Automatic robotic inspection of arbitrary free-form shapes is relevant for many quality control applications in different industries. We propose a method for planning the motion of an industrial robot to perform ultrasonic inspection of varying 3D shapes. Our method starts with the calculation of a set of sub-paths. These sub-paths are derived from streamlines. The underlying vector field is deduced from local curvature of the inspected geometry. Intermediate robot motions are planned to connect individual sub-paths to obtain a single complete inspection path. Coverage is calculated via ray tracing to simulate the propagation of ultrasound signals. This simulation enables the algorithm to proceed adaptively and to find a good trade-off between path length and coverage. We report experiments for four different geometries. The results indicate that shorter paths are achieved by using ray tracing for adaptive adjustment of streamline density. Our algorithm is tailored to ultrasonic inspection. However, the main concept of exploiting local surface curvature and streamlines for coverage path planning generalizes to other robotic inspection problems.