Department of Mathematics

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    Automated generation of circulations within a floorplan
    (CUP, 2025-04) Shekhawat, Krishnendra
    Various factors are considered when designing a floorplan layout, including the plan’s outer boundary, room shape and size, adjacency, privacy, and circulation space, among others. While graph-theoretic approaches have proven effective for floorplan generation, existing algorithms generally focus on defining the boundary of the plan or different room shapes, lacking the investigation of designing circulation space within a floorplan. However, the circulation design in architectural planning is a crucial factor that affects the functionality and efficiency of areas within a building. This paper presents a graph-theoretic approach for integrating circulation within a floorplan. In this study, we use plane graphs to represent floorplans and develop graph algorithms to incorporate various types of circulation within a floorplan as follows: i. The first phase generates a spanning circulation, that is, a corridor leading to each room using a circulation graph. ii. Subsequently, using an approximation algorithm, the circulation space is minimized, that is, generation of minimum circulation space covering all the rooms, thereby enhancing space utilization in the floorplan. iii. Furthermore, customized circulations are generated to cater to user preferences, distinguishing between public and private spaces within the floorplan. In addition to the theoretical framework, we have implemented our algorithms in Python and developed a user-friendly graphical interface (GUI), enabling seamless integration of our algorithms into architectural design processes.
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    Automated generation of floorplans with non-rectangular rooms
    (Elsevier, 2023-05) Shekhawat, Krishnendra
    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.
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    An algorithm for customizing slicing floor plan design
    (Springer, 2023) Shekhawat, Krishnendra
    This paper proposes a linear time algorithm for the customization of a slicing floor plan design, which can be done by customizing its modules in the following two ways: —-by modifying the aspect ratio or by modifying either its width or height while retaining its area,-by modifying its area while keeping either of its aspect ratio or initial width or height. Both of the aforementioned approaches demonstrate that a slicing floor plan can be generated for any aspect ratio and area while preserving the module adjacencies of the original floor plan. A demonstration has been provided for a devised prototype to validate the viability of the aforementioned approaches
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    Generation of dimensioned floor plans for a given boundary layout
    (SSCE, 2024) Shekhawat, Krishnendra
    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.
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    A graph theoretic approach for generating T-shaped floor plans
    (Elsevier, 2024-10) Shekhawat, Krishnendra
    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 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.
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    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.
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    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.
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    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.
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    Linear-time construction of floor plans for plane triangulations
    (ASMU, 2022) Shekhawat, Krishnendra
    This paper focuses on a novel approach for producing a floor plan (FP), either a rectangular (RFP) or an orthogonal (OFP) based on the concept of orthogonal drawings, which satisfies the adjacency relations given by any bi-connected plane triangulation G.
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    Rectangular floorplans with block symmetry
    (CUMINCAD, 2023) Shekhawat, Krishnendra
    The principle of symmetry has beneficial applications in architecture. Symmetry mainly creates order and equilibrium in complex designs. This study presents a graph theoretic approach for the automatic generation of rectangular floorplans with block symmetry. Existing graph theoretical approaches focus on the floorplan’s outer boundary design, different room shapes, and spatial arrangements. This paper introduces block symmetry as a new concept in floorplan generation. Based on this concept, an algorithm is proposed for generating a rectangular floorplan with rectangular blocks for a given adjacency graph if one exists. Further, suppose two blocks are required to be symmetric, i.e., of equal size. In that case, an optimisation framework is used to equate the widths and heights of the blocks, resulting in the generation of a rectangular floorplan with block symmetry. A GUI is provided for users to perform the automatic generation of floorplans.