ISSN:
1572-9125
Keywords:
Parametric rational cubic curves
;
inflection points
;
singularities
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract First we derive conditions that a parametric rational cubic curve segment, with a parameter, interpolating to plane Hermite data {(x i (k) ,y i (k) ),i = 0, 1;k = 0, 1} contains neither inflection points nor singularities on its segment. Next we numerically determine the distribution of inflection points and singularities on a segment which gives conditions that aC 2 parametric rational cubic curve interpolating to dataS = {(x i (k) ,y i (k) ), 0 ≤i ≤n} is free of inflection points and singularities. When the parametric rational cubic curve reduces to the well-known parametric cubic one, we obtain a theorem on the distribution of the inflection points and singularities on the cubic curve segment which has been widely used for finding aC 1 fair parametric cubic curve interpolating toS.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01731988
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