We will prove that a closed connected set S in ET whose points of local nonconvexity can be decomposed into a finite number of convex parts also possesses a simple type of polygonal connectedness. Furthermore, if S has a finite number of points of local nonconvexity, we obtain another result. In order to describe this situation easily we use the notation of Ln set used by Horn and Valentine [l ...

The effect of aperture shape on an image, known in photography as ‘bokeh’, is an important characteristic of depth of field in real-world cameras. However, most real-time depth of field techniques produce Gaussian bokeh rather than the circular or polygonal bokeh that is almost universal in real-world cameras. ‘Scattering’ (i.e. point-splatting) techniques provide a flexible way to model any ap...

A near-polygonal graph is a graph Γ which has a set C of m-cycles for some positive integer m such that each 2-path of Γ is contained in exactly one cycle in C. If m is the girth of Γ then the graph is called polygonal. We introduce a method for constructing near-polygonal graphs with 2-arc transitive automorphism groups. As special cases, we obtain several new infinite families of polygonal gr...

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a polyhedral terrain in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) ...

A solution to the perimeter surveillance problem for one intruder and multiple robots based on set-invariance is presented. The robots, constrained move of a polygonal region, intercept intruders as they cross perimeter. proposed closed-form control laws only depend maximum speed their distances endpoints line segments that make sides polygon. presented results allow groups with members differe...

We consider polygonal Markov fields originally introduced by Arak and Surgailis [1, 2]. Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of salient features with the two-dimensional Ising model. The purpose of this paper is to establish an explicit stochastic representation for th...

The nomenclature we introduce for faceted nanotubes is not as straight-forward as for non-faceted nanotubes. According to the main manuscript, the circumference of the polygonal cross section of an armchair nanotube is equal to nαaα + nβ1aβ + nγaγ + nβ2aβ . In analogy, the circumference of the polygonal cross section of a zigzag nanotube would be equal to nγ1aγ+nδ1aδ+nγ2aγ+nδ2aδ. Connecting the...