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Diffuse Reflection Radius in a Simple Polygon
[article]

2015
*
arXiv
*
pre-print

It is shown that every

arXiv:1402.5303v3
fatcat:smocfjusmncmppedcbgivmufwq
*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 ...##
###
Diffuse reflection diameter in simple polygons

2016
*
Discrete Applied Mathematics
*

We prove a conjecture of Aanjaneya, Bishnu, and Pal that the minimum number of

doi:10.1016/j.dam.2015.04.025
fatcat:hxue6rvkafc2xpoyj7tpc3adhy
*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*. ...##
###
Diffuse Reflection Diameter in Simple Polygons
[article]

2015
*
arXiv
*
pre-print

We prove a conjecture of Aanjaneya, Bishnu, and Pal that the minimum number of

arXiv:1302.2271v2
fatcat:crx4kkfm45h2fdt3kfrescsz5u
*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 ). ...##
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Diffuse Reflection Radius in a Simple Polygon

2015
*
Algorithmica
*

Light

doi:10.1007/s00453-015-0031-9
fatcat:y5byafqni5abzisujktavzf6zi
*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 . ...##
###
Diffuse Reflection Radius in a Simple Polygon
[chapter]

2014
*
Lecture Notes in Computer Science
*

Light

doi:10.1007/978-3-319-08783-2_21
fatcat:4eemb3j5erfudh3qek6lcjnytm
*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 . ...##
###
The Complexity of Diffuse Reflections in a Simple Polygon
[chapter]

2006
*
Lecture Notes in Computer Science
*

The complexity of the visibility region formed by a point light source after k

doi:10.1007/11682462_13
fatcat:23bvp5nfrvczflpid5nh6xxz2q
*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. ...##
###
On multiple connectedness of regions visible due to multiple diffuse reflections
[article]

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. ...

##
###
Visibility with multiple diffuse reflections

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*. ...

##
###
Visibility Extension via Reflection
[article]

2021
*
arXiv
*
pre-print

to cover a

arXiv:2011.03107v2
fatcat:ubbgn67hdvge7l7ifl2tlj56jq
*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. ...##
###
Visibility with One Reflection

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*...

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

2014
*
arXiv
*
pre-print

The minimum

arXiv:1304.4320v2
fatcat:owmrb2spo5an3c3mqucubyineu
*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. ...##
###
Visibility Extension via Reflective Edges to an Exact Quantity
[article]

2018
*
arXiv
*
pre-print

We deal with both single and multiple

arXiv:1811.07649v1
fatcat:h53mbfuptfgnffcvol366afnsq
*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*. ...##
###
Algorithms for Computing Diffuse Reflection Paths in Polygons
[chapter]

2009
*
Lecture Notes in Computer Science
*

The problem of computing a

doi:10.1007/978-3-642-00202-1_5
fatcat:4w22ryzdmjfrtdix42gkit7ana
*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 ...##
###
Algorithms for computing diffuse reflection paths in polygons

2012
*
The Visual Computer
*

The problem of computing a

doi:10.1007/s00371-011-0670-z
fatcat:k5h5zyboyvaibbioqz5fcjs3na
*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 ...##
###
Local Shape Editing at the Compositing Stage
[article]

2016
*
Eurographics Symposium on Rendering
*

.,

doi:10.2312/sre.20161206
dblp:conf/rt/ZubiagaGVB16
fatcat:mntcj6fxyvfb3orxfmqd3qvshm
*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. ...
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