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Existing graph-theoretic approaches to construct floor-plans for a given plane graph are mainly restricted to floor-plans with rectangular boundary. This paper introduces floor-plans with L -shaped boundary (boundary with only one concave corner). To ensure the L -shaped boundary, we introduce the concept of non-triviality of a floor-plan. A floor-plan with a rectilinear boundary with at least one concave corner is non-trivial if the number of concave corners can not be reduced without affecting the modules' adjacencies. Further, we present necessary and sufficient conditions for the existence of a non-trivial L -shaped floor-plan corresponding to a properly triangulated plane graph (PTPG) G. Also, we develop an O (n 3) algorithm for its construction, if it exists. • Construction of floorplans for a given graph is limited to rectangular boundaries. • We proposed the existence and construction of L-shaped floorplans. • Obtained L-shaped floorplans cannot be transformed into rectangular floorplans. [ABSTRACT FROM AUTHOR]

A non-rectangular floor plan (NRFP) is one with a rectilinear exterior boundary containing rectangular modules. An NRFP is identified as a T -shaped floor plan if the rectilinear exterior boundary forms a T -shape with two concave corners. A T -shaped floor plan is further classified as aligned or non-aligned based on the alignment of its two concave corners. In this work, we aim to investigate graph-theoretic characteristics of properly triangulated plane graphs (PTPGs) for the existence of corresponding aligned and non-aligned T -shaped floor plans. Also, we provide an O (n 3) algorithm for generating T -shaped floor plans (both aligned and non-aligned) for any PTPG with six or fewer corner-implying paths (CIPs), if they exist. Moreover, we claim that the resultant T -shaped floor plans are non-trivial. A T -shaped floor plan is considered non-trivial if the count of concave corners (two) at its exterior boundary can only be lowered by disrupting the modules' horizontal and vertical adjacencies. [ABSTRACT FROM AUTHOR]

This paper aims at automatically generating dimensioned floorplans while considering constraints given by the users in the form of adjacency and connectivity graph. The obtained floorplans also satisfy boundary constraints where users will be asked to choose their preferred location based on cardinal and inter-cardinal directions. Further, spanning circulations are inserted within the generated floorplans. The larger aim of this research is to provide alternative architecturally feasible layouts to users which can be further refined by architects. [ABSTRACT FROM AUTHOR]

A rectangular floor plan (RFP) is a floor plan in which plan's boundary and each room is a rectangle. The problem is to construct a RFP for the given adjacency requirements, if it exists. In this paper, we aim to present a generic solution to the above problem by enumerating a set of RFP that topologically contain all possible RFP. This set of RFP is called generic rectangular floor plans (GRFP). Furthermore, the construction of GRFP leads us to the necessary condition for the existence of a RFP corresponding to a given graph. [ABSTRACT FROM AUTHOR]

An important task in the initial stages of most architectural design processes is the design of planar floor plans, that are composed of non-overlapping rooms divided from each other by walls while satisfying given topological and dimensional constraints. The work described in this paper is part of a larger research aimed at developing the mathematical theory for examining the feasibility of given topological constraints and providing a generic floor plan solution for all possible design briefs. In this paper, we mathematically describe universal (or generic) rectangular floor plans with n rooms, that is, the floor plans that topologically contain all possible rectangular floor plans with n rooms. Then, we present a graph-theoretical approach for enumerating generic rectangular floor plans upto nine rooms. At the end, we demonstrate the transformation of generic floor plans into a floor plan corresponding to a given graph. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we present GPLAN, a software aimed at constructing dimensioned floorplan layouts using graph-theoretical and optimization techniques. For GPLAN, the adjacency requirements are given in the following two forms: i. An adjacency graph: It allow users to draw an adjacency graph on a GUI (graphical user interface) corresponding to which GPLAN produces a set of dimensioned floorplans with a rectangular boundary, where each floorplan is topologically distinct from others. ii. A dimensionless layout: Here, users/designers can draw any layout with a rectangular or a non-rectangular boundary on a GUI and GPLAN transforms it into a dimensioned floorplan while preserving the adjacencies, positions, shapes of the rooms. The above approaches represent different ways of inserting adjacencies and GPLAN generate dimensioned floorplans corresponding to the given adjacencies. The larger aim of this work is to provide alternative platforms to users/designers for producing dimensioned floorplans for all given (architectural) constraints, which can be further refined by architects. [Display omitted] • A software GPLAN has been developed. • GPLAN takes input in the form of dimensions and adjacencies of rooms • GPLAN produces a set of dimensioned floorplans for the given adjacencies • GPLAN can also re-generate existing floorplans [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for the automated construction of rectangular floorplans (RFPs) while addressing dimensional constraints and adjacency relations. Here, adjacency relations are taken in the form of a dimensionless rectangular arrangement (RA) ensuring the existence of an RFP, while dimensional constraints are given in terms of minimum width and aspect ratio range for each room. A linear optimization model is then presented to obtain a feasible dimensioned RFP for the user-defined constraints. A graphical user interface (GUI) is also developed for the automated generation of RFPs. The proposed model is able to generate feasible solutions for every possible RA in a reasonable amount of time. From an architectural perspective, this work can be seen as a re-generation of well-known architectural plans with modified dimensions. At the end, the regeneration of existing legacy floorplans (corresponding to the user defined dimensions) has been demonstrated, with an additional feature to construct symmetric dimensioned solutions. [ABSTRACT FROM AUTHOR]