More and more tasks related to 3D geometry such as measuring, analyzing or (re-)assembling are more comfortable and precise to do on acquired 3D objects than on the real objects themselves, and with the advances in computer graphics acquisition techniques, 3D objects become commonly available. Whereas simple manipulation of these objects is accessible for a wider public, dealing with the precise geometry of acquired 3D surfaces and volumes still remains rather reserved for 3D experts. In this talk, I will show how tangible user interfaces may help untrained users to reason about 3D geometry by means of an interactive experience. For this, I propose to seamlessly integrate feedback about the 3D geometry into the interaction loop via a geometry-driven transfer function. I will provide two examples of concrete tangible interaction metaphors for specific tasks. A first one is targeted for the virtual and semi-automatic reassembly of broken objects, and a second one highlights features on 3D objects and real objects simultaneously by spatial augmented reality. We showcased a variant of the latter example at various museum exhibitions, so I will discuss feedback, opportunities, and further possibilities to make a greater public understand other complex phenomena with tangible interfaces.