We present a method for the automatic detection of vanishing points in urban scenes, based on finding point alignments in a dual space, where converging lines in the image are mapped to aligned points. To compute this mapping the recently introduced PClines transformation is used. A robust point alignment detector is run to detect clusters of aligned points in the dual space. Finally, a post-processing step discriminates relevant from spurious vanishing point detections with two options: using a simple hypothesis of three orthogonal vanishing points (Manhattan-world) or the hypothesis that one vertical and multiple horizontal vanishing points exist. Qualitative and quantitative experimental results are shown. On two public standard datasets, the method achieves state-of-the-art performances. Finally, an optional procedure for accelerating the method is presented.