Here is a link to a site with a picture of how threads were interwoven between the old material and new patch.
http://www.factsplusfacts.com/
The invisible weave is a technique done on expensive/precious clothe that has been around quite a while. It is not technologically advnaced it just takes a lot of patience, time and technique born of experience. A weaver/tailor takes the threads in the individual fibres, unravels them and then splices them back together, one thread at a time.
If you have an expensive jacket that gets a clean cut, one could have this done to repair it even today. And it wont even be noticable in strong bright daylight.