Description
In the pedestrian-flow setting, the eikonal equation |∇φ| = 1 / f(ρ) (or similar) defines a travel-time field φ(x) whose gradient gives the locally optimal direction of motion under a density-dependent speed function. It is the standard route-choice machinery inside continuum-crowd-model formulations (Hughes' dynamic model in particular) and gives a physically grounded alternative to hand-tuned floor fields.
When it's used
- Continuum-model implementation of agent route choice
- Pre-computed travel-time potentials for evacuation planning
- Coupling density fields with goal-directed movement
Limitations
- Assumes a single dominant goal; multiple exits need superposition heuristics
- Numerical solvers (fast marching) need careful boundary handling
- Cannot capture strategic / cognitive route deviations