Graphs and Combinatorics
We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.
Unfolding, Folding, Collision-free motion
Demaine, Erik D.; Demaine, Martin L.; Hart, Vi; Iacono, Joan; Langerman, Stefan; and O'Rourke, Joseph, "Continuous Blooming of Convex Polyhedra" (2011). Computer Science: Faculty Publications, Smith College, Northampton, MA.