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Diffuse Reflection Diameter in Simple Polygons [article]

Gill Barequet, Sarah M. Cannon, Eli Fox-Epstein, Benjamin Hescott, Diane L. Souvaine, Csaba D. Tóth, Andrew Winslow
2015 arXiv   pre-print
We prove a conjecture of Aanjaneya, Bishnu, and Pal that the minimum number of diffuse reflections sufficient to illuminate the interior of any simple polygon with n walls from any interior point light  ...  Light reflecting diffusely leaves a surface in all directions, rather than at an identical angle as with specular reflections.  ...  By contrast, no polynomial time algorithm is known for computing the diffuse reflection diameter of a simple polygon.  ... 
arXiv:1302.2271v2 fatcat:crx4kkfm45h2fdt3kfrescsz5u

Diffuse reflection diameter in simple polygons

Gill Barequet, Sarah M. Cannon, Eli Fox-Epstein, Benjamin Hescott, Diane L. Souvaine, Csaba D. Tóth, Andrew Winslow
2016 Discrete Applied Mathematics  
We prove a conjecture of Aanjaneya, Bishnu, and Pal that the minimum number of diffuse reflections sufficient to illuminate the interior of any simple polygon with n walls from any interior point light  ...  Light reflecting diffusely leaves a surface in all directions, rather than at an identical angle as with specular reflections. .  ...  By contrast, no polynomial time algorithm is known for computing the diffuse reflection diameter of a simple polygon.  ... 
doi:10.1016/j.dam.2015.04.025 fatcat:hxue6rvkafc2xpoyj7tpc3adhy

Diffuse Reflection Radius in a Simple Polygon [article]

Eli Fox-Epstein, Csaba Tóth, Andrew Winslow
2015 arXiv   pre-print
It is shown that every simple polygon in general position with n walls can be illuminated from a single point light source s after at most (n-2)/4 diffuse reflections, and this bound is the best possible  ...  It is also shown that the minimum number of diffuse reflections needed to illuminate a given simple polygon from a single point can be approximated up to an additive constant in polynomial time.  ...  The diffuse reflection diameter of a polygon with m + 2 vertices is (m + 2)/2 − 1 = m/2 from [7] .  ... 
arXiv:1402.5303v3 fatcat:smocfjusmncmppedcbgivmufwq

Diffuse Reflection Radius in a Simple Polygon

Eli Fox-Epstein, Csaba D. Tóth, Andrew Winslow
2015 Algorithmica  
Light reflecting diffusely off of a surface leaves in all directions.  ...  It is shown that every simple polygon with n vertices can be illuminated from a single point light source s after at most (n − 2)/4 diffuse reflections, and this bound is the best possible.  ...  For every k ≥ 1, the diffuse reflection diameter of the zig-zag polygon (cf. Fig. 1 ) with n = 4k + 2 vertices is k = (n − 2)/4 .  ... 
doi:10.1007/s00453-015-0031-9 fatcat:y5byafqni5abzisujktavzf6zi

Diffuse Reflection Radius in a Simple Polygon [chapter]

Eli Fox-Epstein, Csaba D. Tóth, Andrew Winslow
2014 Lecture Notes in Computer Science  
Light reflecting diffusely off of a surface leaves in all directions.  ...  It is shown that every simple polygon with n vertices can be illuminated from a single point light source s after at most (n − 2)/4 diffuse reflections, and this bound is the best possible.  ...  For every k ≥ 1, the diffuse reflection diameter of the zig-zag polygon (cf. Fig. 1 ) with n = 4k + 2 vertices is k = (n − 2)/4 .  ... 
doi:10.1007/978-3-319-08783-2_21 fatcat:4eemb3j5erfudh3qek6lcjnytm

An Algorithm for Computing Constrained Reflection Paths in Simple Polygon [article]

Arijit Bishnu, Subir Kumar Ghosh, Partha Pratim Goswami, Sudebkumar Prasant Pal, Swami Sarvattomananda
2014 arXiv   pre-print
The minimum diffuse reflection path may not be simple. The problem of computing the minimum diffuse reflection path in low degree polynomial time has remained open.  ...  For computing a minimum constrained diffuse reflection path from s to t, we present an O(n(n+β)) time algorithm, where β =Θ (n^2) in the worst case. Here, β depends on the shape of the polygon.  ...  The number of turning points in such a path is called the diffuse reflection diameter of P .  ... 
arXiv:1304.4320v2 fatcat:owmrb2spo5an3c3mqucubyineu

Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography

Kyoji Matsushima
2012 Journal of Electronic Imaging (JEI)  
This problem is resolved by introducing a simple rendering technique that is almost the same as that in common computer graphics, since the polygon-based method has similarity to rendering techniques in  ...  A simple and practical technique is presented for creating fine three-dimensional (3D) images with polygon-based computergenerated holograms.  ...  This work was supported in part by research grants from the JSPS (KAKENHI, 21500114) and Kansai University (Grant-in-aid for Joint Research 2011-2012).  ... 
doi:10.1117/1.jei.21.2.023002 fatcat:4vn2t3e2lnhx7bizyizsftyg3m

