> To be honest I've never really liked how GA results in all kinds of mixed elements if you're not careful what you multiply with what. Requiring up to 2^n terms for what was an n-dimensional space seems a bit hard to deal with.
Agreed, but the confusion is already there, and the traditional approach deals with it by just sweeping it under the rug. If you're dealing with normals, for example, you have at least 2 different n-dimensional spaces to keep track of that transform quite differently.
Having points, planes, lines, normals, translations, and rotations all represented as a single multivector type with consistent rules seems quite liberating once you grasp it. (I'm admittedly still working on it.)
Agreed, but the confusion is already there, and the traditional approach deals with it by just sweeping it under the rug. If you're dealing with normals, for example, you have at least 2 different n-dimensional spaces to keep track of that transform quite differently.
Having points, planes, lines, normals, translations, and rotations all represented as a single multivector type with consistent rules seems quite liberating once you grasp it. (I'm admittedly still working on it.)