On fair parametric rational cubic curves |
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Authors: | M Sakai R A Usmani |
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Institution: | (1) Department of Mathematics, Faculty of Science, University of Kagoshima, 890 Kagoshima, Japan;(2) Department of Applied Mathematics, University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada |
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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. |
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Keywords: | Parametric rational cubic curves inflection points singularities |
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