Given a decomposition into a linear equation of the form a * x + b, where a is a scalar multipying a rotation maxtrix, one should be able to create a linear rel

Given a decomposition into a linear equation of the form a * x + b, where a is a scalar multipying a rotation maxtrix, one should be able to create a linear relation between two equations of this form with the variable being time. The time factor should still follow the same rules as specified by the transition, so one shouldn't have much issue piecing these together, if it is so desired to have this behavior. Edit: Sorry, linear relation is not what I meant - one should be able to construct a parametric equation in terms of t where t = 0 is the initial transform and t = 1 is the final transform.