This paper presents a new approach to the recovery of dense orientation estimates for curved textured surfaces. We show how the affine distance between pairs of power spectra can be used to estimate the slant and tilt angles of local tangent planes to the textured surface. The main practical benefit furnished by our analysis is that it allows us to estimate the orientation angles in closed form without recourse to numerical optimization. Based on these theoretical properties we present an algorithm for the analysis of regularly textured curved surfaces. We apply the method to a variety of real-world and synthetic imagery. We show that the new shape-from-texture method can reliably estimate surface topography.