# Residential Buildings Complex Boundaries Generation Based on Spatial Grid System
## 6 Discussion  
The problem of building boundary generation is widely addressed in contemporary research and publications. In the referenced publications discussed methodologies, methods, algorithms, and more or less automated frameworks and software tools tend to cluster into coherent groups that use the related principles but with different impacts on the abstraction level and generality of proposed solutions. Figure 14: Comparison of our method to all methods selected from research [10; 13; 18; 19] and to our selection of real-life buildings with complex building floor plan borders. Figure 13: Border shapes of our selection of complex real-life buildings. One cluster is mainly oriented to simple regular building boundaries development that solely serves as the container of internal. They are usually constrained by the internal functionality disposition. For this group, the main focus appears to be the building floor plan layout or the architectural style they analyzed observed is not contemporary or visually challenging by the form. A few of those researches argue the possibility of combining simple building boundary shapes to get more complex variations or offer low-resolution results, but most of them are significantly limited in the number of variations achieved in a specific time frame. The external constraints are more or less ignored and do not represent a driving force of the automatic building boundary generation process. The other cluster, with a significantly lower number of research works, focuses on relatively complex building boundaries generation that makes them suitable for cross-reference performance comparison with the approach described in this article. The results of three research works from this group are compared with regard to the presented novel approach. They were selected because their algorithms produced results that are more complex compared to others, listed in Section 2 making them an ideal validation benchmark. The smallest research cluster uses external boundary constraints as the driving force of building boundaries generation but different methods used (knowledge-based system) were the main obstacle in strict comparisons. There were no research works seriously focusing on the methodology, methods, and algorithms that support the production of complex boundary shapes in large quantities within a reasonable time frame. The results of the research methods of the papers used as benchmarks for validation [10; 13; 19] are derived from a maximum of a 174 square meter building area. The results for larger buildings could not be obtained from the current examples. The algorithm presented in this paper produces results for buildings up to 350 square meters. The possibility of other methodologies generating similar results is currently highly unlikely but may be possible in further development. The main obstacle of the methodology presented in research papers [10; 13; 19] was the heavy internal functionality interrelations and dependencies that are computationally demanding. That is why the inherent limitation of variations is understandable. The goal of this paper is to create the building boundaries in the form of constraints influenced by outer forces but not to completely exclude the premises of interior functionality either. There are research works [9; 18] that can produce building layouts if the border constraint of the building is provided. The expanded version of the methodology applying grid systems, used in this paper, is also planned to be upgraded for the internal layout generation in the future. Figure 11 summarizes the advantages and disadvantages of the benchmark set with regard to the proposed method and algorithm. Almost all of the compared research methods produce results that are below the minimum value of the algorithm presented in this paper. The results clearly show that the novel method, proposed by this paper, fills in the current research gap in the referenced scientific field.