Sketcher BSplineIncreaseDegree/de: Difference between revisions

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<languages/>
<languages/>

<div class="mw-translate-fuzzy">
{{Docnav/de
{{Docnav/de
|[[Sketcher_BSplineConvertToNURBS/de|BSplineUmwandelnInNURBS]]
|[[Sketcher_ConvertToNURB/de|Umwandeln Geometrie zu B-spline]]
|[[Sketcher_BSplineDecreaseDegree/de|BSplineGradVerringern]]
|[[Sketcher_BSplineIncreaseKnotMultiplicity/de|Knotenvielfalt erhöhen]]
|[[Sketcher_Workbench/de|Skizzierer]]
|[[Sketcher_Workbench/de|Sketcher]]
|IconL=Sketcher_BSplineApproximate.svg
|IconL=Sketcher_BSplineConvertToNURBS.svg
|IconR=Sketcher_BSplineDecreaseDegree.svg
|IconC=Workbench_Sketcher.svg
|IconC=Workbench_Sketcher.svg
}}
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg}}
</div>


<div class="mw-translate-fuzzy">
{{GuiCommand/de
{{GuiCommand/de
|Name=Sketcher BSplineIncreaseDegree
|Name=Sketcher BSplineIncreaseDegree
|Name/de=Skizzierer BSplineErhöhungsgrad
|Name/de=Sketcher BSplineGradErhöhen
|MenuLocation=Sketch → B-Spline-Werkzeuge → Grad des B-Splines erhöhen
|Icon=Sketcher BSplineIncreaseDegree.svg
|Workbenches=[[Sketcher Workbench/de|Skizzierer]]
|Workbenches=[[Sketcher_Workbench/de|Sketcher]]
|MenuLocation=Skizze Skizzierer B-spline Werkzeuge → Grad der B-spline erhöhen
|Version=0.17
|Version=0.17
|SeeAlso=[[Sketcher CompCreateBSpline/de|Erstelle B-spline]]
|SeeAlso=[[Sketcher_BSplineDecreaseDegree/de|Sketcher BSplineGradVerringern]]
}}
}}
</div>


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


Das Werkzeug [[Image:Sketcher_BSplineIncreaseDegree.svg|24px]] [[Sketcher_BSplineIncreaseDegree/de|Sketcher BSplineGradErhöhen]] Erhöht den Grad (Ordnung) der [[B-Splines|B-Splines]].
Erhöht den Grad des B-Splines (siehe [https://en.wikipedia.org/wiki/B-spline B-Spline]).


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


# Einen oder mehrere B-Splines auswählen.
{{Caption|Gleicher B-Spline mit steigendem Grad.}}
# Es gibt mehrere Möglichkeiten, das Werkzeug aufzurufen:
#* Die Schaltfläche {{Button|[[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree/de|Grad des B-Splines erhöhen]]}} drücken.
#* Den Menüeintrag {{MenuCommand|Skizze → B-Spline-Werkzeuge → [[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] Grad des B-Splines erhöhen}} auswählen.
#* {{Version/de|1.0}}: Ein Rechtsklick in die [[3D_view/de|3D-Ansicht]] und die Menüoption {{MenuCommand|[[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] Grad des B-Splines erhöhen}} im Kontextmenü auswählen.


<span id="Example"></span>
==Anwendung==
==Beispiel==


B-Splines sind im Grunde eine Kombination aus [[B-Splines/de#B.C3.A9zierkurven|Bézierkurven]] (sehr schön erklärt in [https://www.youtube.com/watch?v=bE1MrrqBAl8 diesem] und [https://www.youtube.com/watch?v=xXJylM2S72s diesem] Video).
<div class="mw-translate-fuzzy">

# Wähle einen B-Spline aus und wende sie an.
In diesem kubischen B-Spline (Grad 3) gibt es 3 Abschnitte, d.h. 3 Kurven, die an 2 Knoten verbunden sind.
</div>

Der Grad wird durch die Zahl in der Mitte repräsentiert. Siehe [[File:Sketcher_BSplineDegree.svg|16px]] [[Sketcher_BSplineDegree/de|B-Spline-Grad ein- / ausblenden]].

[[File:Sketcher_BSplineDegree3.png|400px]]
{{Caption|B-Spline mit Grad 3 und 2 Knoten, die jeweils die Vielfachheit 1 besitzen.}}

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.


{{Emphasis|Note:}} at the moment there is no {{Button|[[File:Sketcher_BSplineDecreaseDegree.svg|16px]] B-spline decrease degree}} command.


<div class="mw-translate-fuzzy">
{{Docnav/de
{{Docnav/de
|[[Sketcher_BSplineConvertToNURBS/de|BSplineUmwandelnInNURBS]]
|[[Sketcher_ConvertToNURB/de|Umwandeln Geometrie zu B-spline]]
|[[Sketcher_BSplineDecreaseDegree/de|BSplineGradVerringern]]
|[[Sketcher_BSplineIncreaseKnotMultiplicity/de|Knotenvielfalt erhöhen]]
|[[Sketcher_Workbench/de|Skizzierer]]
|[[Sketcher_Workbench/de|Sketcher]]
|IconL=Sketcher_BSplineApproximate.svg
|IconL=Sketcher_BSplineConvertToNURBS.svg
|IconR=Sketcher_BSplineDecreaseDegree.svg
|IconC=Workbench_Sketcher.svg
|IconC=Workbench_Sketcher.svg
}}
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg}}
</div>


{{Sketcher Tools navi{{#translation:}}}}
{{Sketcher_Tools_navi{{#translation:}}}}
{{Userdocnavi{{#translation:}}}}
{{Userdocnavi{{#translation:}}}}
{{clear}}

Latest revision as of 19:42, 14 May 2024

Sketcher BSplineGradErhöhen

Menüeintrag
Sketch → B-Spline-Werkzeuge → Grad des B-Splines erhöhen
Arbeitsbereich
Sketcher
Standardtastenkürzel
Keiner
Eingeführt in Version
0.17
Siehe auch
Sketcher BSplineGradVerringern

Beschreibung

Das Werkzeug Sketcher BSplineGradErhöhen Erhöht den Grad (Ordnung) der B-Splines.

Anwendung

  1. Einen oder mehrere B-Splines auswählen.
  2. Es gibt mehrere Möglichkeiten, das Werkzeug aufzurufen:

Beispiel

B-Splines sind im Grunde eine Kombination aus Bézierkurven (sehr schön erklärt in diesem und diesem Video).

In diesem kubischen B-Spline (Grad 3) gibt es 3 Abschnitte, d.h. 3 Kurven, die an 2 Knoten verbunden sind.

Der Grad wird durch die Zahl in der Mitte repräsentiert. Siehe B-Spline-Grad ein- / ausblenden.

B-Spline mit Grad 3 und 2 Knoten, die jeweils die Vielfachheit 1 besitzen.

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.