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Raph Levien (talk | contribs) →Algorithms: Add a few references to papers and blog post |
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{{expand section|date=August 2014}}
In general, the parallel curve of a [[Bézier curve]] is not another Bézier curve, a result proved by Tiller and Hanson in 1984<ref>{{cite journal |last1=Tiller |first1=Wayne |last2=Hanson |first2=Eric |title=Offsets of Two-Dimensional Profiles |journal=IEEE Computer Graphics and Applications |year=1984 |volume=4 |issue=9 |pages=36-46 |doi=10.1109/mcg.1984.275995}}</ref>. Thus, in practice, approximation techniques are used. Any desired level of accuracy is possible by repeatedly subdividing the curve, though better techniques require fewer subdivisions to attain the same level of accuracy. A 1997 survey by Elber, Lee and Kim<ref>{{cite journal |last1=Elber |first1=Gershon |last2=Lee |first2=In-Kwon |last3=Kim |first3=Myung-Soo
|url=https://ieeexplore.ieee.org/document/586019/ |doi=10.1109/38.586019 |title=Comparing offset curve approximation methods |journal=IEEE Computer Graphics and Applications |volume=17 |issue=3 |pages=62-71 |date=May–Jun 1997}}</ref> is widely cited, though better techniques have been proposed more recently. A modern technique based on [[curve fitting]], with references and comparisons to other algorithms, as well as open source JavaScript source code, was published in a blog post<ref>{{cite web |url=https://raphlinus.github.io/curves/2022/09/09/parallel-beziers.html |title=Parallel curves of cubic Béziers |last=Levien |first=Raph |date=September 9, 2022 |access-date=September 9, 2022}}</ref> in September 2022.
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