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Arbitrary-shaped text detection is a challenging task due to the complex geometric layouts of texts such as large aspect ratios, various scales, random rotations and curve shapes. Most state-of-the-art methods solve this problem from bottom-up perspectives, seeking to model a text instance of complex geometric layouts with simple local units (e.g., local boxes or pixels) and generate detections with heuristic post-processings. In this work, we propose an arbitrary-shaped text detection method, namely TextRay, which conducts top-down contour-based geometric modeling and geometric parameter learning within a single-shot anchor-free framework. The geometric modeling is carried out under polar system with a bidirectional mapping scheme between shape space and parameter space, encoding complex geometric layouts into unified representations. For effective learning of the representations, we design a central-weighted training strategy and a content loss which builds propagation paths between geometric encodings and visual content. TextRay outputs simple polygon detections at one pass with only one NMS post-processing. Experiments on several benchmark datasets demonstrate the effectiveness of the proposed approach. The code is available at https://github.com/LianaWang/TextRay.