Maximum unobstructed shortest path between multipart-continuous geometries: Enabling novel type of access evaluations for urban safety

In safety planning, preparing for worst-case scenarios is critical. For instance, fire stations are strategically located aiming to respond within four minutes in the worst-case. Similarly, hydrant-to-structure access adheres to this principle. Fire codes require that the furthest projection on a building's exterior must be within a specified distance from fire access roads via an unobstructed route. This ensures that all parts of a building are reachable by a fire hose from parked fire apparatus. This requirement involves a novel spatial optimization problem: the Maximum Generalized Euclidean shortest path problem. The Euclidean shortest path problem is an approach for determining an unobstructed shortest path, however, constrained to single-point representations for origin and destination. This research generalizes this problem to identify unobstructed paths between multipart-continuous geometries, such as road segments and building structures. A novel solution approach is also proposed, expanding the scope of access evaluation and advocating safety planning.