According to the formula I provided, to slerp for example, rotors require lambda and theta. Whereas quaternions only require the lambda. Is there an alternative I'm missing?
“Slerp” just means follow a path on a circle at uniform speed (i.e. “use trigonometry”). In this case, we are talking about a circle on the conceptual unit 4-sphere. It doesn’t really matter what names we call the basis elements.