Machine learning (ML) emerges and facilitates rapid channel modeling for 5G and beyond wireless communication systems. Many existing techniques require 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, without any knowledge of the city map, to jointly construct the 3D geometry of the propagation environment and the radio map. While many existing ML approaches use convolution neural network (CNN) to construct radio map by treating it as an image, this paper adopts the diffraction mechanism from radio propagation to construct a 3D virtual environment, which in turn, helps reconstruct the radio map. In addition, instead of mapping the global environment to the radio map, this paper learns the common obstruction features of local environment, and use these features to reconstruct the shadowing. Numerical experiments demonstrate that, in addition to reconstructing the 3D geometry of the environment, the proposed method also constructs a more accurate radio map with 10%-15% accuracy improvement. In the application of UAV relay placement, the proposed method can reduce 99% search distance compared with the other radio-map-based methods.