Fence ownership laws and organic parcel mosaics: Towards a complete, algorithmic regulation

Building laws establish responsibilities and limitations for various building activities that occur on the geometric mosaics of land parcels, such as the construction and maintenance of fences. Fence ownership can be determined by agreements between neighbors, local or national regulations based on the geometric properties of parcels, established customs, or cadastral parcel registries. Despite their advantages, geometric rules have lost popularity in the 20th century due to existing policies being incomplete and lacking clear guidelines for irregularly shaped parcels. In this paper, we identify the requirements for an effective fence ownership policy, including clarity, cost-effectiveness, robustness, and alignment with established rules.We also develop a family of geometric algorithms based on a historical regulation once widespread across Europe, which is still part of the building laws in several countries. The proposed algorithms meet all these requirements and can serve as the foundation for efficient future regulations.