Related papers: Locked and Unlocked Polygonal Chains in 3D
Prune-and-search is an important paradigm for solving many important geometric problems. We show that the general prune-and-search technique can be implemented where the objects are given in read-only memory. As examples we consider…
A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be folded into any member of S. We present a hinged dissection of all edge-to-edge gluings of n congruent copies of a…
We explore the transport features of a single flexible polymer chain that walks on a periodic ratchet potential coupled with spatially varying temperature. At steady state the polymer exhibits a fast unidirectional motion where the…
We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider…
While rectangular and box-shaped objects dominate the classic discourse of theoretic investigations, a fascinating frontier lies in packing more complex shapes. Given recent insights that convex polygons do not allow for constant…
To a closed braid in a solid torus we associate a trace graph in a thickened torus in such a way that closed braids are isotopic if and only if their trace graphs can be related by trihedral and tetraherdal moves. For closed braids with a…
We analyse the conformational behaviour of a linear semiflexible homo-polymer chain confined by two geometrical constraints under a good solvent condition in two dimensions. The constraints are stair shaped impenetrable surfaces. The…
Strictly-convex straight-line drawings of $3$-connected planar graphs in small area form a classical research topic in Graph Drawing. Currently, the best-known area bound for such drawings is $O(n^2) \times O(n^2)$, as shown by…
This paper considers the problem of manipulating a uniformly rotating chain: the chain is rotated at a constant angular speed around a fixed axis using a robotic manipulator. Manipulation is quasi-static in the sense that transitions are…
Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper, we study the limits of unfoldability by studying nonconvex polyhedra with the same combinatorial structure as convex polyhedra. In…
Deciding whether the union of two convex polyhedra is itself a convex polyhedron is a basic problem in polyhedral computations; having important applications in the field of constrained control and in the synthesis, analysis, verification…
We propose a simple friction model for isolated polymer chains on a solid substrate. The chains are pulled at constant velocity by one end, the other end can be trapped on the solid substrate on localised sites. We focus on the energy…
Let $P$ be a polygon with $r>0$ reflex vertices and possibly with holes and islands. A subsuming polygon of $P$ is a polygon $P'$ such that $P \subseteq P'$, each connected component $R$ of $P$ is a subset of a distinct connected component…
In a recent paper, {\it Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (II)}, we discussed two algorithms for deforming and contracting a simply connected discrete closed manifold into a discrete sphere.…
We study geometrical clues of a rigidity transition due to the emergence of a system-spanning state of self stress in under-constrained systems of individual polygons and spring networks constructed from such polygons. When a polygon with…
An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a *net*, a connected planar piece with no overlaps. A *grid unfolding* allows additional cuts along grid edges induced by coordinate planes…
The problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones in 3D has led Bereg et al. to pose the Chain Pair Simplification problem (CPS). In this problem, given two polygonal chains…
We prove that every polynomially convex arc is contained in a polynomially convex simple closed curve. We also establish results about polynomial hulls of arcs and curves that are locally rectifiable outside a polynomially convex subset.
We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the topology of a sphere in which three mutually-perpendicular edges meet at each vertex. By analogy to Steinitz's theorem characterizing the graphs of…
We analyse the nature of the confinement of an infinitely long (and finite) linear semiflexible homo-polymer chain confined in between two geometrical constraints (A&B) under good solvent condition in two dimensions. The constraints are…