In this paper, we address a problem of mapping an unknown region of interest by a mobile robot. Unlike the conventional exploration and mapping techniques where the occupancy map of a spatially discretized environment is obtained, in the proposed Geometric Mapping (G-Mapping) strategy, the map is obtained in the form of geometric models of the obstacles, in a continuous space. For simplicity, we consider convex polygonal obstacles within a convex region. The proposed exploration strategy is implemented using MATLAB. The simulation results are presented to illustrate and demonstrate the G-Mapping strategy.