Difference between revisions of "Sketcher BSplineIncreaseKnotMultiplicity/de"

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<languages/>
 
<languages/>
{{Docnav|[[Sketcher_BSplineIncreaseDegree|Increase degree]]|[[Sketcher_BSplineDecreaseKnotMultiplicity|Decrease knot multiplicity]]|[[Sketcher_Workbench|Sketcher]]|IconL=Sketcher_BSplineIncreaseDegree.svg|IconC=Workbench_Sketcher.svg|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg}}
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<div class="mw-translate-fuzzy">
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{{Docnav/de
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|[[Sketcher_BSplineIncreaseDegree/de|Grad Erhöhen]]
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|[[Sketcher_BSplineDecreaseKnotMultiplicity/de|Knotenvielfalt Verringern]]
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|[[Sketcher_Workbench/de|Skizzierer]]
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|IconL=Sketcher_BSplineIncreaseDegree.svg
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|IconC=Workbench_Sketcher.svg
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|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg
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}}
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</div>
  
{{GuiCommand
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<div class="mw-translate-fuzzy">
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{{GuiCommand/de
 
|Name=Sketcher BSplineIncreaseKnotMultiplicity
 
|Name=Sketcher BSplineIncreaseKnotMultiplicity
|Workbenches=[[Sketcher Workbench|Sketcher]]
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|Name/de=Skizzierer BSplineErhöheKnotenVielfalt
|MenuLocation=Sketch Sketcher B-spline tools Increase knot multiplicity
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|MenuLocation=Skizze Skizzierer B-spline Werkzeuge Erhöhe Knoten Vielfalt
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|Workbenches=[[Sketcher Workbench/de|Skizzierer]]
 
|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 die Knotenvielfalt eines B-Spline Kurvenknotens (siehe [https://en.wikipedia.org/wiki/B-spline B-Spline]).
 
Erhöht die Knotenvielfalt eines B-Spline Kurvenknotens (siehe [https://en.wikipedia.org/wiki/B-spline B-Spline]).
  
[[File:sketcher_SampleBSplineIncreaseKnotMultiplicity.png]]
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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). The points where two Bézier curves are connected to form the spline are called knots. A knot on a degree ''d'' spline with the multiplicity ''m'' means that the curve left and right to the knot has at least an equal ''n'' order derivative (called ''C''<sup>''n''</sup> continuity) whereas n=d-m.<br/>
{{Caption|B-Spline Kurve mit zunehmender Knotenvielfalt.}}
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Here is a cubic (degree 3) spline whose knots have the multiplicity 1 (indicated by the number in parentheses, <br/>indication can be changed using the toolbar button {{Button|[[File:Sketcher_BSplineKnotMultiplicity.svg|24px]] [[Sketcher_BSplineKnotMultiplicity|Show/hide B-spline knot multiplicity]]}}):
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[[File:Sketcher_KnotMultiplicity_multiplicity1.png|386px]]
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{{Caption|B-spline where both knots have the multiplicity 1.}}
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A multiplicity of 3 will change this spline so that even the first order derivatives are not equal (''C''<sup>0</sup> continuity). Here is the same spline where the left's knot multiplicity was increased to 3:
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[[File:Sketcher_KnotMultiplicity_multiplicity3.png|386px]]
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{{Caption|B-spline from above with knot multiplicity 3. A control point was moved to show that the knot has ''C''<sup>0</sup> continuity.}}
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A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. This means the change of one control point only affects the spline locally to this changed point. This can be seen in this example, where the spline from the first image above was taken and its second control point from the right side was moved up:
  
==Anwendung==
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[[File:Sketcher_KnotMultiplicity_locality.png]]
# Wähle einen B-Spline Knoten aus und wende sie an.
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{{Caption|Effect of locality due to different multiplicity.}}
  
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One can see that the spline with knot multiplicity 1 is completely changed while the one with multiplicity 2 kept its form at its left side.
  
{{Docnav|[[Sketcher_BSplineIncreaseDegree|Increase degree]]|[[Sketcher_BSplineDecreaseKnotMultiplicity|Decrease knot multiplicity]]|[[Sketcher_Workbench|Sketcher]]|IconL=Sketcher_BSplineIncreaseDegree.svg|IconC=Workbench_Sketcher.svg|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg}}
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==Anwendung==
  
{{Sketcher Tools navi/de}}
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<div class="mw-translate-fuzzy">
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# Wähle einen B-Spline Knoten aus.
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# Rufe das Werkzeug mit mehreren Methoden auf:
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#* Drücke die {{KEY|[[Image:Sketcher_BSplineIncreaseKnotMultiplicity.svg|24px]]}}  Schaltfläche in der Werkzeugleiste.
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#* Verwende den {{MenuCommand|Skizze → Skizzierer B-Spline Werkzeuge → Knotenvervielfalt erhöhen}} Eintrag im oberen Menü.
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</div>
  
{{Userdocnavi}}
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<div class="mw-translate-fuzzy">
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{{Docnav/de
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|[[Sketcher_BSplineIncreaseDegree/de|Grad Erhöhen]]
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|[[Sketcher_BSplineDecreaseKnotMultiplicity/de|Knotenvielfalt Verringern]]
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|[[Sketcher_Workbench/de|Skizzierer]]
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|IconL=Sketcher_BSplineIncreaseDegree.svg
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|IconC=Workbench_Sketcher.svg
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|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg
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}}
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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 13:52, 2 December 2020

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

Sketcher BSplineIncreaseKnotMultiplicity.svg Skizzierer BSplineErhöheKnotenVielfalt

Menüeintrag
Skizze → Skizzierer B-spline Werkzeuge → Erhöhe Knoten Vielfalt
Arbeitsbereich
Skizzierer
Standardtastenkürzel
None
In der Version eingeführt
0.17
Siehe auch
Erstelle B-spline


Beschreibung

Erhöht die Knotenvielfalt eines B-Spline Kurvenknotens (siehe B-Spline).

B-splines are basically a combination of Bézier curves (nicely explained in this and this video). The points where two Bézier curves are connected to form the spline are called knots. A knot on a degree d spline with the multiplicity m means that the curve left and right to the knot has at least an equal n order derivative (called Cn continuity) whereas n=d-m.
Here is a cubic (degree 3) spline whose knots have the multiplicity 1 (indicated by the number in parentheses,
indication can be changed using the toolbar button Sketcher BSplineKnotMultiplicity.svg Show/hide B-spline knot multiplicity):

Sketcher KnotMultiplicity multiplicity1.png

B-spline where both knots have the multiplicity 1.


A multiplicity of 3 will change this spline so that even the first order derivatives are not equal (C0 continuity). Here is the same spline where the left's knot multiplicity was increased to 3:

Sketcher KnotMultiplicity multiplicity3.png

B-spline from above with knot multiplicity 3. A control point was moved to show that the knot has C0 continuity.


A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. This means the change of one control point only affects the spline locally to this changed point. This can be seen in this example, where the spline from the first image above was taken and its second control point from the right side was moved up:

Sketcher KnotMultiplicity locality.png

Effect of locality due to different multiplicity.


One can see that the spline with knot multiplicity 1 is completely changed while the one with multiplicity 2 kept its form at its left side.

Anwendung

  1. Wähle einen B-Spline Knoten aus.
  2. Rufe das Werkzeug mit mehreren Methoden auf:
    • Drücke die Sketcher BSplineIncreaseKnotMultiplicity.svg Schaltfläche in der Werkzeugleiste.
    • Verwende den Skizze → Skizzierer B-Spline Werkzeuge → Knotenvervielfalt erhöhen Eintrag im oberen Menü.