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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 radius R(P ) of a simple polygon P is the minimum diffuse reflection depth over all points s ∈ int(P ), and diffuse reflection center of P is the set of points s ∈ int(P ) that attain  ... 
arXiv:1402.5303v3 fatcat:smocfjusmncmppedcbgivmufwq

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. .  ...  Winslow, Diffuse reflections in simple polygons, Electronic Notes in Discrete Mathematics 44(5) Two types of reflections.  ... 
doi:10.1016/j.dam.2015.04.025 fatcat:hxue6rvkafc2xpoyj7tpc3adhy

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.  ...  We prove that in every simple polygon P with n ≥ 3 vertices, there exists a diffuse reflection path with at most n/2 − 1 reflections between any two points s, t ∈ int(P ).  ... 
arXiv:1302.2271v2 fatcat:crx4kkfm45h2fdt3kfrescsz5u

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.  ...  Finally, every simple polygon with 3 ≤ n ≤ 5 vertices is star-shaped, and so its diffuse reflection radius is 0 = (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.  ...  Finally, every simple polygon with 3 ≤ n ≤ 5 vertices is star-shaped, and so its diffuse reflection radius is 0 = (n − 2)/4 .  ... 
doi:10.1007/978-3-319-08783-2_21 fatcat:4eemb3j5erfudh3qek6lcjnytm

The Complexity of Diffuse Reflections in a Simple Polygon [chapter]

Boris Aronov, Alan R. Davis, John Iacono, Albert Siu Cheong Yu
2006 Lecture Notes in Computer Science  
The complexity of the visibility region formed by a point light source after k diffuse reflections in a simple n-sided polygon is O(n 9 ), which is the first result polynomial in n, with no dependence  ...  A fixed simple polygon P with n edges is implicit in all notation. Definition 1 (Time). By time k, we mean the state of the visible region after exactly k diffuse reflections. Definition 2 (Edge).  ...  diffuse reflections are allowed.  ... 
doi:10.1007/11682462_13 fatcat:23bvp5nfrvczflpid5nh6xxz2q

On multiple connectedness of regions visible due to multiple diffuse reflections [article]

Sudebkumar Prasant Pal, Dilip Sarkar
2003 arXiv   pre-print
In this paper we establish that the region V_2(s), visible from s due to at most two diffuse reflections may be multiply connected; we demonstrate the construction of an n-sided simple polygon with a point  ...  Aronov et al. addpp981 established that the region V_1(s) of a simple polygon visible from an internal point s due to at most one diffuse reflection on the boundary of the polygon P, is also simply connected  ...  Combinatorial complexity and multiple connectedness of regions visible due to diffuse reflections Regions visible due to reflections inside simple polygons were first studied by Aronov et al.  ... 
arXiv:cs/0306010v1 fatcat:fe6pnfvnazh27fhf5gx35oevkq

Visibility with multiple diffuse reflections

D.Chithra Prasad, Sudebkumar P. Pal, Tamal K. Dey
1998 Computational geometry  
In contrast to the result of (Aronov et al., 1996) , the combinatorial complexity of the region lit up from a point inside a simple n-gon after k diffuse reflections is established here to be O(nZF(k+l  ...  In a real situation, surfaces may not be perfect mirrors; indeed most surfaces may be non-shiny or rough, causing diffuse reflection, rather than specular reflection.  ...  In this paper, we study properties of the region visible from a point light source inside a simple polygon due to multiple diffuse reflections on the edges of the polygon.  ... 
doi:10.1016/s0925-7721(97)00021-7 fatcat:gwxvq77rqvfqvcgvszt7hsntgu

Visibility Extension via Reflection [article]

Arash Vaezi, Bodhayan Roy, Mohammad Ghodsi
2021 arXiv   pre-print
to cover a simple polygon P.  ...  required to cover P without reflection. funnel or a weak visibility polygon, then the problem becomes more straightforward and can be solved in polynomial time.  ...  In this paper, either a simple polygon, a weak visible polygon, or a funnel may be considered as the given polygon P that contains the viewer.  ... 
arXiv:2011.03107v2 fatcat:ubbgn67hdvge7l7ifl2tlj56jq

