Grid-Geometry Sampling Technique: Identifying Optimal Alternatives for Housing Developments on Hillsides

Partitioning development sites into gridded networks for slope/gradient analysis is one of the most important steps for housing development on hillsides. In concept, different housing development alternatives can be created by fusing various gridded networks and slope calculation methods. This study proposes a grid-geometry sampling technique (${\mathrm{G}}^2\mathrm{ST}$) and an optimal model of housing development (OMHD) as an assistant tool for solving the problem of housing development on hillsides. Applying the ${\mathrm{G}}^2\mathrm{ST}$, enormous gridded networks can be generated by altering the origin shift and axis rotation. Each gridded network represents a feasible alternative of the OMHD. Based on slope analysis, the OMHD has two objectives: the area of permitted housing development (APHD) and the floor area of housing unit (FAHU). By calculating the objective value of all gridded networks for a housing development side, the optimal alternatives can be identified from the gridded networks. Results obtained in experiments using field-survey contours show that the APHD and FAHU are dependent not only the gridded network, but also the slope calculation method. With the aid of the ${\mathrm{G}}^2\mathrm{ST}$ and OMHD, governments and developers can easily and quickly obtain diverse gridded networks and slope analysis results for hillside development applications, despite the fact that the generation of gridded networks is highly complex and difficult to solve manually. Integrating the ${\mathrm{G}}^2\mathrm{ST}$ and OMHD enables identifying approximately optimal alternatives and provides diverse alternatives and flexible ways to review the problem of housing development on hillsides. If authorities want to mitigate the effect of disasters for housing development on hillsides, they can adopt the minimum APHD or OMHD alternatives as the basis for housing development. Because of the efficient and diverse characteristics, the ${\mathrm{G}}^2\mathrm{ST}$ is applicable to any analysis based on gridded networks, including terrain analysis, flow routing analysis, and the analysis of landscape metrics.