Vertex-Unfoldings of Simplicial Manifolds

TL;DR

This paper introduces a linear-time algorithm for unfolding triangulated 2-manifolds into non-overlapping planar layouts by cutting along edges, with extensions to higher-dimensional simplicial manifolds.

Contribution

The paper presents a novel linear-time algorithm for vertex-unfolding of triangulated 2-manifolds and extends it to higher-dimensional simplicial manifolds.

Findings

Unfolds any triangulated 2-manifold into a connected planar layout.

Operates in linear time, cutting only along edges.

Extends the method to higher-dimensional simplicial manifolds.

Abstract

We present an algorithm to unfold any triangulated 2-manifold (in particular, any simplicial polyhedron) into a non-overlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is connected, but it may have a disconnected interior; the triangles are connected at vertices, but not necessarily joined along edges. We extend our algorithm to establish a similar result for simplicial manifolds of arbitrary dimension.