Increasing haptic feedback has been shown to improve the accuracy of task performance in virtual and telemanipulated environments. This work seeks to determine how virtual object stiffness and geometry, as well as human exploration technique, affect shape understanding. During exploration of arcs with a two-degree-of-freedom haptic interface, understanding of shape geometry improved with higher radii of curvature, and identification of object stiffness was found to plateau above 450 N/m. User bias in understanding of geometry was found to be influenced by the "horizontal-vertical illusion", where users underestimated lateral distances while overestimating vertical ones. It was found that users misperceived some differences in stiffness as differences in shape. The experience level of the user affected exploration time and the accuracy of shape understanding. The stiffness threshold found in this study indicates that limited stiffness can be used to render objects without significant loss of information, and the biases found for understanding of shape geometry can also be used to improve shape rendering.