"Light diffusion" in the singular metric
P. Souères, J.Y
Fourquet and J.P. Laumond, "Set of reachable positions for
a car", IEEE Trans. on Automatic Control, 39 (8), 1994.
The picture below shows the wave-fronts in the the singular metric: all the
points on a same red curve are located at the same distance from the
Only three types of paths allow to reach a position (x,y) from the origin
(0,0,0) along an optimal path. They define a partition of the plane into
regions bounded by the white curves.