Inflection points of certain planar quartics

Inflection points and singularities on planar rational cubic curve segments

We obtain the distribution of inflection points and singularities on a parametric rational cubic curve segment with aid of Mathematica (A System of for Doing Mathematics by Computer). The reciprocal numbers of the magnitudes of the end slopes determine the occurrence of inflection points and singularities on the segment. Its use enables us to check whether the segment has inflection points or a...

Rational Points on Quartics

Inflection Points, Extatic Points and Curve Shortening

As the name suggests, Curve Shortening is a gradientflow for the length functional on the space of immersed curves in the surfaceM. One can therefore try to use Curve Shortening to prove existence of geodesics by variational methods. In my talk at S’Agarro I observed that geodesics always are curves without self-tangencies, and recalled that the space of such curves has many different connected...

Inflection points of coherent reliability polynomials

Examples of coherent reliability polynomials with more than one inflection point are given. They are created by examining the structure of a reliability polynomial using a convex basis.

Inflection points and singularities on C-curves

We show that all so-called C-curves are affine images of trochoids or sine curves and use this relation to investigate the occurrence of inflection points, cusps, and loops. The results are summarized in a shape diagram of C-Bézier curves, which is useful when using C-Bézier curves for curve and surface modeling.  2003 Elsevier B.V. All rights reserved.