A new method is presented for reasoning with constraints on the three orientation parameters of an object which arise from the identification of features discovered in a single image. The method uses a geometrical model of the object and a tetrahedral representation of view-direction. The final angle parameter, the roll angle, is computed for each view direction. This method is subject to errors from the data and the assumptions inherent in the use of view directions. These errors are taken into account by considering upper and lower bounds on the roll angle. A method is presented for using constraints on the orientation parameters to prune the search for a consistent set of labelled image lines and to guide an iterative inversion of the view perspective. One of the major problems with the recognition of a three dimensional object from a single view is that the geometry of the image of the object can change radically as the object rotates with respect to the camera. This