next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

POLYNOMIAL CURVE

Cartesian parametrization:
where P and Q are two polynomials with real coefficients,
coprime, and such that the polynomials
and are
coprime (proper representation). |

A *polynomial* curve is a curve that can be parametrized
by polynomial functions of R[*x*],
so it is a special case of rational
curve.

Therefore, any polynomial curve is an algebraic
curve of degree equal to the higher degree of the above polynomials *P*
and *Q* of a proper representation.

A polynomial curve cannot be bounded, nor have asymptotes, except if it is a line.

Examples:

- the lines are polynomial

- the only polynomial conic is the
parabola

- the rational divergent
parabolas (polynomial cubics with a symmetry axis)

- the cubical
parabolas (polynomial cubics with a symmetry centre).

- a Lissajous
polynomial quartic.

- the L'Hospital
quintic is polynomial.

next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

© Robert FERRÉOL 2017