Diffuse reflection diameter in simple polygons

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 source is ź n / 2 ź - 1 . Light reflecting diffusely leaves a surface in all directions, rather than at an identical angle as with specular reflections.

[1]  Subir Kumar Ghosh,et al.  Visibility Algorithms in the Plane , 2007 .

[2]  Dilip Sarkar,et al.  A linear worst-case lower bound on the number of holes inside regions visible due to multiple diffuse reflections , 2004 .

[3]  Sudebkumar Prasant Pal,et al.  Directly Visible Pairs and Illumination by Reflections in Orthogonal Polygons , 2008 .

[4]  George William Tokarsky,et al.  Polygonal Rooms Not Illuminable from Every Point , 1995 .

[5]  Tetsuo Asano,et al.  Visibility in the Plane , 2000, Handbook of Computational Geometry.

[6]  Andrew Granville,et al.  Visibility in the plane , 2009 .

[7]  Boris Aronov,et al.  Visibility with Multiple Reflections , 1996, SWAT.

[8]  S. Suri.  A linear time algorithm with minimum link paths inside a simple polygon , 1986 .

[9]  Subhash Suri,et al.  On some link distance problems in a simple polygon , 1990, IEEE Trans. Robotics Autom..

[10]  Esther M. Arkin,et al.  Logarithmic-time link path queries in a simple polygon , 1995, Int. J. Comput. Geom. Appl..

[11]  Boris Aronov,et al.  The Complexity of Diffuse Reflections in a Simple Polygon , 2006, LATIN.

[12]  Tamal K. Dey,et al.  Visibility with multiple diffuse reflections , 1998, Comput. Geom..

[13]  Jörg-Rüdiger Sack,et al.  Link Distance Problems , 2000, Handbook of Computational Geometry.

[14]  Victor Klee.  Is Every Polygonal Region Illuminable from Some Point , 1969 .

[15]  Boris Aronov,et al.  Visibility with One Reflection , 1998, Discret. Comput. Geom..

[16]  Anil Maheshwari,et al.  Algorithms for computing diffuse reflection paths in polygons , 2011, The Visual Computer.

[17]  V. Klee.  Some Unsolved Problems in Plane Geometry , 1979 .