The theory of multivectors and the geometric product.
Curated by: All Angles (17 videos)
#geometricalgebra #projections #reflections #rotations In this video, we discover a simple formula for projections, and we figure out its geometric interpretation. We will need projections in the next video, because they will provide the building blocks for reflections and rotations. You can support us on Patreon, where you can already watch all the Geometric Algebra videos and get access to exclusive content. Unfortunately, we won't be publishing any new videos after Geometric Algebra, at least not in the near future. Your support is still more than welcome of course: https://www.patreon.com/user?u=86649007 [DORST 1] The paper by Leo Dorst I mentioned in the video, is called "An Algebraic Approach to Programming Geometry". I can't seem to find it back online at the moment. If you know a link, share it in the comments below! On page 15, he gives a derivation of the projection & rejection formulas, starting from their geometric requirements. 0:00 Constructing all transformations from reflections 3:09 The formula for the projection 6:00 The formula for the rejection 6:12 The formulas look almost like sandwich products 7:25 The formula does not depend on the length of v 9:40 What the formula means geometrically 11:30 Extensions to other kinds of shapes This video is published under a CC Attribution license ( https://creativecommons.org/licenses/by/4.0/ )