Improving the haptic exploration and identification of virtual shapes and objects provides great potential for numerous applications. However, many challenges exist because subjects experience various difficulties during the exploration and recognition process of virtual models when using a standard force-feedback device. One of those difficulties refers to the unreliable haptic discrimination of virtual curved surfaces. Curvature plays an especially important role because it is a frequently occurring geometric characteristic. However, Stamm et al. found in a previous study that the haptic discrimination of similarly curved surfaces requires a high level of concentration and takes a long time to perform well. The subjects also felt quite uncertain relying only on haptic cues. Furthermore, problems arise if identically curved surfaces are differently oriented in the virtual space because curvature perception seems to differ if the orientation of the curves is varied. In particular, this would be quite problematic and critical for various applications. Thus, the purpose of this work is to experimentally investigate if curvature perception depends on the orientation of virtual, three-dimensional haptic curves. Participants' task was to match the curvature of a specifically oriented cylindrical segment (test curve) to the curvature of another cylindrical segment (reference curve) until both are perceived to be just identically curved. It is shown that results vary in dependence of the orientation of the test curve. Finally, a promising approach to enhance haptic feedback utilizing multimodal cues is suggested. This approach can contribute to eliminate the influence of stimulus orientation on haptic curvature perception.