Explicit Formulas for $μ$-Bases of Planar Rational Quartic Curves

Weizhen Han; Weikun Sun

Explicit Formulas for $μ$-Bases of Planar Rational Quartic Curves

Algebraic Geometry 2026-07-17 v1 Symbolic Computation

Authors: Weizhen Han , Weikun Sun

Abstract

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.

Keywords

mu-basis rational quartic curve moving curve parametric curve explicit formula

Cite

@article{arxiv.2607.15571,
  title  = {Explicit Formulas for $μ$-Bases of Planar Rational Quartic Curves},
  author = {Weizhen Han and Weikun Sun},
  journal= {arXiv preprint arXiv:2607.15571},
  year   = {2026}
}

Comments

10 pages