Decomposing a 3D PGA Rotor

Transcript

a couple weeks ago I showed how to decompose a 3D PGA B Vector into simple commuting bi vectors but what about the inverse problem decomposing a 3D PGA rotor into simple commuting rotors each 3D PGA rotor can be written as the product of two simple commuting factors R1 and R2 where R1 is a rotation and R2 is a translation to find R1 and R2 we can use the idea from last week's short writing R1 and R2 in terms of generalized cosiness and SS notice that if we take the bi Vector part of R and divide by the scalar part of R the result is the sum of the generalized tangents of B1 and B2 let's call this B Vector T because T is a bi Vector we can use the decomposition formula from a couple weeks ago to find the generalized tangent of B2 this expression actually simplifies a bit as well because T of B2 squares to zero adding one to it already makes it normalized so this is R2 and then R1 is just R / R2