Simulation of Chloride Diffusion in Concrete Based on a New Mesoscopic Numerical Method

Ling Yao, Lixia Ren, Guoli Gong, Jianqiang Zhang
2020 Advances in Civil Engineering  
The aggregates are randomly distributed convex polygons. The chloride diffusion is assumed to occur only in the mortar matrix phase.  ...  The simulation results indicate that the polygonal aggregate random distribution has a negligible influence on chloride diffusion in concrete, the polygonal aggregate content has a certain effect, and  ...  Taking all these into account, to reveal the particulars of chloride diffusion in a heterostructural concrete, a simple two-phased structure model was constructed and used in this present article. e aggregate  ... 
doi:10.1155/2020/5318106 fatcat:4ncqekozl5b55h4sv5yj44m4o4

Page 5284 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
A simple two-cell caricature, with one cell enlarged to mimic diameter increase, is developed and analyzed.  ...  Let P be a plane point set having a known, constant density function, whose boundary is a simple polygon.  ... 

Dicotyledonous Fossil Wood Flora and Early Evolution of Wood Characters in the Cretaceous of Hokkaido, Japan

Ken'ichi Takahashi, Mitsuo Suzuki
2003 IAWA Journal  
in seven genera.  ...  The species distribution by age is: Albian: one species; Cenomanian: four species in four genera; Turonian : ten species in eight genera; Coniacian: six species in five genera; Santonian: eight species  ...  The first three species have scalariform perforat ion plates, and the last has exclusively simple one s. Paraphyllanthoxylon is the earliest taxon found in Japan with simple perforation plates.  ... 
doi:10.1163/22941932-90001597 fatcat:t5bybpy62jeu3lc5eay6annxl4

Starch columns: Analog model for basalt columns

Gerhard Müller
1998 Journal of Geophysical Research  
The speed difference, in turn, results from the difference of the diffusion constants: the hydraulic diffusivity of starch is 2 orders of magnitude lower than the thermal diffusivity of basalt.  ...  They are produced by lamp drying starch specimens with dimensions of several centimeters and have diameters in the millimeter range.  ...  The materials mentioned in Section 8 were made available to me by G. Merkler, by the kaolin quarry Dorfner in Hirschau, eastern Bavaria, and by H6chster Porzellanmanufaktur  ... 
doi:10.1029/98jb00389 fatcat:k65fzhawmzalbnequgey67yrta

Wood Anatomy of Scytopetalaceae

Sherwin Carlquist
1988 Aliso  
account of numerous resemblances in wood anatomy.  ...  Eight wood samples representing six species in two genera of Scytopetalaceae are examined with respect to qualitative and quantitative features.  ...  Lateral wall pitting consisting of alternate pits, mostly polygonal in outline, about 6 1Lm in diameter (apertures 1-2 1Lm in diameter) on vessel-vessel interfaces.  ... 
doi:10.5642/aliso.19881201.08 fatcat:5pjru35d4zafbknolsgjrh7n5i

Structure and phase behavior of a two-dimensional system with core-softened and long-range repulsive interactions

Philip J. Camp
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
At low temperatures a variety of interesting states are in evidence, including: fluids with chainlike, striped, and 6 -10 sided polygon structural motifs; low-density and highdensity triangular crystalline  ...  It is shown that clustering is driven by the presence of the repulsive shoulder in the pair potential.  ...  The most common examples of such systems are colloidal ferrofluids, which are suspensions of roughly spherical, homogeneously magnetized particles of diameter 10 nm-10 m, dispersed in a simple solvent.  ... 
doi:10.1103/physreve.68.061506 pmid:14754211 fatcat:3sa55xqgdjcr5bsaaewnk4y4cy

Wood Anatomy of Trees and Shrubs from China. I. Oleaceae

Pieter Baas, Zhang Xinying
1986 IAWA Journal  
(i.e., Linociera Sw. and Chionanthus L. s. s.) there is an abrupt and significant set of wood anatomical differences between the species previously treated in Linociera (diffuse-porous, small intervessel  ...  The wood anatomy of 34 species belonging to nine genera of Oleaceae, native or commonly cultivated in China, is described in detail, and a key to the identification of the genera is given.  ...  , alternate, round to oval or polygonal, 3-5 (-6) J..Lm in diameter, with round to slit-like apertures.  ... 
doi:10.1163/22941932-90000987 fatcat:ozmk2pygmjal3jacknegrcjzim

Finite Element Transport Using Wachspress Rational Basis Functions on Quadrilaterals in Diffusive Regions

Gregory G. Davidson, Todd S. Palmer
2008 Nuclear science and engineering  
We J)erform an asymptotic analysis of the transport. discretization in the niterior of thick diffusive regions. and derive an asyinptotic-P1 diffusion synthetic acceleration preconditioiicr.  ...  In addition. it had been theorized that Wachspress rationa.l weight. functions should Provide a. full-resolution discretization of the neutral particle transport. equation in thick diffusive regions, but  ...  The external diameter is no longer linear (and is no longer simple to calculate), but is instead a second-order conic.  ... 
doi:10.13182/nse159-242 fatcat:jzpjdvud4rhn3fc3x2lfsnz32i
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