Browsing by Author "Shekhawat, Krishnendra"

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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.
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
An annotated review on graph drawing and its applications
(Taylor & Francis, 2023-07) Shekhawat, Krishnendra
A 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
Automated Best Connected Rectangular Floorplans
(Springer, 2017-01) Shekhawat, Krishnendra
As part of a larger research aimed at developing design aids for architects, this paper presents the “automated” generation of the “best connected” rectangular floor plans, satisfying given topological and dimensional constraints. It has been seen that architects, knowingly or unknowingly, have often used either the golden rectangle or the Fibonacci rectangle in their works throughout history. But it was hard to find any specific reason for such use, other than aesthetic. In 2015, Shekhawat showed that they are among the best connected rectangular arrangements (dimensionless rectangular floor plans) and that this may well be another reason for their frequent use in architectural design. In this work, an alternative algorithm is presented which generates n − 3 best connected rectangular arrangements, being n the number of rooms. Then, this concept is further extended for constructing the best connected dimensioned rectangular floor plans. The goal is to provide an optimal solution for the rectangular space allocation problem, while satisfying given topological and dimensional requirements.
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.
Automated Generation of Dimensioned Rectangular Floorplans
(ARXIV, 2023) Shekhawat, Krishnendra
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 a 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 user-defined constraints. A 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 the architectural prospective, 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 RFPs (corresponding to the user defined dimensions) has been demonstrated, taking their image as input.
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.
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.
Automated space allocation using mathematical techniques
(Elsevier, 2015-09) Shekhawat, Krishnendra
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.
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.
Characterization of Graphs Based on Number of Bends in Corresponding Floor plans
(ACM Digital Library, 2022-09) Shekhawat, Krishnendra
Let G = (V, E) be a maximal planar graph (MPG), where every face is triangular. A floor plan (FP) of an n-vertex MPG G is a partition of a rectangle into n rectilinear polygons called modules where two modules are adjacent if and only if there is an edge between the corresponding vertices in G. It can be easily found that it is not possible to construct a FP for a given MPG while maintaining the rectangularity of the modules of a FP (for an example, consider the complete graph K4). Hence, to satisfy adjacency requirements of a MPG, bends need to be introduced within the FPs, where a bend is a concave corner of a module in a FP. A FP with rectilinear modules or with at least one bend is called orthogonal floor plan (OFP). There exist algorithms for the construction of an OFP for a given MPG but the notion of minimum bends within an OFP is not yet discussed in the literature. In this paper, a mathematical procedure for computing the minimum number of bends required in an OFP for a MPG G has been presented. Further, it has been shown that the number of bends in an OFP depends only on critical separating triangles and K4’s.
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.
Computer-aided architectural designs and associated covariants
(Elsevier, 2015-09) Shekhawat, Krishnendra
To compare two architectural designs or to characterize them, some numbers are needed. These numbers are said to be covariants. In this paper, we present a software prototype that generates a floor plan design and its adjacency graph for a given set of data, and computes some mathematical covariants associated with the obtained design. In addition, we discuss and demonstrate the usefulness of covariants in comparing the architectural designs and in obtaining a best design among many possible solutions.
A computer-generated plus-shaped arrangement and its architectural applications
(Elsevier, 2017-10) Shekhawat, Krishnendra
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.
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.
Construction of non-rectangular floor plans for properly triangulated planar graphs
(Springer, 2024-10) Shekhawat, Krishnendra
A majority of previous research on the problem of floor planning has been limited to constructing floor plans with rectangular exterior boundaries. It includes rectangular floor plans (RFPs) (Kozminski and Kinnen in IEEE Trans-Actions Circuits Syst 35:1401–1416, 1988, [1]) for properly triangulated plane graphs (PTPGs) having four or fewer corner implying paths (CIPs), where both the modules and exterior boundary are considered rectangular, and orthogonal floor plans (OFPs) (Liao et al in J Algorithms 2:441–451, 2003, [2]) for the remaining graphs (which do not possess RFPs), where the exterior boundary is rectangular but modules are taken of rectilinear shapes (L-shaped, T-shaped, Z-shaped, etc.). As an alternative to OFPs, sometimes floor plans containing rectilinear external boundaries and rectangular modules can also be obtained, known as non-rectangular floor plans (Raveena Shekhawat in Theor Comput Sci 942:57–92, 2023, [3]). This work aims to investigate non-rectangular floor plans (NRFPs) providing the best alternative solution in terms of the least number of concave corners (comparing with the number of bends in OFPs) for the PTPGs having more than four CIPs. We present a linear time algorithm to construct NRFPs with the least possible number of concave corners at the exterior boundary corresponding to the PTPGs with more than four CIPs. Further, we claim that the obtained NRFPs are non-trivial. An NRFP is considered non-trivial if the count of concave corners at its exterior boundary cannot be lowered without disrupting the horizontal and vertical adjacencies of the modules. In addition, we demonstrate that it is always feasible to produce an NRFP with precisely concave corners for any PTPG with k; CIPs.
End-to-end Graph-constrained Vectorized Floorplan Generation with Panoptic Refinement
(ARXIV, 2022-07) Shekhawat, Krishnendra
The automatic generation of floorplans given user inputs has great potential in architectural design and has recently been explored in the computer vision community. However, the majority of existing methods synthesize floorplans in the format of rasterized images, which are difficult to edit or customize. In this paper, we aim to synthesize floorplans as sequences of 1-D vectors, which eases user interaction and design customization. To generate high fidelity vectorized floorplans, we propose a novel two-stage framework, including a draft stage and a multi-round refining stage. In the first stage, we encode the room connectivity graph input by users with a graph convolutional network (GCN), then apply an autoregressive transformer network to generate an initial floorplan sequence. To polish the initial design and generate more visually appealing floorplans, we further propose a novel panoptic refinement network(PRN) composed of a GCN and a transformer network. The PRN takes the initial generated sequence as input and refines the floorplan design while encouraging the correct room connectivity with our proposed geometric loss. We have conducted extensive experiments on a real-world floorplan dataset, and the results show that our method achieves state-of-the-art performance under different settings and evaluation metrics.
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.
Existence and construction of a C-shaped module within a floorplan
(Elsevier, 2025-06) Shekhawat, Krishnendra
For a given graph, this paper presents a graph-theoretic approach for creating a floorplan with a specific module, i.e., a C-shaped module. Unlike traditional methods that only consider boundary layouts for floorplan generation, this research considers constraints related to constructing the desired modules. The central objective is to explore how graph theoretic properties can ensure the integration of C-shaped modules within floorplans that have rectangular boundaries. A key innovation lies in introducing the concept of non-triviality for these modules, which becomes crucial for achieving the desired non-trivial C-shaped module (a non-trivial module means that it cannot be transformed into other shaped modules by stretching or shrinking its module walls, i.e. if its module walls are stretched or shrinked, then either the bends of its neighboring modules may increase or the given adjacency may not be preserved). The proposed solution involves a linear-time algorithm based on the concept of canonical labeling. The algorithm introduces prioritized canonical labeling to generate a non-trivial C-shaped module within the floorplan. It operates on a given plane triangulated graph (PTG) that contains at least one interior . The paper outlines the algorithm and establishes the essential conditions for constructing a non-trivial C-shaped module within the floorplan of a given plane triangulated graph (PTG) G. Notably, the algorithm's simplicity and ease of implementation set it apart. In future work, we will focus on generating the existence and construction of other desired shaped modules for the given input graphs.
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.