When setting up global ocean circulation models one faces the problem of in
cluding the Arctic Ocean where the traditional spherical coordinate system
has a singularity at the pole. In addition, in regional model applications
one has to deal with open boundaries where assumptions are made about the n
ormally poorly known boundary conditions. Here an analytical reversible coo
rdinate transformation on a sphere that preserves the orthogonality and the
shape of infinitesimal figures is presented. Starting from a standard sphe
rical coordinate system, the transformation is able to map the North and So
uth Poles to two arbitrary locations of the earth and this is readily done
with the aid of a conformal mapping in the extended complex plane. The resu
lting coordinate system will have enhanced resolution along the geodesic cu
rve between the new poles. Examples are given where the transformation is u
sed to strongly increase the resolution in a particular region of interest
in the model domain.