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This paper proposes a methodology for computing, visualizing, and analyzing critical decision boundaries for the selection of shortest paths in a given environment. Decision boundaries are defined as the points in a map from which two or more different shortest paths exist towards a destination. This paper introduces the problem of visualizing their evolution, taking into account moving obstacles, moving goals, and as well multiple goals. The proposed visualizations enable analyzing which paths should be taken and at which departure times, such that a destination can be reached by the shortest possible path when taking into account a moving target or time-varying areas to be avoided. The proposed techniques are also applied to the analysis and improvement of exit placement in a given environment, in order to improve the evacuation flow in emergency situations. [Display omitted] • This research presents a unique method for detecting decision boundaries in a given environment, based on the analysis of the generator points of the Shortest Path Map (SPM) rather than employing traditional scalar field topological methods relying on cell neighborhood information which can be affected by the representation resolution. • The proposed approach introduces tools and techniques to visualize the evolution of decision boundaries when considering dynamically-changing obstacles and targets, and to design exit placement to equalize the escape flow distribution. • This novel approach supports decision-making applications related to navigation and environment modeling in emergency evacuation planning. • By analyzing and visualizing SPM decision boundaries, the lengths of globally-optimal Euclidean shortest paths are taken into account, instead of grid-based accumulated distances used in other approaches. [ABSTRACT FROM AUTHOR]