Abstract
It is known that the region V(s) of a simple polygon P, directly visible (illuminable) from an internal point s, is simply connected. Aronov et al. [2] established that the region V1(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. In this paper we establish that the region V2(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 s inside it so that the region of P visible from s after at most two diffuse reflections is multiply connected. We also show that V-3(s), the region of P visible from s after at most three diffuse reflections, can have ω(n) holes.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 5-14 |
| Number of pages | 10 |
| Journal | Journal of Geometry |
| Volume | 81 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - Dec 1 2004 |
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Keywords
- Diffuse reflection
- Multiple connectedness
- Simple polygon
- Visibility
ASJC Scopus subject areas
- Geometry and Topology
Cite this
A linear worst-case lower bound on the number of holes inside regions visible due to multiple diffuse reflections. / Brahma, Siddhartha; Pal, Sudebkumar Prasant; Sarkar, Dilip.
In: Journal of Geometry, Vol. 81, No. 1-2, 01.12.2004, p. 5-14.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A linear worst-case lower bound on the number of holes inside regions visible due to multiple diffuse reflections
AU - Brahma, Siddhartha
AU - Pal, Sudebkumar Prasant
AU - Sarkar, Dilip
PY - 2004/12/1
Y1 - 2004/12/1
N2 - It is known that the region V(s) of a simple polygon P, directly visible (illuminable) from an internal point s, is simply connected. Aronov et al. [2] established that the region V1(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. In this paper we establish that the region V2(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 s inside it so that the region of P visible from s after at most two diffuse reflections is multiply connected. We also show that V-3(s), the region of P visible from s after at most three diffuse reflections, can have ω(n) holes.
AB - It is known that the region V(s) of a simple polygon P, directly visible (illuminable) from an internal point s, is simply connected. Aronov et al. [2] established that the region V1(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. In this paper we establish that the region V2(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 s inside it so that the region of P visible from s after at most two diffuse reflections is multiply connected. We also show that V-3(s), the region of P visible from s after at most three diffuse reflections, can have ω(n) holes.
KW - Diffuse reflection
KW - Multiple connectedness
KW - Simple polygon
KW - Visibility
UR - http://www.scopus.com/inward/record.url?scp=55449088668&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=55449088668&partnerID=8YFLogxK
U2 - 10.1007/S00022-004-1726-2
DO - 10.1007/S00022-004-1726-2
M3 - Article
AN - SCOPUS:55449088668
VL - 81
SP - 5
EP - 14
JO - Journal of Geometry
JF - Journal of Geometry
SN - 0047-2468
IS - 1-2
ER -