Earlier quoted context omitted.
I did Invisalign a few years ago. Manufacturing the retainers is surely only a small part of the puzzle. They used a specialized sort of 3D camera on a stick to get an incredibly accurate model of my mouth, any open source solution would need an equivalent. And you’d also need open source code from somewhere to work out which teeth need to move where and at what stage in the treatment.
They also use this camera system when creating implants. After the implant post was installed, they scan your mouth to determine the optimum shape for your crown (that goes on the post).
My doctor knows I'm into this so he always does it right next to me and turns the PC monitor so I can watch the entire process. The software is so simple almost anyone could use it. Generating a medically correct result is obviously where all the skill lies.