When it comes to computing motions, and interpolating between motions, this might be a nice way of doing it: https://www.youtube.com/watch?v=pq9YfdPHhIo https:/

When it comes to computing motions, and interpolating between motions, this might be a nice way of doing it: https://www.youtube.com/watch?v=pq9YfdPHhIo https://www.youtube.com/watch?v=pq9YfdPHhIo I think that some computational geometry problems admit nice solutions using Projective Geometric Algebra. Using it is fairly intuitive: You have some elements of the algebra that represent Euclidean motions, and some other elements that represent flat objects like points, lines and planes; you can then intersect these objects, "join" them into larger objects, and apply transformations to them. If it looks to you like it could make some things you're doing easier, then you might try using it. I think there are already some Common Lisp implementations out there -- but if there aren't, then it shouldn't be difficult to make one from scratch. There's also Conformal Geometric Algebra, which is notable for allowing you to represent circles and spheres as elements of the algebra. But efficiently implementing it appears to be harder than PGA.