A computer-generated plus-shaped arrangement and its architectural applications

This work consider the problem of rectilinear arrangement which is about arranging given rectangular objects of different sizes in the frame of a given rectilinear polygon while considering dimension and position of each rectangle and adjacency relations among the rectangles. The current work is part of a larger work aimed at automated generation of rectilinear arrangements while satisfying given dimensional and topological constraints. In this paper, we present a set of algorithms for obtaining a plus-shaped arrangement. In addition, we present some heuristic techniques for reducing the size of extra spaces present inside the obtained arrangement. At the end, we demonstrate architectural application of the presented work. Highlights Problem is to arrange given sub-rectangles within a given predefined contour shape. Required arrangement must satisfies given adjacency and size constraints. An algorithm for generation of plus-shaped arrangements is presented. Architectural application of the work has been demonstrated.

OPTIMAL BSPs AND RECTILINEAR CARTOGRAMS

A cartogram is a thematic map that visualizes statistical data about a set of regions like countries, states or provinces. The size of a region in a cartogram corresponds to a particular geographic variable, for example, population. We present an algorithm for constructing rectilinear cartograms (each region is represented by a rectilinear polygon) with zero cartographic error and correct region adjacencies, and we test our algorithm on various data sets. It produces regions of very small complexity—in fact, most regions are rectangles—while still ensuring both exact areas and correct adjacencies for all regions. Our algorithm uses a novel subroutine that is interesting in its own right, namely a polynomial-time algorithm for computing optimal binary space partitions (BSPs) for rectilinear maps. This algorithm works for a general class of optimality criteria, including size and depth. We use this generality in our application to computing cartograms, where we apply a dedicated cost function leading to BSPs amenable to the constructing of high-quality cartograms.