Dear @UwePongs, there are quite a few ways:
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Using reflector will generate a copy of your iphone or ipad in a live frame on your laptop. Syphon won’t detect this by default, but you can use ScreenCaptureSyphon (fwe bucks) or Syphoner (free) to capture this frame into your syphon. I prefer the first one.
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Use VDMX or Millumin. Both have built in screen capture options. Besides, with them you can create any layout for projection you can imagine. They are great vj tools. VDMX is actually free, except if you want to save projects or presets. For a tagtool session, you may not need too much of saving.
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VDMX, on the other hand, has a nice feature. If you connect your ipad or iphone via lighting cable, it will take it as a source camera, meaning that everything you see (and hear) on your device will be regarded as a video/audio source straight into your computer. It’s much more stable, though not mobile, as it is cable attached. Awesome.
http://vdmx.vidvox.net/tutorials/ios-device-as-live-input-for-vdmx -
Besides Reflector, you also have AirServer, also quite good.
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Finally, you can use a Mini Recorder from Blackmagic (150 dollars aprox) to input your HDMI signal from your device -with the right adaptor- into your laptop via Thunderbolt.
Quite a few options, uh?