Abstract: We present and comparatively evaluate two new object transformation techniques for multi-touch surfaces. Specifying complete two-dimensional similarity transformations requires a minimum of four degrees of freedom: two for position, one for rotation, and another for scaling. Many existing techniques for object transformation are designed to function with traditional input devices such as mice, single-touch surfaces, or stylus pens. The challenge is to map controls appropriately for each of these devices. A few multi-touch techniques have been proposed in the past, but no comprehensive evaluation has been presented. par XNT is a new three-finger object transformation technique, designed for multi-touch surfaces. It provides a natural interface for two-dimensional manipulation. XNT and several existing techniques were evaluated in a user study. The results show that XNT is superior for all tasks that involve scaling and competitive for tasks that involve only rotation and positioning.