Edges are one of the most ubiquitous geometric features of physical objects. They provide accurate haptic feedback and easy-totrack features for camera systems, making them an ideal basis for Tangible User Interfaces (TUI) in Augmented Reality (AR). We introduce Ubi Edge, an AR authoring tool that allows end-users to customize edges on daily objects as TUI inputs to control varied digital functions. We develop an integrated AR-device and an integrated vision-based detection pipeline that can track 3D edges and detect the touch interaction between fingers and edges. Leveraging the spatial-awareness of AR, users can simply select an edge by sliding fingers along it and then make the edge interactive by connecting it to various digital functions. We demonstrate four use cases including multi-function controllers, smart homes, games, and TUI-based tutorials. We also evaluated and proved our system’s usability through a two-session user study, where qualitative and quantitative results are positive.