Sketcher BSplineDecreaseKnotMultiplicity/de: Difference between revisions

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<languages/>
<languages/>

{{Docnav
{{Docnav/de
|[[Sketcher_BSplineIncreaseKnotMultiplicity|Increase knot multiplicity]]
|[[Sketcher_BSplineIncreaseKnotMultiplicity/de|BSplineKnotenVielfachheitErhöhen]]
|[[Sketcher_SwitchVirtualSpace|Switch Virtual Space]]
|[[Sketcher_BSplineInsertKnot/de|BSplineKnotenEinfügen]]
|[[Sketcher_Workbench|Sketcher]]
|[[Sketcher_Workbench/de|Sketcher]]
|IconC=Workbench_Sketcher.svg
|IconL=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconL=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconR=Sketcher_SwitchVirtualSpace.svg‎
|IconR=Sketcher_BSplineInsertKnot.svg‎
|IconC=Workbench_Sketcher.svg
}}
}}


<div class="mw-translate-fuzzy">
{{GuiCommand
{{GuiCommand/de
|Name=Sketcher BSplineDecreaseKnotMultiplicity
|Name=Sketcher BSplineDecreaseKnotMultiplicity
|Name/de=Sketcher BSplineKnotenVielfachheitVerringern
|Workbenches=[[Sketcher Workbench|Sketcher]]
|MenuLocation=Sketch → Sketcher B-spline toolsDecrease knot multiplicity
|MenuLocation=Sketch → B-Spline-WerkzeugeVielfachheit eines Spline-Knotens verringern
|Workbenches=[[Sketcher_Workbench/de|Sketcher]]
|Version=0.17
|Version=0.17
|SeeAlso=[[Sketcher_BSplineKnotMultiplicity/de|BSplineKnotenVielfachheit]], [[Sketcher_BSplineIncreaseKnotMultiplicity/de|BSplineKnotenVielfachheitErhöhen]]
|SeeAlso=[[Sketcher CompCreateBSpline|Create B-spline]]
}}
}}
</div>


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


<div class="mw-translate-fuzzy">
Verringert die Knotenvielfalt eines B-Spline-Kurvenknotens (siehe [https://en.wikipedia.org/wiki/B-spline B-Spline]).
Verringert die Vielfachheit eines B-Spline-Knotens. (Siehe die Seite [[B-Splines|B-Splines]] für weitere Informationen über B-Splines).
</div>


<span id="Usage"></span>
[[File:sketcher_SampleBSplineDecreaseKnotMultiplicity.png]]
==Anwendung==
{{Caption|B-spline curve zeigt abnehmende Knoten Vielzahl.}}


<div class="mw-translate-fuzzy">
<div class="mw-translate-fuzzy">
# Einen B-Spline-Knoten auswählen.
==Anwendung==
# Es gibt mehrere Möglichkeiten den Befehl aufzurufen:
# Wähle einen B-Spline Knoten aus und wende sie an.
#* Die Schaltfläche {{Button|[[File:Sketcher_BSplineDecreaseKnotMultiplicity.svg|16px]] [[Sketcher_BSplineDecreaseKnotMultiplicity/de|Vielfachheit eines B-Spline-Knotens verringern]]}} drücken.
#* Den Menüeintrag {{MenuCommand|Sketch → B-Spline-Werkzeuge → [[File:Sketcher_BSplineDecreaseKnotMultiplicity.svg|16px]] Vielfachheit eines B-Spline-Knotens verringern}} auswählen.
</div>
</div>


==Example==
# Select a B-spline knot
# Invoke the tool using several methods:
#* Press the {{KEY|[[Image:Sketcher_BSplineDecreaseKnotMultiplicity.svg|24px]]}} button in the toolbar.
#* Use the {{MenuCommand|Sketch → Sketcher B-spline tools → Decrease knot multiplicity}} entry in the top menu.


See [[Sketcher_BSplineIncreaseKnotMultiplicity#Example|Sketcher_BSplineIncreaseKnotMultiplicity]]
{{Docnav

|[[Sketcher_BSplineIncreaseKnotMultiplicity|Increase knot multiplicity]]
==Notes==
|[[Sketcher_SwitchVirtualSpace|Switch Virtual Space]]

|[[Sketcher_Workbench|Sketcher]]
If you decrease the multiplicity of a knot to zero, the knot vanishes. Mathematically it then appears zero times in the knot vector, meaning there is no longer a basis function. Understanding this requires some math, but it will also be clear if you look at the multiplicity. For example a knot with multiplicity 0 on a B-spline with degree 3
means that at the position of the knot two Bézier pieces are connected with ''C<sup>3</sup>'' continuity. So the third derivative should be equal on both sides of the knot. However for a cubic Bézier curve this means that both sides must be part of the same curve. There is then effectively no longer a knot connecting two Bézier curves.


{{Docnav/de
|[[Sketcher_BSplineIncreaseKnotMultiplicity/de|BSplineKnotenVielfachheitErhöhen]]
|[[Sketcher_BSplineInsertKnot/de|BSplineKnotenEinfügen]]
|[[Sketcher_Workbench/de|Sketcher]]
|IconL=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconL=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconR=Sketcher_BSplineInsertKnot.svg‎
|IconC=Workbench_Sketcher.svg
|IconC=Workbench_Sketcher.svg
|IconR=Sketcher_SwitchVirtualSpace.svg‎
}}
}}


{{Sketcher_Tools_navi{{#translation:}}}}
{{Sketcher Tools navi/de}}
{{Userdocnavi{{#translation:}}}}

{{Userdocnavi/de}}

{{clear}}

Latest revision as of 07:36, 22 April 2024

Sketcher BSplineKnotenVielfachheitVerringern

Menüeintrag
Sketch → B-Spline-Werkzeuge → Vielfachheit eines Spline-Knotens verringern
Arbeitsbereich
Sketcher
Standardtastenkürzel
Keiner
Eingeführt in Version
0.17
Siehe auch
BSplineKnotenVielfachheit, BSplineKnotenVielfachheitErhöhen

Beschreibung

Verringert die Vielfachheit eines B-Spline-Knotens. (Siehe die Seite B-Splines für weitere Informationen über B-Splines).

Anwendung

  1. Einen B-Spline-Knoten auswählen.
  2. Es gibt mehrere Möglichkeiten den Befehl aufzurufen:

Example

See Sketcher_BSplineIncreaseKnotMultiplicity

Notes

If you decrease the multiplicity of a knot to zero, the knot vanishes. Mathematically it then appears zero times in the knot vector, meaning there is no longer a basis function. Understanding this requires some math, but it will also be clear if you look at the multiplicity. For example a knot with multiplicity 0 on a B-spline with degree 3 means that at the position of the knot two Bézier pieces are connected with C3 continuity. So the third derivative should be equal on both sides of the knot. However for a cubic Bézier curve this means that both sides must be part of the same curve. There is then effectively no longer a knot connecting two Bézier curves.