An indirect interaction input device, such as but not limited to a touch sensor, can provide multiple points of input, such as two or more positions in a coordinate space where a user is touching the sensor. These multiple points are in turn mapped to multiple positions on an output device such as a display. The mapping can be relative or absolute. With a relative mapping, boundary conditions for single and multiple displays are applied and, if appropriate, remedial offsets are added to the input points to maintain a desired user interaction model.