Fisheye views of graphs are pictures of layouted graphs as seen through a fisheye lens. They allow to display, in one picture, a small part of the graph enlarged while the graph is shown completely. Thus they combine the features of a zoom—presenting details— and of an overview picture—showing global structure. In previous work the part of the graph to be enlarged—the focus region—was defined by a focus point. We generalize fisheye views such that the focus region can be defined by a simple polygon and show efficient algorithms to compute generalized fisheye views. We present experimental results on two applications where generalized fisheye views are advantageous: travel planning and ray tracing.