For small stimuli, it has been shown that subjects are very accurate in distinguishing a cylinder with an elliptical cross-section from one with a circular cross-section. In such a task, both curvature and length are integrated effectively. Large cylinders are explored differently: either by one hand or by two hands sliding over the surface. However, the same cues are available. We investigated the integration of position and curvature in unimanual and bimanual exploration. In Experiment 1, curved surfaces were presented as part of a horizontal cylinder with a cross-section that was either a horizontally or a vertically elongated ellipse. We found that discrimination thresholds for unimanual exploration were significantly larger than for bimanual exploration. In Experiment 2, we found that position discrimination thresholds were independent of type of exploration (unimanual or bimanual) and surprisingly also independent of reference length. In Experiment 3, we found that discrimination thresholds for the position of the midsagittal plane were on average lower than the position discrimination thresholds found in Experiment 2. From these findings, we conclude that the lower thresholds in Experiment 1 for bimanual exploration compared to unimanual exploration are due to integration of curvature, not position or uncertainty of the midsagittal plane in unimanual exploration.