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<languages/>
<languages/>
{{Docnav|[[Sketcher_ConvertToNURB|Convert Geometry to B-spline]]|[[Sketcher_BSplineIncreaseKnotMultiplicity|Increase knot multiplicity]]|[[Sketcher_Workbench|Sketcher]]|IconL=Sketcher_BSplineApproximate.svg|IconC=Workbench_Sketcher.svg|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg}}


<div class="mw-translate-fuzzy">
{{GuiCommand
{{Docnav/ru
|Name=Sketcher BSplineIncreaseDegree
|[[Sketcher_BSplineApproximate/ru|Преобразовать геометрию в B-Сплайн]]
|Icon=Sketcher BSplineIncreaseDegree.svg
|[[Sketcher_BSplineDecreaseDegree/ru|Уменьшить степень B-сплайна]]
|Workbenches=[[Sketcher Workbench|Sketcher]]
|[[Sketcher_Workbench/ru|Верстак "Sketcher"]]
|MenuLocation=Sketch → Sketcher B-spline tools → Increase Degree of B-spline
|IconL=Sketcher_BSplineApproximate.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconC=Workbench_Sketcher.svg
}}
</div>

<div class="mw-translate-fuzzy">
{{GuiCommand/ru
|Name/ru=Увеличить степень B-сплайна
|Name=Sketcher_BSplineIncreaseDegree
|MenuLocation=Sketch → B-сплйан инструменты эскиза → Увеличить степень B-сплайна
|Workbenches=[[Sketcher_Workbench/ru|Sketcher]]
|Version=0.17
|Version=0.17
|SeeAlso=[[Sketcher_BSplineDegree/ru|Показать/скрыть степень B-сплайна]], [[Sketcher_BSplineDecreaseDegree/ru|Уменьшить степень B-сплайна]]
|SeeAlso=[[Sketcher CompCreateBSpline|Create B-spline]]
}}
}}
</div>


==Description==
<span id="Description"></span>
==Описание==


The [[Image:Sketcher_BSplineIncreaseDegree.svg|24px]] [[Sketcher_BSplineIncreaseDegree|Sketcher BSplineIncreaseDegree]] tool increases the degree (order) of [[B-Splines|B-splines]].
Increases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]).


<span id="Usage"></span>
[[File:Sketcher_SampleBSplineIncreaseDegree.png|350px]]
==Применение==


# Select one or more B-splines.
{{Caption|Same B-spline with increasing Degree.}}
# There are several ways to invoke the tool:
#* Press the {{Button|[[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree|Increase B-spline degree]]}} button.
#* Select the {{MenuCommand|Sketch → Sketcher B-spline tools → [[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] Increase B-spline degree}} option from the menu.
#* {{Version|1.0}}: Right-click in the [[3D_view|3D view]] and select the {{MenuCommand|[[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] Increase B-spline degree}} option from the context menu.


==How to use==
==Example==
# Select a B-spline and apply .


B-splines are basically a combination of [[B-Splines#B.C3.A9zier_curves|Bézier curves]] (nicely explained in [https://www.youtube.com/watch?v=bE1MrrqBAl8 this] and [https://www.youtube.com/watch?v=xXJylM2S72s this] video).
{{Docnav|[[Sketcher_ConvertToNURB|Convert Geometry to B-spline]]|[[Sketcher_BSplineIncreaseKnotMultiplicity|Increase knot multiplicity]]|[[Sketcher_Workbench|Sketcher]]|IconL=Sketcher_BSplineApproximate.svg|IconC=Workbench_Sketcher.svg|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg}}


In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots.
{{Sketcher Tools navi}}


The degree is indicated by the number in the center. See [[File:Sketcher_BSplineDegree.svg|16px]] [[Sketcher_BSplineDegree|Show/hide B-spline degree]].
{{Userdocnavi}}

[[File:Sketcher_BSplineDegree3.png|400px]]
{{Caption|B-spline with degree 3 and 2 knots that each have multiplicity 1.}}

The outer segments each have 2 control points, the inner segment has none to ensure the knots have multiplicity 1. See [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation about multiplicity.

Increasing the degree to 4 will add control points without changing the shape of the B-spline:

[[File:Sketcher_BSplineDegree4.png|400px]]
{{Caption|Same B-spline where the degree was changed from 3 to 4. Note that the knot multiplicity has also increased.}}

From this result you cannot get back to the initial state of the B-spline by decreasing the degree. Some information is lost when the degree of a B-spline is changed. Decreasing the degree back to 3 leads to this:

[[File:Sketcher_BSplineDegree3from4.png|400px]]
{{Caption|Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity has increased again. Depending on the B-spline, the algorithm to decrease the degree may add a lot of knots to preserve the shape as has happened here.}}

Each segment now has 2 control points and each knot is coincident with an additional control point. The knots have ''C<sup>0</sup>'' continuity so that the B-spline will get "corners" if you move a control point. The information of a higher continuity is therefore lost. See [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation about continuity.


<div class="mw-translate-fuzzy">
{{Docnav/ru
|[[Sketcher_BSplineApproximate/ru|Преобразовать геометрию в B-Сплайн]]
|[[Sketcher_BSplineDecreaseDegree/ru|Уменьшить степень B-сплайна]]
|[[Sketcher_Workbench/ru|Верстак "Sketcher"]]
|IconL=Sketcher_BSplineApproximate.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconC=Workbench_Sketcher.svg
}}
</div>


{{Sketcher_Tools_navi{{#translation:}}}}
{{clear}}
{{Userdocnavi{{#translation:}}}}

Latest revision as of 07:28, 22 April 2024

Увеличить степень B-сплайна

Системное название
Sketcher_BSplineIncreaseDegree
Расположение в меню
Sketch → B-сплйан инструменты эскиза → Увеличить степень B-сплайна
Верстаки
Sketcher
Быстрые клавиши
Нет
Представлено в версии
0.17
См. также
Показать/скрыть степень B-сплайна, Уменьшить степень B-сплайна

Описание

The Sketcher BSplineIncreaseDegree tool increases the degree (order) of B-splines.

Применение

  1. Select one or more B-splines.
  2. There are several ways to invoke the tool:

Example

B-splines are basically a combination of Bézier curves (nicely explained in this and this video).

In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots.

The degree is indicated by the number in the center. See Show/hide B-spline degree.

B-spline with degree 3 and 2 knots that each have multiplicity 1.

The outer segments each have 2 control points, the inner segment has none to ensure the knots have multiplicity 1. See this page for an explanation about multiplicity.

Increasing the degree to 4 will add control points without changing the shape of the B-spline:

Same B-spline where the degree was changed from 3 to 4. Note that the knot multiplicity has also increased.

From this result you cannot get back to the initial state of the B-spline by decreasing the degree. Some information is lost when the degree of a B-spline is changed. Decreasing the degree back to 3 leads to this:

Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity has increased again. Depending on the B-spline, the algorithm to decrease the degree may add a lot of knots to preserve the shape as has happened here.

Each segment now has 2 control points and each knot is coincident with an additional control point. The knots have C0 continuity so that the B-spline will get "corners" if you move a control point. The information of a higher continuity is therefore lost. See this page for an explanation about continuity.