# Residential Buildings Complex Boundaries Generation Based on Spatial Grid System
## 3 Overview
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Research** & **Method/Problem That Is Addressed** & **Dimensionality** & **Interior Layout** & \begin{tabular}{c} **Boundary** \\ **Type** \\ \end{tabular} \\ \hline [PERSON] [1] & Spiral based layout generation & 2D & Yes & Rectangular \\ \hline [PERSON] et al. [2] & Algorithm for finding a rectangular dual of a planar triangulated graph & 2D & Yes & Rectangular \\ \hline [PERSON] et al. [3] & Algorithm to construct a total of an \(n\)-vertex planar triangulated graph & 2D & Yes & Rectangular \\ \hline [PERSON] et al. [4] & Algorithm for floor plan generation from existing floor plans based on graph transformations & 2D & Yes & Rectangular \\ \hline [PERSON] [5] & Algorithm for procedural house generation based on the Monte Carlo method (one example without the code or detailed method description) & 2D & \begin{tabular}{c} Only as a predefined \\ rectangular shape \\ \end{tabular} & \begin{tabular}{c} Complex, derived from rectangular rooms \\ \end{tabular} \\ \hline [PERSON] et al. [6] & Expert system for solving building layouts based on design grammars & 2D & \begin{tabular}{c} Only as a \\ predefined \\ rectangular shape \\ \end{tabular} & \begin{tabular}{c} Complex, derived from \\ rectangular rooms \\ \end{tabular} \\ \hline [PERSON] et al. [7] & Expert system based on route search as a problem of AI optimization & 2D & Yes & Rectangular \\ \hline [PERSON] et al. [8] & Relational generative adversarial neural network for graph-constrained house generation & 2D & Yes & \begin{tabular}{c} Simple, derived from \\ mostly rectangular rooms \\ \end{tabular} \\ \hline [PERSON] et al. [9] & Layout computation using deformable templates & 2D & Yes & Boundary is an input \\ \hline [PERSON] et al. [10] & Algorithm based on mixed-integer quadratic programming formulation & 2D & Yes & \begin{tabular}{c} Simple, but also Boundary \\ can be an input \\ \end{tabular} \\ \hline [PERSON] et al. [11] & Nonlinear programming techniques for floor layout generation & 2D & Yes & Rectangular \\ \hline [PERSON] et al. [12] & \begin{tabular}{c} Mixed continuous/discrete models \\ where user can manipulate objects \\ within constrains \\ \end{tabular} & 2D & Yes & \begin{tabular}{c} Simple, derived from \\ mostly rectangular rooms \\ \end{tabular} \\ \hline [PERSON] et al. [13] & Algorithm that uses reserved graph grammar formalism & 2D & Yes & \begin{tabular}{c} Simple with required \\ input for each deviation \\ from rectangle form \\ \end{tabular} \\ \hline [PERSON] [14] & \begin{tabular}{c} Discursive grammar that consists of programming and a \\ designing grammar \\ \end{tabular} & 3D & Yes & \begin{tabular}{c} Rectangular, because of \\ the architectural style \\ \end{tabular} \\ \hline [PERSON] et al. [18] & Data-driven method for generating floor plans where building boundary is an input & 2D & Yes & Boundary is an input \\ \hline [PERSON] et al. [19] & Bayesian network trained on real-world data & 3D & Yes & \begin{tabular}{c} Mostly simple, with \\ limited complexity \\ \end{tabular} \\ \hline [PERSON] [20], [PERSON] [21] & Irregular architectural layout synthesis with graphical inputs & 2D & \
\begin{tabular}{c} Yes, with errors in \\ the output area \\ \end{tabular} & Irregular, from pattern \\ \hline [PERSON] et al. [22] & Complex adaptive systems applied to architecture form & 3D & No & Mostly simple \\ \hline [PERSON] and [PERSON] [29] & Cellular automata-based algorithm for 3D building generation & 3D & No &
\begin{tabular}{c} Complex, but with \\ low resolution \\ (\(10\times 10\) m cells) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The comparative analysis of related work relevant to this article. impact on any previously added (existing) concepts. It is especially important in software engineering where it is known as an Open/Close quality design principle [34].