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