Department of Mathematics
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Item A Graph Theoretical Approach for Creating Building Floor Plans(Springer, 2019) Shekhawat, KrishnendraExisting floor planning algorithms are mostly limited to rectangular room geometries. This restriction is a significant reason why they are not used much in design practice. To address this issue, we propose an algorithm (based on graph theoretic tools) that generates rectangular and, if required, orthogonal floor plans while satisfying the given adjacency requirements. If a floor plan does not exist for the given adjacency requirements, we introduce circulations within a floor plan to have a required floor plan.Item Construction of architectural floor plans for given adjacency requirements(CAADRIA, 2020) Shekhawat, KrishnendraFor 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.Item A Graph Theoretic Approach for the Automated Generation of Dimensioned Floorplans(CAADRIA, 2021) Shekhawat, KrishnendraThe automated generation of architectural layouts is an intensively studied research area where the aim is to generate a variety of (initial) layouts for the given constraints which can be further modified by designers and architects. From a mathematical perspective, one of the well-known constraints is given in the form of an adjacency graph which represents the adjacency relations of the given rooms and problem is to generate multiple layouts satisfying the adjacency relations. In the literature, the adjacency graph is usually taken as a bi-connected planar triangular graph. In this paper, we present the results of a prototype GPLAN that generates multiple dimensioned layouts for any given planar graph. The larger aim of this work is to develop software that can produce a variety of architecturally acceptable floorplans corresponding to the given constraints.Item Rectangular floorplans with block symmetry(CUMINCAD, 2023) Shekhawat, KrishnendraThe 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.Item Enumerating generic rectangular floor plans(Elsevier, 2018-08) Shekhawat, KrishnendraA 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.Item A tool for computer-generated dimensioned floorplans based on given adjacencies(Elsevier, 2021-07) Shekhawat, KrishnendraIn 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.Item Graph-based approach for enumerating floorplans based on users specifications(CUP, 2022-02) Shekhawat, KrishnendraThis 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.Item Transforming an Adjacency Graph into Dimensioned Floorplan Layouts(Wiley, 2022-03) Shekhawat, KrishnendraIn recent times, researchers have proposed several approaches for building floorplans using parametric/generative design, shape grammars, machine learning, AI, etc. This paper aims to demonstrate a mathematical approach for the automated generation of floorplan layouts. Mathematical formulations warrant the fulfilment of all input user constraints, unlike the learning-based methods present in the literature. Moreover, the algorithms illustrated in this paper are robust, scalable and highly efficient, generating thousands of floorplans in a few milliseconds. We present G2PLAN, a software based on graph-theoretic and linear optimization techniques, that generates all topologically distinct floorplans with different boundary rooms in linear time for given adjacency and dimensional constraints. G2PLAN builds on the work of GPLAN and offers solutions to a wider range of adjacency relations (one-connected, non-triangulated graphs) and better dimensioning customizability. It also generates a catalogue of dimensionless as well as dimensioned floorplans satisfying user requirements.Item A theory of L-shaped floor-plans(Elsevier, 2023-01) Shekhawat, KrishnendraExisting 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 algorithm for its construction, if it exists.Item An annotated review on graph drawing and its applications(Taylor & Francis, 2023-07) Shekhawat, KrishnendraA 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