Interior Performance Art

Art Galleries with Interior Walls

Consider an art gallery formed by a polygon on n vertices with m pairs of vertices joined by interior diagonals, the interior walls. Each interior wall has an arbitrarily placed, arbitrarily small doorway. We will show that the minimum number of guards that suffice to guard all art galleries with n vertices and m interior walls is min{b(2n−3)/3c, b(2n+m−2)/4c, b(2m+n)/3c}. If we restrict oursel...

Performance Art/Life Art/ Mediafication

An Addition to Art Galleries with Interior Walls

The Importance of Islamic Art in Mosque Interior

Mosques, as symbol of Islamic architecture must play an important role in reflecting the superiority of Allah the Almighty. There are many ways in making it successful and one of them is through the high quality of aesthetic value. Aesthetic value in Islamic art and architecture is normally portrayed by the highest degree of motifs and ornamentation. Contemporary mosque designers normally focus...

Maximizing the Guarded Interior of an Art Gallery

In the Art Gallery problem a polygon is given and the goal is to place as few guards as possible so that the entire area of the polygon is covered. We address a closely related problem: how to place a fixed number of guards on the vertices or the edges of a simple polygon so that the total guarded area inside the polygon is maximized. Recall that an optimization problem is called APX-hard, if t...