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We describe the results of two comprehensive controlled observer experiments intended to yield insight into the following question: If we could design the ideal texture pattern to apply to an arbitrary smoothly curving surface in order to enable its 3D shape to be most accurately and effectively perceived, what would the characteristics of that texture pattern be? We begin by reviewing the results of our initial study in this series, which were presented at the 2003 IEEE Symposium on Information Visualization, and offer an expanded analysis of those findings. We continue by presenting the results of a follow-on study in which we sought to more specifically investigate the separate and combined influences on shape perception of particular texture components, with the goal of obtaining a clearer view of their potential information carrying capacities. In each study, we investigated the observers' ability to identify the intrinsic shape category of a surface patch (elliptical, hyperbolic, cylindrical, or flat) and its extrinsic surface orientation (convex, concave, both, or neither). In our first study, we compared performance under eight different texture type conditions, plus two projection conditions (perspective or orthographic) and two viewing conditions (head-on or oblique). We found that: 1) shape perception was better facilitated, in general, by the bidirectional "principal direction grid" pattern than by any of the seven other patterns tested; 2) shape type classification accuracy remained high under the orthographic projection condition for some texture types when the viewpoint was oblique; 3) perspective projection was required for accurate surface orientation classification; and 4) shape classification accuracy was higher when the surface patches were oriented at a (generic) oblique angle to the line of sight than when they were oriented (in a nongeneric pose) to face the viewpoint straight on. In our second study, we compared performance under eight new t- - exture type conditions, redesigned to facilitate gathering insight into the cumulative effects of specific individual directional components in a wider variety of multidirectional texture patterns. We found that shape classification accuracy was equivalently good under a variety of test patterns that included components following either the first or first and second principal directions, in addition to other directions, suggesting that a principal direction grid texture is not the only possible "best option" for enhancing shape representation.