  Calibration of fixtures in robotic work cells is essential but also time
consuming and error-prone, and poor calibration can easily lead to wasted
debugging time in downstream tasks. Contact-based calibration methods let the
user measure points on the fixture's surface with a tool tip attached to the
robot's end effector. Most such methods require the user to manually annotate
correspondences on the CAD model, however, this is error-prone and a cumbersome
user experience. We propose a correspondence-free alternative: The user simply
measures a few points from the fixture's surface, and our method provides a
tight superset of the poses which could explain the measured points. This
naturally detects ambiguities related to symmetry and uninformative points and
conveys this uncertainty to the user. Perhaps more importantly, it provides
guaranteed bounds on the pose. The computation of such bounds is made tractable
by the use of a hierarchical grid on SE(3). Our method is evaluated both in
simulation and on a real collaborative robot, showing great potential for
easier and less error-prone fixture calibration. Project page at
https://sites.google.com/view/ttpose
