Abstract
A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles. A layout is area-universal if any assignment of areas to rectangles can be realized by a combinatorially equivalent rectangular layout. We identify a simple necessary
and sufficient condition for a rectangular layout to be area-universal: a rectangular layout is area-universal if and only if it is one-sided. More generally, given any rectangular layout L and any assignment of areas to its regions, we show that there can be at most one
layout (up to horizontal and vertical scaling) which is combinatorially equivalent to L and achieves a given area assignment. We also investigate similar questions for perimeter assignments. The adjacency requirements for the rectangles of a rectangular layout
can be specified in various ways, most commonly via the dual graph of the layout. We show how to find an area-universal layout for a given set of adjacency requirements whenever such a layout exists.
| Original language | English |
|---|---|
| Pages | 247-250 |
| Publication status | Published - 2009 |
| Event | 25th European Workshop on Computational Geometry (EuroCG 2009) - Brussels, Belgium Duration: 16 Mar 2009 → 18 Mar 2009 Conference number: 25 |
Workshop
| Workshop | 25th European Workshop on Computational Geometry (EuroCG 2009) |
|---|---|
| Abbreviated title | EuroCG |
| Country/Territory | Belgium |
| City | Brussels |
| Period | 16/03/09 → 18/03/09 |