Explicit Formulas for $\mu$-Bases of Planar Rational Quartic Curves

The $\mu$-basis is an algebraic tool originating from the theory of moving curves and moving surfaces, and it is widely used in the study of rational curves and surfaces.

In this paper, we give the explicit formulas for the $\mu$-basis of planar quartic rational parametric curves based on redefined vector polynomials, and several illustrative examples are provided.

Meanwhile, we also discuss the corresponding cases for quadratic and cubic curves.