An electronic device, with a touch-sensitive surface and display, displays a user interface at a first display rate. While displaying the user interface, the device detects, at a first detection rate that is greater than the first display rate, movement of a touch input at a sequence of locations on the touch-sensitive surface; and, at each of a sequence of update times, updates the user interface from a respective current state to a respective next state in accordance with a selected subset of the sequence of locations of the touch input. Each selected subset of the sequence of locations includes a plurality of locations of the touch input.