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developer:onperiodiccurvesurface [2015/09/14] 127.0.0.1 external edit |
developer:onperiodiccurvesurface [2015/10/28] (current) sandy |
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A periodic knot vector can be either uniform or non-uniform. | A periodic knot vector can be either uniform or non-uniform. | ||

- | A periodic degree d [[rhino:nurbs|NURBs]] curve has (d-1) continuous derivatives at the start/end point. | + | A periodic degree d NURBs curve has (d-1) continuous derivatives at the start/end point. |

- | The differences between successive knot values are equal near the start and end of the spline; that is, the differences repeat themselves and hence the term "periodic". | + | The differences between successive knot values are equal near the start and end of the spline; that is, the differences repeat themselves and hence the term //periodic//. |

Specifically, when -degree < i < degree, a periodic knot vector satisfies | Specifically, when -degree < i < degree, a periodic knot vector satisfies | ||

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with a < b < c < d < e and e < p+a. | with a < b < c < d < e and e < p+a. | ||

- | Chapter 12 of The [[rhino:nurbs|NURBs]] Book has a few pages discusssing periodic [[rhino:nurbs|NURBs]] (look in the index), but the discussion is limited. Chapter 14 of DeBoor's Practical Guide to Splines provides a few more details. | + | Chapter 12 of The [[rhino:nurbs|NURBs]] Book has a few pages discussing periodic NURBs (look in the index), but the discussion is limited. Chapter 14 of [[http://www.amazon.com/Practical-Splines-Applied-Mathematical-Sciences/dp/0387953663|Carl de Boor's Practical Guide to Splines]] provides a few more details. |

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{{tag>Developer openNURBS}} | {{tag>Developer openNURBS}} | ||

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developer/onperiodiccurvesurface.txt ยท Last modified: 2015/10/28 by sandy