Fast numerical methods based on SDEs for several problems related to the shortest path (Q2511251)

A description is given of how the evolving junctions on obstacle boundaries (E-JOB) method is implemented to provide algorithms for determining the shortest path for moving a disk between two points; the shortest path between two sets in \(n\)-dimensional space; and the shortest path between two points when obstacles appear or disappear over time. It is noted that E-JOB applies intermittent diffusion global optimization, which requires the use of the numerical solution of a stochastic differential equation (SDE), and the E-JOB uses the level set method to overcome geometrical difficulties introduced by the obstacles. Potential uses in robotics, computer-aided design, and computer graphics are mentioned.