Department of Mathematics

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1920

Browse

Filters

2014 - 201962020 - 20253

Settings

Has files: NoSubject: search.filters.subject.Floor plan

Search Results

Now showing 1 - 9 of 9
  • No Thumbnail Available
    Item
    Automated generation of floor plans with minimum bends
    (CUP, 2025-02) Shekhawat, Krishnendra
    The generation of floor plan layouts has been extensively studied in recent years, driven by the need for efficient and functional architectural designs. Despite significant advancements, existing methods often face limitations when dealing with specific input adjacency graphs or room shapes and boundary layouts. When adjacency graphs contain separating triangles, the floor plan must include rectilinear rooms (non-rectangular rooms with concave corners). From a design perspective, minimizing corners or bends in rooms is crucial for functionality and aesthetics. In this article, we present a Python-based application called G-Drawer for automatically generating floor plans with a minimum number of bends. G-Drawer takes any plane triangulated graph as an input and outputs a floor plan layout with minimum bends. It prioritizes generating a rectangular floor plan (RFP); if an RFP is not feasible, it then generates an orthogonal floor plan or an irregular floor plan. G-Drawer modifies orthogonal drawing techniques based on flow networks and applies them on the dual graph of a given PTG to generate the required floor plans. The results of this article demonstrate the efficacy of G-Drawer in creating efficient floor plans. However, in future, we need to work on generating multiple dimensioned floor plans having non-rectangular rooms as well as non-rectangular boundary. These enhancements will address both mathematical and architectural challenges, advancing the automated generation of floor plans toward more practical and versatile applications.
  • No Thumbnail Available
    Item
    A compositional schema for the automated generation of best connected rectangular floor plans
    (Cambridge Scholars Publishing, 2018) Shekhawat, Krishnendra
    The work described here is part of a larger research aimed at developing design aids for architects that could be particularly useful in the design of large buildings with complex and specialized programs like hospitals.
  • No Thumbnail Available
    Item
    A Mathematical Approach for Generating a Floor Plan for Given Adjacency Requirements
    (Springer, 2022-02) Shekhawat, Krishnendra
    One of the preliminary steps in designing architectural floor plans is to build floor plans for a given adjacency graph. Here, we present a mathematical procedure for enumerating maximal rectangular floor plans that would address the following two purposes: i. Provides a catalogue of maximal rectangular floor plans, which can be seen as a super set of all possible rectangular floor plans, ii. Maximal rectangular floor plans can be used to generate floor plans for the adjacency requirements for which rectangular floor plans do not exist. Hence, in this paper, we present an algorithmic approach for producing a floor plan corresponding to any adjacency requirements provided by the user/architect/designer. This work aims to build a computerized system to generate floor plans, i.e., we aspire to provide design tools to architects for generating feasible layouts that can be further adjusted or modified.
  • No Thumbnail Available
    Item
    Algorithm for constructing an optimally connected rectangular floor plan
    (Elsevier, 2014-09) Shekhawat, Krishnendra
    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.
  • No Thumbnail Available
    Item
    Construction of architectural floor plans for given adjacency requirements
    (CAADRIA, 2020) Shekhawat, Krishnendra
    For most of the architectural design problems, there are underlying mathematical sub-problems, they may require to consider for generating architectural layouts. One of these sub-problems is to satisfy adjacency constraints for obtaining an initial layout. But in the literature, there does not exist a mathematical procedure that can address any given adjacency requirements, i.e., there does not exist a tool for generating a floor plan corresponding to any given adjacency (planar) graph (there exist algorithms for constructing floor plans for planar triangulated graphs only). In this paper, we are going to present an algorithm that would generate a floor plan corresponding to any given planar graph. The larger aim of this research is to develop a user-friendly tool that can generate a variety of initial layouts corresponding to a given graph, which can be further modified by the architects/designers.
  • No Thumbnail Available
    Item
    Why golden rectangle is used so often by architects: A mathematical approach
    (Elsevier, 2015-06) Shekhawat, Krishnendra
    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.
  • No Thumbnail Available
    Item
    Best connected rectangular arrangements Author links open overlay panel
    (Elsevier, 2016-03) Shekhawat, Krishnendra
    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 best connected rectangular arrangements so that the proposed solutions can be further used by architects for their designs.
  • No Thumbnail Available
    Item
    Mathematical propositions associated with the connectivity of architectural designs
    (Elsevier, 2017-12) Shekhawat, Krishnendra
    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.
  • No Thumbnail Available
    Item
    Enumerating generic rectangular floor plans
    (Elsevier, 2018-08) Shekhawat, Krishnendra
    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.