A) As shown in the Practical Perspective, the self...

a) As shown in the Practical Perspective, the self capacitance design does not permit a true multitouch 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 $(1.8,2.4)$ and (3.0., 4.6), what are the four touch locations that will be identified? (Assume the touch coordinates are measured in inches from the upper left conner 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 $t_1$ the two touch points are those identified in part (a), and at time $t_2$ four touch points associated with the $x, y$ coordinates $(2.2,2.8)$ and $(2.5,3.4)$ are identified. Comparing the four points at $t_1$ with the four points at $t_2$, software can recognize a pinch gesture-should the screen be zoomed in or zoomed out? c) Repeat part (b), assuming that at time $t_2$ four touch points associated with the $x, y$ coordinates $(1.2,1.8)$ and $(3.6,5.0)$ are identified.

a) As shown in the Practical Perspective, the self capacitance design does not permit a true multitouch 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 $(1.8,2.4)$ and (3.0., 4.6), what are the four touch locations that will be identified? (Assume the touch coordinates are measured in inches from the upper left conner 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 $t_1$ the two touch points are those identified in part (a), and at time $t_2$ four touch points associated with the $x, y$ coordinates $(2.2,2.8)$ and $(2.5,3.4)$ are identified. Comparing the four points at $t_1$ with the four points at $t_2$, software can recognize a pinch gesture-should the screen be zoomed in or zoomed out?
c) Repeat part (b), assuming that at time $t_2$ four touch points associated with the $x, y$ coordinates $(1.2,1.8)$ and $(3.6,5.0)$ are identified.

Key Concepts

Pinch Gesture Recognition and Zooming

Multi-touch software interprets the relative movements of multiple touch points as gestures. In pinch gestures, by comparing the positions of touches over time, the system can decide whether the user’s motion indicates zooming in (fingers moving apart) or zooming out (fingers moving together).

Self-Capacitance Touchscreen

This technology detects touch by measuring changes in capacitance at electrodes arranged on the screen. When touched, a human finger alters the local electric field, and the device uses these variations to determine where contact has occurred.

Ghost Points in Self-Capacitive Systems

In self-capacitance touchscreens, when more than one point is touched, the system can erroneously register extra touch locations at the intersections of the detected signals. These 'ghost points' are artifacts of the method by which the screen locally measures capacitance instead of true multi-contact detection.

Transcript

00:02 For part a, first we know that once the object is dropped, it is in free fall.

00:05 So we can take down as the negative y direction, and we can say the positive distance d from the lower dot to the mark corresponding to a certain reaction time t, this would be given by delta y, equalling negative d.

00:23 And this would be equalling negative 1 half gt squared, which in this case, d would then be equalling to gt squared over 2.

00:35 So we can say that for t sub 1, equaling 50 milliseconds.

00:42 So we have a 50 millisecond reaction time.

00:44 D sub 1, which should be equalling, 9 .8 meters per second squared, multiplied by 50 .0 times 10, to the negative third seconds quantity squared divided by 2 and this is giving us 0 .0123 meters or we can simply say 1 .23 centimeters.

01:12 For part b now we have d sub 2 equaling 100 milliseconds.

01:19 So for 100 milliseconds well we're simply doubling the time the reaction time and we know that this distance d is directly proportional to the time squared.

01:33 So we can simply say that this would be equaling d sub 2 would be equaling 4 times d sub 1 given that t sub 2 is equaling 2 times t sub 1.

01:48 This would equal approximately 4 .92 meters, or 4 .92 centimeters rather.

02:03 For part c then, we have t sub 3 equaling 150 milliseconds, which is three times the three times t sub 1.

02:20 And again, the distance is directly proportional to the time squared...

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