Thanks for the questions. > re: introductory materials The 3 links I compiled here (https://www.jeremyong.com/klein/references/ https://www.jeremyong.com/klei

Thanks for the questions. > re: introductory materials The 3 links I compiled here (https://www.jeremyong.com/klein/references/ https://www.jeremyong.com/klein/references/) I consider an absolute must for starting to consume GA. The book (ref #3) has one chapter undergoing revision regarding the usefulness of the degenerate metric for modeling projective geometry. My understanding is the chapter will be released for free once finished. From this alone, I was able to piece together enough to write one working implementation of GA that I was able to use to verify the computations and my understanding. Klein is my third GA library which I wrote once I was pretty sure I was comfortable with the formalism. Another great set of resources is anything posted on bivector.net. > re: question 2 The elegance of the math does help me identify better optimizations in a number of cases, but in other cases, it makes a whole series of operations well-defined (for which there was no good analog before). I posted some examples in another comment, but essentially, quats and dual-quats generally only work on points, and in a somewhat awkward manner. I can't easily compose 2 rotations, a translation, a dual quat, and a quat, and then expect it to work on a line for example. In GA, this is ... completely trivial. And because it all fits nicely in the framework, all the above benefits from the same SIMD optimizations. I believe the reason GA was not considered well-suited for production/perf reasons is twofold. First, prior art focused on GA with arbitrary dimensionality/metric (results in either increased compilation time, or reduced performance). Second, there wasn't much overlap between practicitioners of GA, and graphics/animation engineers on the other side. I view Klein as "low-hanging fruit" in that sense, and consider myself fortunate to have come across the theory in the manner I did. I had written it off as just "an easier to understand Quaternion," but once I realized how much I (and perhaps some of my colleagues) were missing, I opted to actually try and productionize GA to "fill the gap" so to speak. (FYI tried to send this over an hour ago but HN keeps rate limiting me :( )