If we could design the perfect texture pattern to apply to any smooth surface in order to enable observers to more accurately perceive the surface's shape in a static monocular image taken from an arbitrary generic viewpoint under standard lightingconditions, what would the characteristics of that texture pattern be? In order to gain insight into this question, our group has developed an efficient algorithm for synthesizing a high resolution texture pattern (derived from a provided 2D image, e.g. from the Brodatz album) over an arbitrary doubly curved surface in such a way that both seams and projective distortion are practically eliminated, and, most importantly, the orientation of the texture pattern is constrained to follow an underlying vector field over the surface at a perpixel level. We are using this algorithm to generate stimuli for a series of experiments investigating the effects of various texture characteristics, including orientation, on surface shape judgments. The results of earlier studies that we conducted using a more restricted class of uni-directional texture patterns seemed to support the hypothesis that shape perception is most severely impeded when the texture pattern consists of lines that turn in the surface, and that shape perception is not significantly different in the case of a texture pattern consisting of lines that are locally aligned with the first principal direction than in the case of an isotropic texture pattern of similar spatial frequency. Our new texture synthesis method enables us to extend these studies to a much broader class of textures, including patterns that contain 90-degree rotational symmetry, which is useful in enabling us to maintain continuity in a principal-direction oriented pattern as it passes through umbilic points where the first and second principal directions switch places. Images are available at www.cs.umn.edu/~interran/texture. Upon publication, our software will be made available via the web.