Previously discussed here:
https://news.ycombinator.com/item?id=30597061
My thinking is to approach the problem from a fundamentally different angle. There's already constructive solid geometry (CSG) kernels, triangle mesh kernels, and NURBS-based kernels. Their mathematical foundations are very different, which results in wildly different behaviour and capabilities.
I came across PGA while studying physics, saw some vaguely CAD-like CSG demos and I realised that it could be yet another mathematical foundation on top of which CAD applications could be built.
Notably, variants of GA and PGA are already used in robotics, inverse kinematics, etc... including 5-axis milling, so it's not unheard of in industry. However, it's always used as a "spot" solution to work around a problem such as gimbal lock, or interpolating transformations. Typically by converting back-and-forth between linear algebra representations and some variant of GA temporarily. I'm thinking of using PGA throughout as the foundational geometric elements.
In general, GA and its variants like PGA are good at calculating tangents and offsets for points, lines, planes, spheres, and other parametric surfaces. The key benefit is that the exact same algorithm will work in 2D, 3D, 4D, or any higher number of dimensions. This could in principle allow very elegant formulas for tasks such as "find the biggest thing that won't hit this other thing at any point in time" or the same thing but with a 0.1 mm gap. Similarly, it's possible to reuse the same code and "human intuition" in very high dimensional spaces, such phase space used in more complex motion planning or engineering simulation scenarios.
Even just the pictures on the cover might give you an idea: https://www.amazon.com.au/Projective-Geometric-Algebra-Illum...
