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The authors give an algorithm for recovering the centre and view direction of a one-dimensional camera with known principal point but unknown focal distance, by means of one view with four recognised landmarks. The involved algebra is reduced to solving a quadratic equation. This 4-point-method appears to be more robust than the existing 5-point-algorithm for locating a totally uncalibrated camera by means of chasles conics. On the other hand, the authors' method can offer an alternative for the triangulation method if the value of the focal length is unknown or unreliable (e.g. because of autozoom).