The manipulation system described herein provides a common platform and application-programming interface (API) for applications to communicate with various multi-touch hardware devices, and facilitates the interpretation of multi-touch input as one or more manipulations. Manipulations map more directly to user intentions than do individual touch inputs and add support for basic transformation of objects using multiple touch contacts. An application can use manipulations to support rotating, resizing, and translating multiple objects at the same time. The manipulation system outputs two-dimensional (2D) affine transforms that contain rotation, scale, and translation information. Thus, using the manipulation system the application author can focus more on building touch-capable applications and let the manipulation system handle the underlying transformations and communication with the multi-touch hardware.