We introduce a new model in the context of non-planar orthogonal graph drawing that we call slanted orthogonal graph drawing. While in traditional orthogonal drawings each edge is made of alternating axis-aligned line segments, in slanted orthogonal drawings intermediate diagonal segments on the edges are permitted, which allows for: (a) smoothening the bends of the produced drawing (as they ar...

A simple geometric condition that defines the class of classical (stereographic, conic and cylindrical) conformal mappings from a sphere onto a plane is derived. The problem of optimization of computational grid for spherical domains is solved in an entire class of conformal mappings on spherical (geodesic) disk. The characteristics of computational grids of classical mappings are compared for ...

It is proved that the family of Ahlfors extremal mappings of a multiply connected region in the plane onto the unit disc can be expressed as a rational combination of two fixed Ahlfors mappings in much the same way that the family of Riemann mappings associated to a simply connected region can be expressed in terms of a single such map. The formulas reveal that this family of mappings extends t...