a) As shown in the Practical Perspective, the self capacitance design does not permit a true multi touch screen – if the screen is touched at two difference points, a total of four touch points are identified, the two actual touch points and two ghost points. If a self-capacitance touch screen is touched at the x, y coordinates (2.1, 4.3) and (3.2, 2.5), what are the four touch locations that will be identified? (Assume the touch coordinates are measured in inches from the upper left corner of the screen.)

b) A self-capacitance touch screen can still function as a multi-touch screen for several common gestures. For example, suppose at time t₁ the two touch points are those identified in part (a), and at time t₂ four touch points associated with the x, y coordinates (1.8, 4.9) and (3.9, 1.8) are identified. Comparing the four points at t₁ with the four points at t₂ software can recognize a pinch gesture – should the screen be zoomed in or zoomed out?

c) Repeat part (b),assuming that at time t₂ four touch points associated with the x, y coordinates (2.8, 3.9) and (3.0, 2.8) are identified.