The problem of incremental terrain acquisition is addressed in this paper. Through a systematic planning of movements in an unknown terrain filled with polygonal obstacles, a sensor-based robot is shown to be able to incrementally build the entire terrain model; the model will be described in terms of visibility graph and visibility window. The terrain model is built area by area without any overlapping between explored areas. As a consequence, the terrain is obtained as a tessellation of disjoint star polygons. And the adjacency relations between star polygons are represented by a star polygon adjacency graph (SPAG graph). The incremental exploration process consists of two basic tasks: local exploration and exploration merging. Useful lemmas are derived for these two tasks and, then, the algorithms for the tasks are given. Examples are used to illustrate the algorithms. Two strategies for planning robot movements in the unknown terrain environment are suggested and compared. They are the depth-first search and the breadth-first search applied to the SPAG graph. Finally, the performance evaluation of the method and comparison with some existing methods are presented.