Continuous Blooming of Convex Polyhedra

TL;DR

This paper introduces the first methods for continuously blooming all convex polyhedra through unfolding techniques, enabling smooth transformations and refinements.

Contribution

It presents the first continuous blooming constructions for all convex polyhedra, including source unfoldings and refined unfoldings with linear cuts.

Findings

First continuous blooming of source unfoldings.

Refinement of any convex polyhedron unfolding with linear cuts.

Enables smooth transformations of convex polyhedra.

Abstract

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.