Multiple vanishing point detection provides the key to recovering the perspective pose of textured planes. If vanishing points are to be detected from spectral information then two computational problems need to be solved. Firstly, the search of the extended image plane is unbounded, and hence the location of vanishing points at or near infinity is difficult. Secondly, correspondences between local spectra need to be established so that vanishing points can be triangulated. In this paper, we offer a way of overcoming these two difficulties. We overcome the problem of unbounded search by mapping the information provided by local spectral moments onto a unit-sphere. According to our representation, the position and direction of each local spectrum maps onto a great circle on the unit-sphere. The need for correspondences is overcome by accumulating the great circle intercepts. Vanishing points occur at local accumulator maxima on the unit-sphere. We experiment with the new shape-from-texture technique on planar textures in buildings.