Ivory: Secure, Contain, Project
Point of view is worth eighty IQ points — Alan Kay
TODO: - Basic intro to projective geometry and homogeneous
coordinates - Build up a library for PGA on top of raw GA units - Can we
remain agnostic about the number of dimensions? - Should work, since
it’s like “the” Clifford Algebra - If not, parameterise it. - Might be
relevant for taking duals. - Try to remain interoperable with conformal
geometric algebra: - If we can use the same underlying representation
then great - If not, can we parameterise the operations? - Is it worth
adding synonyms for the first few dimensions? - 2D is nice: -
→ and ↑ for the first two non-ideal GA units -
← and ↓ for the negative of each - Bivector
(pseudoscalar) is ↺, negative is ↻ - 3D is
harder to represent: - Arrow pointing into ⨂ (fletches) and
out-of ⨀ (tip) the screen - Make sure to pick the
positive/negative for whatever the customary orientation is!
We should probably have a projective “point at infinity” in our rational level, since