Explicit Formulas for $μ$-Bases of Planar Rational Quartic Curves
Symbolic Computation
Summary
The authors focus on a mathematical tool called the μ-basis, which helps describe complicated shapes like curves and surfaces in algebra. They specifically provide clear formulas for the μ-basis related to four-degree (quartic) rational curves drawn on a plane. They also include examples to show how their method works and briefly talk about simpler cases involving second- and third-degree curves. Their work aims to make these algebraic descriptions more accessible and practical.
Authors
Weizhen Han, Weikun Sun
Abstract
The $μ$-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 $μ$-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.