Prescribing the length of parametric curves

Theorems and corresponding algorithms are presented which produce a parametric curve of a specified arc length subject to certain constraints. Extraneous inflection points are avoided. The problem is reduced to expressing the arc length as a function of a single variable. A general theorem is presen...

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Bibliographic Details
Published inComputer aided geometric design Vol. 13; no. 1; pp. 3 - 22
Main Authors Roulier, John A., Piper, Bruce
Format Journal Article
LanguageEnglish
Published Elsevier B.V 1996
Subjects
Arc length
Bézier curve
Convex curve
Parametric curve
Bézier curve
Arc length
Parametric curve
Convex curve
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ISSN0167-8396
1879-2332
DOI10.1016/0167-8396(95)00004-6

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Summary:Theorems and corresponding algorithms are presented which produce a parametric curve of a specified arc length subject to certain constraints. Extraneous inflection points are avoided. The problem is reduced to expressing the arc length as a function of a single variable. A general theorem is presented which gives conditions under which the arc length function is convex or strictly convex. It is also shown that initial parameters may be automatically chosen so that the secant method will produce a solution to this problem with performance comparable to the Newton-Raphson method. Earlier results of one of the authors for Bézier polynomial curves are strengthened and extended using these results.
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ISSN:0167-8396
1879-2332
DOI:10.1016/0167-8396(95)00004-6