpler proof of non-overlap of the star unfolding. Both the source and star unfolding can be generalized to use a simple geodesic curve instead of a source point. The star unfolding from a geodesic curve cuts the geodesic curve and a shortest path from each vertex to the geodesic curve. Demaine and Lubiw conjectured that the star unfolding from a geodesic curve does not overlap. We prove a special case of the conjecture. Our special case includes the previously known case of unfolding from a geodesic loop. For the general case we prove that the star unfolding from a geodesic curve can be separated into at most two non-overlapping pieces. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Stephen Kiazyk and Anna Lubiw 2015 Is Part Of LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SOCG.2015.390 urn:nbn:de:0030-drops-51380 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.390 eng https://creativecommons.org/licenses/by/3.0/legalcode