Smooth Magnifying Lens Effects

Regular magnifying lens tools come with a disadvantage: They cause discontinuities in the map, they break roads and borders and cover up some underlying areas:

Smooth magnifying lens tools solve this problem. The idea is not new:

… but it’s not implemented in any of the widely used toolboxes. In fact, I’m not aware of any implementation up-to-date.

[Harrie, L., Sarjakoski, T., Lehto, L. A variable-scale map for small-display cartography. In: Joint International Symposium on GeoSpatial Theory, Processing and Applications (ISPRS/Commission IV, SDH2002). Ottawa, Canada, July 2002] present an algorithm for a smooth magnifying lens effect.

As barrycarter pointed out on gis. stackexchange,  this visualization can be seen as a kind of cartogram and could probably be implemented in a similar fashion. I’d love to see such a tool in QGIS and probably even OpenLayers.