  Very recently, a kind of spatial network constructed with power-law distance
distribution and total energy constriction is proposed. Moreover, it has been
pointed out that such spatial networks have the optimal exponents $\delta$ in
the power-law distance distribution for the average shortest path, traffic
dynamics and navigation. Because the distance is estimated approximately in
real world, we present an distance coarse graining procedure to generate the
binary spatial networks in this paper. We find that the distance coarse
graining procedure will result in the shifting of the optimal exponents
$\delta$. Interestingly, when the network is large enough, the effect of
distance coarse graining can be ignored eventually. Additionally, we also study
some main dynamic processes including traffic dynamics, navigation,
synchronization and percolation on this spatial networks with coarse grained
distance. The results lead us to the enhancement of spatial networks'
specifical functions.
