Tactile sensing enables robots to perceive rich contact information at the grasp, supporting tasks such as object recognition, in-hand pose estimation, and slip detection. However, in many tool-mediated manipulation tasks, the interaction that determines task success occurs at the tool tip, away from the tactile sensor, making direct sensing of tool-environment contact difficult, particularly when the contact moves during interaction. In this work, we reconstruct the trajectory of extrinsic tool-tip contact using tactile sensing and robot proprioception. We formulate tool-tip trajectory reconstruction as a geometric inference problem under a single-point contact assumption. Our method first estimates the global tool-tip contact location from a calibration segment designed to approximate fixed-point behavior, and then reconstructs the full trajectory by composing relative tool motion estimated from tactile marker observations under continuous contact. Across n=51 trials with multiple trajectories, tools, wrist poses, and grasp configurations, the proposed pipeline achieves a trajectory RMSE of 8.59 +/- 2.41 mm in the world frame and a shape RMSE of 5.96 +/- 1.16 mm, while operating online at 14.00 +/- 4.11 Hz. Overall, the results show that extrinsic tool-tip trajectory geometry can be recovered consistently from grasp-level tactile sensing, with trajectory shape remaining stable across variations in tools, wrist poses, and grasp configurations.

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