Manipulating a three-dimensional object displayed in a multi-touch display device includes displaying a three-dimensional object in two dimensions on the multi-touch display device. Placement of one or more touch points on the multi-touch display device is detected. For each detected touch point, a location of the touch point on the multi-touch display device is determined and a matching contact point on a surface of the three-dimensional object that is displayed by the multi-touch display device at the location of the touch point is also determined. Movement of at least one of the touch points is detected. Subsequent to the detected movement of the one or more touch points, a three-dimensional transformation of the three-dimensional object is determined that results in a display in which the contact points on the surface of the three-dimensional object remain displayed substantially at the locations of their matching touch points.