This paper presents a method for recognition of 3D objects with curved surfaces from linear tactile data. For every surface model in a given database, a lookup table is constructed to store principal curvatures precomputed at points of discretization on the surface. To recognize an object, a robot hand with touch sensing capability obtains data points on its surface along three concurrent curves. The two principal curvatures estimated at the curve intersection point are used to look up the table associated with each model to locate surface discretization points that have similar local geometries. Local searches are then performed starting at these points to register the tactile data onto the model. The model with the best registration result is recognized. The presented method can recognize closed-form surfaces as well as triangular meshes, as demonstrated through simulation and robot experiments. Potential applications include recognition of (manufactured) home items that are grasped daily, and dexterous manipulation during which recognition is simultaneously performed.