In the common approach to the generic camera calibration (GCC), one uses dense ray coding (with e.g. active grids displayed on an LCD screen) in order to find the ray origin and direction for each camera pixel independently. While applicable to many types of imaging sensors, the GCC fails to describe the local differential properties of ray bundles that are important in e.g. studying the geometry of infinitesimal scene changes via optical flow. In this report, we investigate the alternative approach to the GCC where the camera ray origins and directions are assumed to be differentiable functions of the sensor position. In particular, we present a novel calibration technique based on finite element method that unites the ray update and bundle adjustment stages of the common GCC and accommodates arbitrary anisotropic coding uncertainties and non-planar coding surfaces. The accuracy and the stability of the resulting smooth generic camera calibration (sGCC) algorithm are verified based on some non-trivial synthetic examples.