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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., ECCV 2022

Existing graph theoretic approaches are mainly restricted to floor-plans with rectangular boundary. In this paper, we introduce 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 within it. Further, we present necessary and sufficient conditions for the existence of a non-trivial L-shaped floor-plan corresponding to a properly triangulated planar graph (PTPG) $G$. Also, we develop an $O(n^2)$ algorithm for its construction, if it exists., 35 pages, 61 figures

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 fitted in a rectangular enclosure. Only planar graphs can be dualized. If the dual of a plane graph is a rectangular graph, then the plane graph is a rectangularly dualizable graph. In 1985, Ko\'zmi\'nski and Kinnen presented a necessary and sufficient condition for the existence of a rectangularly dualizable graph for a separable connected plane graph. In this paper, we present a counter example for which the conditions given by them for separable connected plane graphs fail and hence, we derive a necessary and sufficient condition for a plane graph to be a rectangularly dualizable graph.

A plane graph is said to be a rectangular graph if each of its edges can be oriented horizontal or vertical, its internal regions are four-sided and it has a rectangular enclosure. If dual of a planar graph is a rectangular graph, then the graph is said to be a rectangular dualizable graph (RDG). In this paper, we present adjacency transformations between RDGs and present polynomial time algorithms for their transformations. An RDG $\mathcal{G}=(V, E)$ is called maximal RDG (MRDG) if there does not exist an RDG $\mathcal{G'}=(V, E')$ with $E' \supset E$. An RDG $\mathcal{G}=(V, E)$ is said to be an edge-reducible if there exists an RDG $\mathcal{G'}=(V, E')$ such that $E\supset E'$. If an RDG is not edge-reducible, it is said to be an edge-irreducible RDG. We show that there always exists an MRDG for a given RDG. We also show that an MRDG is edge-reducible and can always be transformed to a minimal one (an edge-irreducible RDG).

In this paper, we present GPLAN, software aimed at constructing dimensioned floorplan layouts based on graph-theoretical and optimization techniques. GPLAN takes user requirements as input in the following two forms: i. Adjacency graph: It allows user 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. Dimensionless layout: Here, user can draw any layout with rectangular or non-rectangular boundary on a GUI and GPLAN transforms it into a dimensioned floorplan while preserving 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 is to provide alternative platforms to user for producing dimensioned floorplans for all given (architectural) constraints, which can be further refined by architects.

Let G = (V, E) be a planar triangulated graph (PTG) having every face triangular. A rectilinear dual or an orthogonal floor plan (OFP) of G is obtained by partitioning a rectangle into \mid V \mid rectilinear regions (modules) where two modules are adjacent if and only if there is an edge between the corresponding vertices in G. In this paper, a linear-time algorithm is presented for constructing an OFP for a given G such that the obtained OFP has B_{min} bends, where a bend in a concave corner in an OFP. Further, it has been proved that at least B_{min} bends are required to construct an OFP for G, where \rho - 2 \leq B_{min} \leq \rho + 1 and \rho is the sum of the number of leaves of the containment tree of G and the number of K_4 (4-vertex complete graph) in G.

In this work, for the given adjacency matrix of a graph, we present an algorithm which checks the connectivity of a graph and computes all of its connected components. Also, it is mathematically proved that the algorithm presents all the desired results.

In this work, we focus on Tiling by rectangles, its Connectivity and associated Covariants. Tiling by rectangles is the geometric problem of arranging a given family of rectangles in a larger specific frame. A primitive version is rectangle tiling. Then the notion of rectangle tiling is extended to tiling rectangles inside some other shapes. This generalization is achieved through another object of a mathematical nature, namely the allocation matrix. This problem also involves the study of another mathematical concept the extra spaces which are introduced in the geometric distribution process. When tiling by rectangles, an effort has been made to obtain a tiling which is best from the point of view of connectivity. To refine the number of solutions originating from the algorithm, we have studied and developed several covariants related to tilings and their graph. The presented research work opens a new field for applied mathematicians, in that it combines various aspects of geometry, topology, graph theory and optimization theory, towards the solution of a problem which is well known to architects, but which has rarely been attacked by mathematical methods.