I would love to see a functional open source CAM software that would compete with basic tiers of Mastercam/Fusion360/etc. I think it would be of huge benefit to the manufacturing industry, education and hobbyists. There are a lot of machinists/CNC programmers very worried about Autodesk's dominance over the field and the consequences of further consolidation and crapification. Many machinists are currently learning hard lessons about SaaS.
Unfortunately in my observations (as a user and CAM software purchaser, not a CAM dev) writing toolpathing engines seems to be a Hard Problem with most of the expertise concentrated within entrenched companies. There are a few smaller companies developing CAM software but most seem to build either on one of a couple licensed CAM engines or very old legacy software from back before the big players dominated the field. Lots of the functional requirements for a CAM system have been stable for years (decades even), so a casual observer would think it is ripe for an open source alternative. However I haven't yet seen an open source alternative that could plausibly compete or even achieve feature parity with any of the commercial CAM software I use.
Best of luck to the PolarCam dev. I don't have high expectations given the magnitude of the task and the hobbyist nature of the associated hardware, but I'd love to be proven wrong.
About recommendation; Toolpath generation is based on 2d and 3d geometry math. Simply dive into 2D and 3D geometry and try to understand some libraries. This is a very good one: http://www.angusj.com/delphi/clipper.php
Most 2d and 3d calculations are based on triangle calculations. There are also solved algorithms like finding the closest point on a curve. Once you start playing with triangles, I'm sure with some software development and machining background you can easily begin to understand how toolpath generation works. It's easier to create toolpaths from stl files. Because stl models only consist of triangles. Thanks to the gaming industry, triangle-based math isn't a cutting-edge science these days, and there are many open source libraries.
You also need tons of coffee and tons of dedicated time.
> It's kind of necessary. Because there is no powerful and complete open source CAM software that is useful and easy for everyone.
That helps me understand where this falls on the plausibility scale