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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}}


{{Docnav/de
{{GuiCommand
|[[Sketcher_BSplineConvertToNURBS/de|BSplineUmwandelnInNURBS]]
|[[Sketcher_BSplineDecreaseDegree/de|BSplineGradVerringern]]
|[[Sketcher_Workbench/de|Sketcher]]
|IconL=Sketcher_BSplineConvertToNURBS.svg
|IconR=Sketcher_BSplineDecreaseDegree.svg
|IconC=Workbench_Sketcher.svg
}}

{{GuiCommand/de
|Name=Sketcher BSplineIncreaseDegree
|Name=Sketcher BSplineIncreaseDegree
|Icon=Sketcher BSplineIncreaseDegree.svg
|Name/de=Sketcher BSplineGradErhöhen
|MenuLocation=Sketch → B-Spline-Werkzeuge → Grad des B-Splines erhöhen
|Workbenches=[[Sketcher Workbench|Sketcher]]
|Workbenches=[[Sketcher_Workbench/de|Sketcher]]
|MenuLocation=Sketch → Sketcher B-spline tools → Increase Degree of B-spline
|Version=0.17
|Version=0.17
|SeeAlso=[[Sketcher CompCreateBSpline|Create B-spline]]
|SeeAlso=[[Sketcher_BSplineDecreaseDegree/de|Sketcher BSplineGradVerringern]]
}}
}}


<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==


<div class="mw-translate-fuzzy">
{{Caption|Gleicher B-Spline mit steigendem Grad.}}
# Eine Kante eines existierenden B-Splines auswählen.
# Die Schaltfläche {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|24px]] '''Grad des B-Splines erhöhen''' drücken}}.
</div>


==Anwendung==
==Example==
# Wähle einen B-Spline aus und wende sie an.


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.


{{Docnav/de
|[[Sketcher_BSplineConvertToNURBS/de|BSplineUmwandelnInNURBS]]
|[[Sketcher_BSplineDecreaseDegree/de|BSplineGradVerringern]]
|[[Sketcher_Workbench/de|Sketcher]]
|IconL=Sketcher_BSplineConvertToNURBS.svg
|IconR=Sketcher_BSplineDecreaseDegree.svg
|IconC=Workbench_Sketcher.svg
}}


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

Latest revision as of 06:19, 13 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. Eine Kante eines existierenden B-Splines auswählen.
  2. Die Schaltfläche Grad des B-Splines erhöhen drücken.

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.