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In literature, the generation of floor plans has mainly been confined to dimensionless floor plans with rectangular boundaries having no open spaces within the floor plan. In this paper, the user is allowed to construct a dimensioned boundary using slant, horizontal and vertical line segments, where dimensioned open spaces can be drawn within the boundary layout. Once the boundary is finalized, it can be partitioned into dimensioned blocks using vertical and horizontal dissections. Each block can be further partitioned into dimensioned rooms which results in a dimensioned floor plan F for the given boundary layout. The dissection method employed is based on the slicing tree approach, which results in floor plans that are amenable to slicing and consist of non-rectangular rooms, offering the potential for open spaces within floor plan F. As a preliminary step towards automation, we have developed an interactive user interface for generating dissected dimensioned floor plans.

We first prove that there always exists a maximal rectangularly dualizable graph for a given rectangularly dualizable graph and present an algorithm for its construction. Further, we show that a maximal rectangularly dualizable graph can always be transformed to an edge-irreducible rectangularly dualizable graph and present an algorithm that transforms a maximal rectangularly dualizable graph to an edge-irreducible rectangularly dualizable graph.

AbstractA drawing concerns the process of generating geometric representations of relational information, usually for visualization purposes. A good drawing provides an understanding of the system to the reader, while a poor drawing may create confusion. A lot of information related to graphs and graph drawings can be stored using data structures where vertices represent entities and edges correspond to relationships among entities. In this paper, we have reviewed various studies to present the unsolved problems in the domain of graph drawing and to identify its applications in real life. By reviewing the existing approaches related to graph drawings, we found that there exist various drawing strategies that efficiently allow us to create drawings with a confined area, relatively high angular resolution, user-restrained aspect ratio, a lesser number of bends, etc. Moreover, there are several known algorithms for addressing different measures of graph drawing (such as symmetricity, spirality, rotation, etc.) but they are usually restricted to specific sub-classes of planar graphs. The present study provides readers a better understanding of the field of graph drawing and related problems.

Existing approaches (in particular graph theoretic) for generating floorplans focus on constructing floorplans for given adjacencies without considering boundary layout or room shapes. With recent developments in designs, it is demanding to consider multiple constraints while generating floorplan layouts. In this paper, we study graph theoretic properties which guarantee the presence of different shaped rooms within the floorplans. Further, we present a graph-algorithms based application, developed in Python, for generating floorplans with given input room shapes. The proposed application is useful in creating floorplans for a given graph with desired room shapes mainly, L, T, F, C, staircase, and plus-shape. Here, the floorplan boundary is always rectangular. In future,we aim to extend this work to generate any (rectilinear) room shape and floor plan boundary for a given graph.

If there exist many computer-generated architectural designs for a given set of data, then for an architect it is difficult to single one solution out among many possibilities. In this paper, we propose a technique to refine the number of possible designs on the basis of their connectivity, which is given in terms of adjacency relations among the rooms. In addition, we present few mathematical results to study the topological properties of the architectural designs, that would also be useful for the validation of proposed technique and for the classification of different architectural designs.

It can be found quite often in the literature that many well-known architects have employed either the golden rectangle or the Fibonacci rectangle in their works. On contrary, it is rare to find any specific reason for using them so often. Recently, Shekhawat (2015) proved that the golden rectangle and the Fibonacci rectangle are one of the best connected rectangular arrangements and this may be one of the reasons for their high presence in architectural designs. In this work we present an algorithm that generates n-4 best connected rectangular arrangements so that the proposed solutions can be further used by architects for their designs.

This paper presents a systematic pathway for the floor plan design when given the shape of required floor plan, the list of spaces, the dimensions of each space and the weighted matrix of required adjacencies between the spaces. The first step is to partition the given shape into say k possible rectangles. Then using the given adjacencies, divide the given spaces into k groups. Next is to construct a rectangular block for each group and at last adjoin all rectangular blocks to have the required floor plan. The obtained rectangular blocks are one of the best arrangement of spaces inside a rectangle from the point of view of connectivity.

It is often found in the literature that many researchers have studied or documented the use of golden rectangle or Fibonacci rectangle in architectural design. In this way, a lot of well-known architects in the history, knowingly or unknowingly, have employed either the golden rectangle or the Fibonacci rectangle in their works. Using some mathematical tools, this paper tried to approach one of the properties of the golden rectangle (or the Fibonacci rectangle) and its significance to architectural design, which could lead to state one hypothesis about why architects have used them so often. This work begins with an algorithm which constructs a Fibonacci rectangle and a golden rectangle. Then adjacency among the squares (which are arranged inside them) is defined, by considering each square as a room or an architectural space. At the end, using some tools of the graph theory, it has been proved that they are one of the best arrangements of squares (or rectangles) inside a rectangle, from the point of view of connectivity.

In most applications, such as urbanism and architecture, randomly utilizing given spaces is certainly not favorable. This study proposes an explicit algorithm for utilizing the given spaces inside a rectangle with satisfactory results. In the literature, connectivity is not considered as a criterion for floor plan design, but it is deemed essential in architecture. For example, dining rooms are preferably connected to kitchens, toilets should be connected to many rooms, and each bedroom should be separated from the other rooms. This paper describes adjacency among spaces and proves that the obtained rectangular floor plan is one of the best ones in terms of connectivity. An architectural and mathematical object called extra spaces is introduced by the proposed algorithm and is subsequently examined in this work.