record video of the process
unfortunately, the answer to that question is "maybe". It will depend on the camera you select - some can focus under script control in video mode and others might not. And unfortunately, I don't have a list of which ones work and which ones don't.
Also, be aware that the little lenses on Canon Point&Shoot Powershot camera have huge
depth of field. Once you focus out to about 3 meters then everything tends to be in focus. So seeing the effect of moving the focus point around randomly will only be visible with objects near to the camera.
