We consider the problem of terrain model acquisition by a roving point placed in an unknown terrain populated by stationary polyhedral obstacles in .two/three dimensions. The motivation for this problem is that after the terrain model is completely acquired, navigation from a source point to a destination point can be achieved along the collision-free paths. And this can be done without the usage of sensors by applying the existing techniques for the well-known find-path problem. In this communication, the Point Robot Autonomous Machine (PRAM) i s used as a simplified abstract model for real-life roving robots. W e present an algorithm that enables PRAM to autonomously acquire the model of an unexplored obstacle terrain composed of an unknown number of polyhedral obstacles in two/three dimensions. In our method, PRAM undertakes a systematic exploration of the obstacle terrain with its sensor that detects all the edges and vertices visible from the present location, and builds the complete obstacle terrain model.