The Koebe-Andreev-Thurston circle packing theorem, as well as its
generalization to circle patterns due to Bobenko and Springborn, holds for
Euclidean and hyperbolic metrics possibly with conical singularities, but fails
for spherical metrics because of the non-uniqueness coming from M\"obius
transformations. In this paper, we show that a unique existence result for
circle pattern with spherical conical metric holds if one prescribes the
geodesic total curvature of each circle instead of the cone angles.Comment: 9 pages, 6 figure