Visibility with One Reflection

B. Aronov, A. R. Davis, T. K. Dey, S. P. Pal, D. C. Prasad
1998 Discrete & Computational Geometry  
In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions.  ...  We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse.  ...  We show that, with a single reflection, the (point) visibility polygon under specular reflection Vs(S) may be nonsimple, while the (point) visibility polygon under diffuse reflection Vd(S) is always simple  ... 
doi:10.1007/pl00009368 fatcat:ctynlirsybbcvibbbsrt3oyjza

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.  ...  In [2] , Aronov et al. studied the region visible from a point source inside a simple n-vertex polygon where at most one specular (or diffuse) reflection is permitted on the bounding edges.  ... 
arXiv:1304.4320v2 fatcat:owmrb2spo5an3c3mqucubyineu

Visibility Extension via Reflective Edges to an Exact Quantity [article]

Arash Vaezi, Mohammad Ghodsi
2018 arXiv   pre-print
We deal with both single and multiple reflecting mirrors for both specular or diffuse types of reflections.  ...  We consider extending the visibility polygon of a given point q, inside a simple polygon P by converting some edges of P to mirrors.  ...  (or in front of the dark gray area shown in Fig. 4) for the final constructed polygon to be a connected and simple polygon.  ... 
arXiv:1811.07649v1 fatcat:h53mbfuptfgnffcvol366afnsq

Algorithms for Computing Diffuse Reflection Paths in Polygons [chapter]

Subir Kumar Ghosh, Partha Pratim Goswami, Anil Maheshwari, Subhas Chandra Nandy, Sudebkumar Prasant Pal, Swami Sarvattomananda
2009 Lecture Notes in Computer Science  
The problem of computing a diffuse reflection path between two points inside a polygon has not been considered in the past.  ...  The number of reflections in the path produced by this algorithm can be at most 3 times that of an optimal diffuse reflection path.  ...  Computing the greedy diffuse reflection path In this section, we present an algorithm for computing a diffuse reflection path from s to t (denoted as drp(s, t)) inside a simple polygon P using greedy method  ... 
doi:10.1007/978-3-642-00202-1_5 fatcat:4w22ryzdmjfrtdix42gkit7ana

Algorithms for computing diffuse reflection paths in polygons

Subir Kumar Ghosh, Partha Pratim Goswami, Anil Maheshwari, Subhas Chandra Nandy, Sudebkumar Prasant Pal, Swami Sarvattomananda
2012 The Visual Computer  
The problem of computing a diffuse reflection path between two points inside a polygon has not been considered in the past.  ...  The number of reflections in the path produced by this algorithm can be at most 3 times that of an optimal diffuse reflection path.  ...  Computing the greedy diffuse reflection path In this section, we present an algorithm for computing a diffuse reflection path from s to t (denoted as drp(s, t)) inside a simple polygon P using greedy method  ... 
doi:10.1007/s00371-011-0670-z fatcat:k5h5zyboyvaibbioqz5fcjs3na

Local Shape Editing at the Compositing Stage [article]

Carlos Jorge Zubiaga, Gael Guennebaud, Romain Vergne, Pascal Barla
2016 Eurographics Symposium on Rendering  
., diffuse and reflection shading) in post-process, providing for simple but interactive appearance manipulations.  ...  Our method is based on the reconstruction of a pair of diffuse and reflection prefiltered environment maps for each distinct object/material appearing in the image.  ...  A simple alternative to our reconstruction approach would be to compute diffuse and reflection shading environments directly at the rendering stage.  ... 
doi:10.2312/sre.20161206 dblp:conf/rt/ZubiagaGVB16 fatcat:mntcj6fxyvfb3orxfmqd3qvshm
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