I've got a propositon for a pinch-gesture for single-touch screen.

We can call it "tap and swipe"

You tap once on the screen (fixing the center of the movement).

Then (within half a second) you make a swiping movement from a starting point to an end point.


The transformation is defined by two vectors:
- the vector of the center and the beginning point
- the vector of the center and the end point

This is a combination of a rotational matrix and a stretching matrix that is so easy to calculate that you can write it down immediately.



Even better:
Matrices about the same fixed point are easily added linearily.

Therefore: If the swiping movement is not only a straight line but a curve also the components of the matrices describe the same curve. You can extrapolate the mouvement. The impetus of the mouvement can be continued a little bit during the time.


Even better:
Even a 3D mouvement is possible with a pressure sensitive touch-screen: bringing elements more in front or back.


The "Tap and Swipe" gesture can be continued by a "Swipe and swipe" gesture taking the end point of the first swiping gesture as center of mouvement for the second swiping gesture.