27 research outputs found
Rigid Origami Vertices: Conditions and Forcing Sets
We develop an intrinsic necessary and sufficient condition for single-vertex
origami crease patterns to be able to fold rigidly. We classify such patterns
in the case where the creases are pre-assigned to be mountains and valleys as
well as in the unassigned case. We also illustrate the utility of this result
by applying it to the new concept of minimal forcing sets for rigid origami
models, which are the smallest collection of creases that, when folded, will
force all the other creases to fold in a prescribed way
Gossiping with interference in radio chain networks (upper bound algorithms)
International audienceIn this paper, we study the problem of gossiping with interference constraint in radio chain networks. Gossiping (or total exchange information) is a protocol where each node in the network has a message and wants to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and efficient algorithms that attain this makespan
A Study on the Boundary Conditions of 90° Paper Pop-up Structures
The design of a pop-up book or card has hitherto been labour intensive with tasks of trials and errors. The constructions of collapsible pop-up structures can be demanding and inefficient without adequate knowledge of their geometric properties. This paper examines the properties of creases in 90° pop-up structures. A 90° pop-up structure is one that erects fully when two adjacent base pages, on which it sits, are opened to a right angle. In particular, we define a boundary region for creating 90° pop-ups. Similarly, paper folds are able to achieve pop-up effects and can be integrated with 90° pop-up constructions. The development of these pop-up structures can be represented graphically. Through this study, a fundamental foundation for pop-up topology and geometry is built. This foundation would be vital for understanding the applications of pop-up making techniques. The mathematical relationships devised would be useful for developing computer-enhanced pop-up design.Singapore-MIT Alliance (SMA
Monochromatic geometric k-factors for bicolored point sets with auxiliary points
Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We consider the problem of finding such a k-factor of S by using auxiliary points. Two types are considered: white points whose position is fixed, and Steiner points which have no fixed position. Our approach provides algorithms for constructing those k-factors, and gives bounds on the number of auxiliary points needed to draw a monochromatic geometric planar k-factor of S
Locked and unlocked smooth embeddings of surfaces
We study the continuous motion of smooth isometric embeddings of a planar
surface in three-dimensional Euclidean space, and two related discrete
analogues of these embeddings, polygonal embeddings and flat foldings without
interior vertices, under continuous changes of the embedding or folding. We
show that every star-shaped or spiral-shaped domain is unlocked: a continuous
motion unfolds it to a flat embedding. However, disks with two holes can have
locked embeddings that are topologically equivalent to a flat embedding but
cannot reach a flat embedding by continuous motion.Comment: 8 pages, 8 figures. To appear in 34th Canadian Conference on
Computational Geometr