Difference between revisions of "Sketcher BSplineIncreaseDegree/de"

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(Created page with "==Anwendung== # Wähle einen B-Spline aus und wende sie an.")
(Updating to match new version of source page)
 
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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}}
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<div class="mw-translate-fuzzy">
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{{Docnav/de
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|[[Sketcher_BSplineConvertToNURB/de|Umwandeln Geometrie zu B-spline]]
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|[[Sketcher_BSplineIncreaseKnotMultiplicity/de|Knotenvielfalt erhöhen]]
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|[[Sketcher_Workbench/de|Skizzierer]]
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|IconL=Sketcher_BSplineConvertToNURB.svg
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|IconC=Workbench_Sketcher.svg
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|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg}}
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</div>
  
{{GuiCommand
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<div class="mw-translate-fuzzy">
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{{GuiCommand/de
 
|Name=Sketcher BSplineIncreaseDegree
 
|Name=Sketcher BSplineIncreaseDegree
|Icon=Sketcher BSplineIncreaseDegree.svg
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|Name/de=Skizzierer BSplineErhöhungsgrad
|Workbenches=[[Sketcher Workbench|Sketcher]]
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|Workbenches=[[Sketcher Workbench/de|Skizzierer]]
|MenuLocation=Sketch Sketcher B-spline tools Increase Degree of B-spline
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|MenuLocation=Skizze Skizzierer B-spline Werkzeuge Grad der B-spline erhöhen
 
|Version=0.17
 
|Version=0.17
|SeeAlso=[[Sketcher CompCreateBSpline|Create B-spline]]
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|SeeAlso=[[Sketcher CompCreateBSpline/de|Erstelle  B-spline]]
 
}}
 
}}
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</div>
  
 
==Beschreibung==
 
==Beschreibung==
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Erhöht den Grad des B-Splines (siehe [https://en.wikipedia.org/wiki/B-spline B-Spline]).
 
Erhöht den Grad des B-Splines (siehe [https://en.wikipedia.org/wiki/B-spline B-Spline]).
  
[[File:Sketcher_SampleBSplineIncreaseDegree.png|350px]]
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B-splines are basically a combination of [https://en.wikipedia.org/wiki/Bezier_curve#Constructing_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).
  
{{Caption|Gleicher B-Spline mit steigendem Grad.}}
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In this cubic spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots<br>(degree is indicated by the number, indication can be changed using the toolbar button {{Button|[[File:Sketcher_BSplineDegree.svg|24px]] [[Sketcher_BSplineDegree|Show/hide B-spline degree]]}}):
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[[File:Sketcher_BSplineDegree3.png|400px]]
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{{Caption|B-spline with degree 3 and 2 knots that each have the multiplicity 1.}}
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The outer segments have each 2 control points, the inner one none to fulfill the constraint that the knots have multiplicity 1. (see [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation of the multiplicity)
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Increasing the degree will add control points and the shape of the spline is not changed:
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[[File:Sketcher_BSplineDegree4.png|400px]]
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{{Caption|Same B-spline where the degree was changed from 3 to 4. Note that also the knot multiplicity was increased.}}
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If you take this result and decrease the degree, you cannot get the initial state of the spline information will be lost by this operation. For our example decreasing the degree again leads to this:
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[[File:Sketcher_BSplineDegree3from4.png|400px]]
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{{Caption|Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity was increased.}}
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You can see that now each segment has 2 control points and the knots are coincident with each a further control point. The knots have now ''C''<sup>0</sup> continuity so that the spline will get "edges" when you move a control point. So the information of a higher continuity is lost. (see [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] to for an explanation of the continuity)
  
 
==Anwendung==
 
==Anwendung==
# Wähle einen B-Spline aus und wende sie an.
 
  
{{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}}
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<div class="mw-translate-fuzzy">
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# Wähle eine Kante eines existierenden B-Spline und drücke {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree/de|B-spline Grad erhöhen]]}}.
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</div>
  
{{Sketcher Tools navi}}
 
  
{{Userdocnavi}}
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<div class="mw-translate-fuzzy">
 +
{{Docnav/de
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|[[Sketcher_BSplineConvertToNURB/de|Umwandeln Geometrie zu B-spline]]
 +
|[[Sketcher_BSplineIncreaseKnotMultiplicity/de|Knotenvielfalt erhöhen]]
 +
|[[Sketcher_Workbench/de|Skizzierer]]
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|IconL=Sketcher_BSplineConvertToNURB.svg
 +
|IconC=Workbench_Sketcher.svg
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|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg}}
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</div>
  
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{{Sketcher Tools navi{{#translation:}}}}
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{{Userdocnavi{{#translation:}}}}
 
{{clear}}
 
{{clear}}

Latest revision as of 13:53, 2 December 2020

Other languages:
Deutsch • ‎English • ‎français • ‎italiano • ‎русский

Sketcher BSplineIncreaseDegree.svg Skizzierer BSplineErhöhungsgrad

Menüeintrag
Skizze → Skizzierer B-spline Werkzeuge → Grad der B-spline erhöhen
Arbeitsbereich
Skizzierer
Standardtastenkürzel
None
In der Version eingeführt
0.17
Siehe auch
Erstelle B-spline


Beschreibung

Erhöht den Grad des B-Splines (siehe B-Spline).

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

In this cubic spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots
(degree is indicated by the number, indication can be changed using the toolbar button Sketcher BSplineDegree.svg Show/hide B-spline degree):

Sketcher BSplineDegree3.png

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


The outer segments have each 2 control points, the inner one none to fulfill the constraint that the knots have multiplicity 1. (see this page for an explanation of the multiplicity)

Increasing the degree will add control points and the shape of the spline is not changed:

Sketcher BSplineDegree4.png

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


If you take this result and decrease the degree, you cannot get the initial state of the spline information will be lost by this operation. For our example decreasing the degree again leads to this:

Sketcher BSplineDegree3from4.png

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


You can see that now each segment has 2 control points and the knots are coincident with each a further control point. The knots have now C0 continuity so that the spline will get "edges" when you move a control point. So the information of a higher continuity is lost. (see this page to for an explanation of the continuity)

Anwendung

  1. Wähle eine Kante eines existierenden B-Spline und drücke Sketcher BSplineIncreaseDegree.svg B-spline Grad erhöhen.