There are many methods for projecting spherical maps onto the plane. Interactive versions of these projections allow the user to centre the region of interest. However, the effects of such interaction have not previously been evaluated. In a study with 120 participants we find interaction provides significantly more accurate area, direction and distance estimation in such projections. The surface of 3D sphere and torus topologies provides a continuous surface for uninterrupted network layout. But how best to project spherical network layouts to 2D screens has not been studied, nor have such spherical network projections been compared to torus projections. Using the most successful interactive sphere projections from our first study, we compare spherical, standard and toroidal layouts of networks for cluster and path following tasks with 96 participants, finding benefits for both spherical and toroidal layouts over standard network layouts in terms of accuracy for cluster understanding tasks.