Partial fraction decomposition for rational Pythagorean hodograph curves

All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via directions norm, this includes the important case of Pythagorean hodograph curves. We study subspaces defined by fixing denominator and describe construction canonical bases for them. also show (as an analogy to fraction decomposition functions) that any element space can be obtained as finite sum single roots at denominator. Our results give insight into structure these spaces, clarify role their truly (non-polynomial) curves, suggest applications interpolation problems.