@jieun and @bowenli - good questions - in my opinion, the best system for recomputing directions if a turn is missed is any of the GPS systems with voice readouts. Garmin, TomTom, etc. continually use the present driver coords and automatically recalculate the new directions for instance from the wrong spot. Now, these turn-by-turn directions are available on the iPhone (for a pricey subscription) and lately I heard a free version is slated for Android mobiles. In general, these voice-enabled GPS systems have long obsoleted online maps for general purpose driving directions.
If only purely visual geospatial representations are considered, LineDrive does illustrate a couple of nifty design principles (such as local focus+context and redn of clutter) that is more of an afterthought or lacking in most of the early and several current map implementations. Having said that, at the present moment there are several map features and technologies that have long since solved these issues. For one thing, Google StreetView is fantastic when it comes to local navigation. Even without StreetView, Google gives axonometric projections for landmarks at higher zoom levels. Other map providers (CloudMade, etc.) provide rooftop and birdeye views as well. With a full map, it is also possible to get traffic encoded routes and even identify alternative routes.
Instead of a separate map like LineDrive, I asked in class about providing a bi-focal distortion for the local region on mouseovers. Although Dr. Agarwala's answer was correct (difficulty in properly merging the distorted and undistorted areas), I found that there are now newer map imaging techniques with tiles (BingMaps, etc.) that can make this acceptable (similar to http://www.flashxml.net/pyramid-gallery.html). Of course, this requires interaction. For a non-interactive method - if we further consider the use case scenario, a typical user needs expanded/scaled routes for only one end of the To/From location since she/he is likely already familiar with his starting surroundings. So, a single corner inset for the other local area at the higher zoom will likely suffice.