Department of Mathematics: Recent submissions

  • Rectilinear floor plans 
    Shekhawat, Krishnendra (Springer, 2017)
    This work aims at providing a mathematical approach to the problem of allocating given rooms within a given predefined contour shape, while satisfying given adjacency and size constraints. This work is significant with ...
  • A Graph Theoretical Approach for Creating Building Floor Plans 
    Shekhawat, Krishnendra (Springer, 2019)
    Existing 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 ...
  • Construction of architectural floor plans for given adjacency requirements 
    Shekhawat, Krishnendra (CAADRIA, 2020)
    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 ...
  • A Graph Theoretic Approach for the Automated Generation of Dimensioned Floorplans 
    Shekhawat, Krishnendra (CAADRIA, 2021)
    The 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 ...
  • Rectangularly Dualizable Graphs: Area-Universality 
    Shekhawat, Krishnendra (ARXIV, 2021)
    A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be tted in a rectangular ...
  • End-to-end Graph-constrained Vectorized Floorplan Generation with Panoptic Refinement 
    Shekhawat, Krishnendra (ARXIV, 2022-07)
    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 ...
  • Transformations among rectangular partitions 
    Shekhawat, Krishnendra (TOC, 2022)
    We first prove that there always exists a maximal rectangularly dualizable graph for a given rectangularly dualizable graph and present an algorithm for its construction. Further, we show that a maximal rectangularly ...
  • Linear-time construction of floor plans for plane triangulations 
    Shekhawat, Krishnendra (ASMU, 2022)
    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 ...
  • Characterization of Graphs Based on Number of Bends in Corresponding Floor plans 
    Shekhawat, Krishnendra (ACM Digital Library, 2022-09)
    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 ...
  • Uniqueness of rectangularly dualizable graphs 
    Shekhawat, Krishnendra (ASMU, 2023)
    A generic rectangular partition is a partition of a rectangle into a finite number of rectangles provided that no four of them meet at a point. A graph H is called dual of a plane graph G if there is one−to−one ...
  • Rectangular floorplans with block symmetry 
    Shekhawat, Krishnendra (CUMINCAD, 2023)
    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 ...
  • Automated space allocation using mathematical techniques 
    Shekhawat, Krishnendra (Elsevier, 2015-09)
    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 ...
  • Why golden rectangle is used so often by architects: A mathematical approach 
    Shekhawat, Krishnendra (Elsevier, 2015-06)
    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, ...
  • Computer-aided architectural designs and associated covariants 
    Shekhawat, Krishnendra (Elsevier, 2015-09)
    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 ...
  • Best connected rectangular arrangements Author links open overlay panel 
    Shekhawat, Krishnendra (Elsevier, 2016-03)
    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 ...
  • A computer-generated plus-shaped arrangement and its architectural applications 
    Shekhawat, Krishnendra (Elsevier, 2017-10)
    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 ...
  • Mathematical propositions associated with the connectivity of architectural designs 
    Shekhawat, Krishnendra (Elsevier, 2017-12)
    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 ...
  • Introduction to generic rectangular floor plans 
    Shekhawat, Krishnendra (CUP, 2018-05)
    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 ...
  • Enumerating generic rectangular floor plans 
    Shekhawat, Krishnendra (Elsevier, 2018-08)
    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 ...
  • A tool for computer-generated dimensioned floorplans based on given adjacencies 
    Shekhawat, Krishnendra (Elsevier, 2021-07)
    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 ...

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