A self-driving perception model aims to extract 3D semantic representations from multiple cameras collectively into the bird's-eye-view (BEV) coordinate frame of the ego car in order to ground downstream planner. Existing perception methods often rely on error-prone depth estimation of the whole scene or learning sparse virtual 3D representations without the target geometry structure, both of which remain limited in performance and/or capability. In this paper, we present a novel end-to-end architecture for ego 3D representation learning from an arbitrary number of unconstrained camera views. Inspired by the ray tracing principle, we design a polarized grid of ``imaginary eyes" as the learnable ego 3D representation and formulate the learning process with the adaptive attention mechanism in conjunction with the 3D-to-2D projection. Critically, this formulation allows extracting rich 3D representation from 2D images without any depth supervision, and with the built-in geometry structure consistent w.r.t. ~BEV. Despite its simplicity and versatility, extensive experiments on standard BEV visual tasks (e.g., camera-based 3D object detection and BEV segmentation) show that our model outperforms all state-of-the-art alternatives significantly, with an extra advantage in computational efficiency from multi-task learning.