Sketcher BSplineIncreaseDegree/de: Difference between revisions

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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_BSplineApproximate/de|BSplineApproximieren]]
|[[Sketcher_BSplineDecreaseDegree/de|BSplineGradVerringern]]
|[[Sketcher_Workbench/de|Sketcher]]
|IconL=Sketcher_BSplineApproximate.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.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_BSplineDegree/de|BSplineGrad]], [[Sketcher_BSplineDecreaseDegree/de|BSplineGradVerringern]]
|SeeAlso=[[Sketcher CompCreateBSpline|Create B-spline]]
}}
}}


==Beschreibung==
==Beschreibung==


Erhöht den Grad (Ordnung) der B-Spline-Kurve (Siehe die Seite [[B-Splines|B-Splines]] für weitere Informationen über B-splines).
Increases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]).


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).
[[File:Sketcher_SampleBSplineIncreaseDegree.png|350px]]


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]]}}):
{{Caption|Same B-spline with increasing Degree.}}


[[File:Sketcher_BSplineDegree3.png|400px]]
==How to use==
{{Caption|B-spline with degree 3 and 2 knots that each have the multiplicity 1.}}
# Select a B-spline and apply .


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)
{{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}}


Increasing the degree will add control points and the shape of the spline is not changed:
{{Sketcher Tools navi}}


[[File:Sketcher_BSplineDegree4.png|400px]]
{{Userdocnavi}}
{{Caption|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:

[[File:Sketcher_BSplineDegree3from4.png|400px]]
{{Caption|Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity was increased. Depending on the spline, the algorithm to decrease the degree may add a lot of knots to preserve the spline shape as happened in this example.}}

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==

# Eine Kante eines existierenden B-Splines auswählen.
# Die Schaltfläche {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|24px]] '''Grad des B-Splines erhöhen''' drücken}}.


{{Docnav/de
|[[Sketcher_BSplineApproximate/de|BSplineApproximieren]]
|[[Sketcher_BSplineDecreaseDegree/de|BSplineGradVerringern]]
|[[Sketcher_Workbench/de|Sketcher]]
|IconL=Sketcher_BSplineApproximate.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconC=Workbench_Sketcher.svg
}}


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

Latest revision as of 17:04, 9 October 2022

Sketcher BSplineGradErhöhen

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

Beschreibung

Erhöht den Grad (Ordnung) der B-Spline-Kurve (Siehe die Seite B-Splines für weitere Informationen über B-splines).

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 Show/hide B-spline degree):

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:

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:

Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity was increased. Depending on the spline, the algorithm to decrease the degree may add a lot of knots to preserve the spline shape as happened in this example.

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. Eine Kante eines existierenden B-Splines auswählen.
  2. Die Schaltfläche Grad des B-Splines erhöhen drücken.