The Eikonal equation is a nonlinear partial differential equation of the form |∇u(x)| = 1/f(x), where u represents the travel time or distance from a source point and f encodes local speed or traversability of the domain, commonly solved to construct global navigation potential fields that guide agent movement toward goals. In crowd simulation and modeling, it is fundamental for computing shortest-path or least-cost distance maps across continuous environments, enabling both microscopic agents and macroscopic density fields to follow locally optimal trajectories without requiring explicit path planning for each individual. Key variants include the anisotropic Eikonal equation, which accounts for direction-dependent speeds, and viscosity solution formulations solved numerically via the Fast Marching Method or Fast Sweeping Method, both of which are widely used in practice to efficiently compute these navigation fields over discretized spatial grids.
Source Papers
- A high-resolution meshfree particle method for numerical investigation of second-order macroscopic pedestrian flow models ↗ — A high-resolution meshfree particle method for numerical inv
- A review on crowd simulation and modeling ↗ — A review on crowd simulation and modeling
- Body and mind: Decoding the dynamics of pedestrians and the effect of smartphone distraction by coupling mechanical and decisional processes ↗ — Body and mind: Decoding the dynamics of pedestrians and the
- Crowds in Equations ↗ — Crowds in Equations
- Physics of Human Crowds ↗ — Physics of Human Crowds
- Revisiting Hughes’ dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm ↗ — Revisiting Hughes’ dynamic continuum model for pedestrian fl