I would like to run a campaign that involves the PCs exploring an unmapped wilderness, including various dungeons and the like. I have it all mapped out myself, but I want the act of them mapping the world from their experience to be a key part of the game.
I would also like to be able to use terrain and miniatures for combat and various other situations that require that level of detail, however I am concerned that if I draw/model the dungeon around them, my players will not bother mapping it out themselves, since I'm basically doing it for them. I've always run combat verbally before, so having physical representations of the game is new to me.
Are my two needs incompatible? Does anyone have any experience of doing something like this, and if so, how did it go?