Machine learning (ML) facilitates rapid channel modeling for 5G and beyond wireless communication systems. Many existing ML techniques utilize a city map to construct the radio map; however, an updated city map may not always be available. This paper proposes to employ the received signal strength (RSS) data to jointly construct the radio map and the virtual environment by exploiting the geometry structure of the environment. In contrast to many existing ML approaches that lack of an environment model, we develop a virtual obstacle model and characterize the geometry relation between the propagation paths and the virtual obstacles. A multiscreen knife-edge model is adopted to extract the key diffraction features, and these features are fed into a neural network (NN) for diffraction representation. To describe the scattering, as oppose to most existing methods that directly input an entire city map, our model focuses on the geometry structure from the local area surrounding the TX-RX pair and the spatial invariance of such local geometry structure is exploited. Numerical experiments demonstrate that, in addition to reconstructing a 3D virtual environment, the proposed model outperforms the state-of-theart methods in radio map construction with 10%−18% accuracy improvements. It can also reduce 20% data and 50% training epochs when transferred to a new environment.