Using Head-up-Displays (HUD) for Augmented Reality requires to have an accurate internal model of the image generation process, so that 3D content can be visualized perspectively correct from the viewpoint of the user. We present a generic and cost-effective camera-based calibration for an automotive HUD which uses the windshield as a combiner. Our proposed calibration model encompasses the view-independent spatial geometry, i.e. the exact location, orientation and scaling of the virtual plane, and a view-dependent image warping transformation for correcting the distortions caused by the optics and the irregularly curved windshield. View-dependency is achieved by extending the classical polynomial distortion model for cameras and projectors to a generic five-variate mapping with the head position of the viewer as additional input. The calibration involves the capturing of an image sequence from varying viewpoints, while displaying a known target pattern on the HUD. The accurate registration of the camera path is retrieved with state-of-the-art vision-based tracking. As all necessary data is acquired directly from the images, no external tracking equipment needs to be installed. After calibration, the HUD can be used together with a head-tracker to form a head-coupled display which ensures a perspectively correct rendering of any 3D object in vehicle coordinates from a large range of possible viewpoints. We evaluate the accuracy of our model quantitatively and qualitatively.