  A navigation on a set of points $S$ is a rule for choosing which point to
move to from the present point in order to progress toward a specified target.
We study some navigations in the plane where $S$ is a non uniform Poisson point
process (in a finite domain) with intensity going to $+\infty$. We show the
convergence of the traveller path lengths, the number of stages done, and the
geometry of the traveller trajectories, uniformly for all starting points and
targets, for several navigations of geometric nature. Other costs are also
considered. This leads to asymptotic results on the stretch factors of random
Yao-graphs and random $\theta$-graphs.
