# Residential Buildings Complex Boundaries Generation Based on Spatial Grid System
## 2 Related Work  
In the current literature, there are a number of proposed systems suitable for automatic building generation based on different geometry concepts. The layout of rectangular floor plans was introduced by [PERSON] [1]. [PERSON] et al. [2] presented an algorithm for architectural floor plan generation using rectangular planar graphs. [PERSON] et al. [3] proposed a similar approach using triangular planar graphs. This system was further developed by [PERSON] et al. [4], who introduced an approach to generate floor plans from room adjacencies obtained from existing plans. All of these methods only generate rectangular rooms based on predefined (existing) graph structures. [PERSON] [5] has developed an algorithm to generate residential floor plans using the Monte Carlo method for room distribution. [PERSON] et al. [6] have applied an expert system for solving building layouts, introducing many serious disadvantages. As a consequence of the fact that the completeness and consistency of the system are not known to the user, it takes an intolerably lot of time to converge resulting in bad response time. Additionally, real building boundaries usually vary in shape and these variations are ignored in both [PERSON]'s [5] and [PERSON] et al. 's [6] approach. The boundaries are rectangular because they are derived from the internal constraints where all of the rooms have s rectangular shape, (which is not very common in contemporary architectural practice). [PERSON] et al. [7] based the research approach on an expert system where optimization is performed through the use of artificial intelligence. [PERSON] et al. [8] developed a method for house layout generation using relational generative adversarial networks. The presented solution satisfies the majority of addressed problem aspects but generated building boundaries are dominantly simple, due to the fact that rectangular forms are derived from rectangular rooms in most discussed cases. For the generation of building layouts within a known boundary, [PERSON] et al. [9] used a linear programming system of deformable tile templates. The exterior building boundary is the input while the interior layout is divided into tiles that are labeled as rooms. This is one of the research works that use the building boundary as an input that drives function within the object that, in a broader sense, shares a similar idea as the approach presented in this paper. [PERSON] et al. [10] proposed a solution that automatically generates layout designs based on a MIQP (mixed integer quadratic programming) formulation. Nonlinear programming techniques have been used for floor layout problems by [PERSON] et al. [11]. However, the solutions are derived for rectangular shape buildings only. [PERSON] et al. [12] developed a model for interactive manipulation of layouts by the use of shape grammar. The results are within the simple form of building boundary and constant interactive input from a user is required. [PERSON] et al. [13] proposed a framework for the automatic generation of floor plans using graph grammar formalism. The system can reproduce good results, but for each deviation from a rectangular building, interactive user input is required. [PERSON] [14] presented an interactive system for layout generation based on discursive grammar incorporating programming grammar and designing grammar. The described solutions include the 3D aspect and layout of the design space, but, due to the recognizable architectural style that has been analyzed, only produce rectangular forms. Some of the researchers found the solution for house layout automation through the use of genetic algorithms [15; 16; 17]. [PERSON] et al. [18] proposed a data-driven method for generating floor plans for residential buildings. They utilized a dataset of floor plans of real buildings in order to construct a neural network for layout generation.