Perception of the 3D shape of a smoothly curving surface can be facilitated or impeded by the use of different surface texture patterns. In this paper we report the results of a series of experiments intended to provide insight into how to select or design an appropriate texture for shape representation in compute graphics. In these experiments, we examine the effect of the presence and direction of luminance texture pattern anisotropy on the accuracy of observers' judgements of 3D surface shape. Our stimuli consists of complicated, smoothly curving level surfaces from a typical volumetric dataset, across which we have generated four different texture patterns via 3D line integral convolution: one isotropic and three anisotropic, with the anisotropic patterns oriented across the surface either in a single uniform direction, in a coherently varying direction, or in the first principal direction at every surface point. Observers indicated shape judgements via manipulating an array of local probes so that their circular bases appeared to lie in the tangent plane to the surface at the probe's's center, and the perpendicular extensions appeared to point in the direction of the local surface normal. Stimuli were displayed as binocularly viewed flat images in the first trials, and in stereo during the second trials. Under flat viewing, performance was found to be better in the cases of the isotropic pattern and the anisotropic pattern that followed the first principal direction than in the cases of the other two anisotropic and principal direction patterns than for the other two. Our results are consistent with a hypothesis that texture pattern anisotropy impedes surface shape perception in the case that the direction of the anisotropy does not locally follow the direction of greatest normal curvature.