The Cyclemeter app is written for iOS only and has the option to do exactly what you are wanting. On the Map page, you can toggle between a fixed position or have it oriented to your direction of travel. It actually uses maps on several screens so you can get a quick glance of where you are at any point during your ride or go to the Map page and track your route. It also has the option of toggling on or off the ability of shifting the screen. Screen pages are user defined and you can put them in any order you want. Presently, it does not have the turn-by-turn feature but they are working on it for a near future release. Unlike most of the other cycling apps, Cyclemeter allows you to select the mapping app you want it to use - Google Maps, Apple Maps or any other mapping app you have loaded on your phone.