Sketcher BSplineIncreaseKnotMultiplicity/de: Difference between revisions
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{{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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|[[Sketcher_BSplineDecreaseDegree/de|BSplineGradVerringern]] |
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|[[Sketcher_BSplineDecreaseKnotMultiplicity/de|BSplineKnotenVielfachheitVerringern]] |
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|IconL=Sketcher_BSplineDecreaseDegree.svg |
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|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg |
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<div class="mw-translate-fuzzy"> |
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|Name=Sketcher BSplineIncreaseKnotMultiplicity |
|Name=Sketcher BSplineIncreaseKnotMultiplicity |
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|Name/de=Sketcher BSplineKnotenVielfachheitErhöhen |
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|MenuLocation=Sketch → |
|MenuLocation=Sketch → B-Spline-Werkzeuge → Vielfachheit eines Spline-Knotens erhöhen |
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|Version=0.17 |
|Version=0.17 |
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|SeeAlso=[[Sketcher_BSplineKnotMultiplicity/de|BSplineKnotenVielfachheit]], [[Sketcher_BSplineDecreaseKnotMultiplicity/de|BSplineKnotenVielfachheitVerringern]] |
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|SeeAlso=[[Sketcher CompCreateBSpline|Create B-spline]] |
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<span id="Description"></span> |
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==Beschreibung== |
==Beschreibung== |
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<div class="mw-translate-fuzzy"> |
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Erhöht die Knotenvielfalt eines B-Spline Kurvenknotens (siehe [https://en.wikipedia.org/wiki/B-spline B-Spline]). |
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Erhöht die Vielfachheit eines B-Spline-Knotens. (Siehe die Seite [[B-Splines|B-Splines]] für weitere Informationen über B-Splines). |
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</div> |
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[[File:sketcher_SampleBSplineIncreaseKnotMultiplicity.png]] |
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{{Caption|B-Spline Kurve mit zunehmender Knotenvielfalt.}} |
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<span id="Usage"></span> |
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==Anwendung== |
==Anwendung== |
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# Wähle einen B-Spline Knoten aus und wende sie an. |
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# Einen B-Spline-Knoten auswählen. |
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# Es gibt mehrere Möglichkeiten den Befehl aufzurufen: |
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#* Die Schaltfläche {{Button|[[File:Sketcher_BSplineIncreaseKnotMultiplicity.svg|16px]] [[Sketcher_BSplineIncreaseKnotMultiplicity/de|Vielfachheit eines B-Spline-Knotens erhöhen]]}} drücken. |
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#* Den Menüeintrag {{MenuCommand|Sketch → B-Spline-Werkzeuge → [[File:Sketcher_BSplineIncreaseKnotMultiplicity.svg|16px]] Vielfachheit eines B-Spline-Knotens erhöhen}} auswählen. |
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</div> |
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==Example== |
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{{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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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). The points where two Bézier pieces are connected are called knots. A knot with multiplicity ''m'' on a B-spline with degree ''d'' means the curve to the left and right of the knot has at least an equal ''n'' order derivative (called ''C<sup>n</sup>'' continuity) where ''n = d - m''. |
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{{Sketcher Tools navi/de}} |
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In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots. The knots have multiplicity 1. |
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The multiplicity is indicated by the numbers in round brackets. See [[File:Sketcher_BSplineKnotMultiplicity.svg|16px]] [[Sketcher_BSplineKnotMultiplicity|Show/hide B-spline knot multiplicity]]. |
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[[File:Sketcher_KnotMultiplicity_multiplicity1.png|400px]] |
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{{Caption|B-spline where both knots have multiplicity 1.}} |
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A multiplicity of 3 will change this B-spline so that even the first order derivatives are not equal (''C<sup>0</sup>'' continuity). Here is the same B-spline where the multiplicity of the knot on the left was increased to 3: |
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[[File:Sketcher_KnotMultiplicity_multiplicity3.png|400px]] |
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{{Caption|Same B-spline 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. Meaning changing one control point will only affect the B-spline locally. |
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This can be seen in this example, where the B-spline with knot multiplicity 1 from the first image above was taken, and the second control point from the right was moved up. As a result the complete shape of the B-spline has changed: |
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[[File:Sketcher_KnotMultiplicity_locality1.png|400px]] |
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After increasing the multiplicity of the knots to 2, moving the second control point from the right results in significant changes on the right side of the shape only: |
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[[File:Sketcher_KnotMultiplicity_locality2.png|400px]] |
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==Notes== |
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* Knot multiplicity can also be increased with [[Sketcher_BSplineInsertKnot|Sketcher BSplineInsertKnot]]. |
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{{Docnav/de |
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|[[Sketcher_BSplineDecreaseDegree/de|BSplineGradVerringern]] |
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|IconL=Sketcher_BSplineDecreaseDegree.svg |
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|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg |
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|IconC=Workbench_Sketcher.svg |
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Latest revision as of 07:34, 22 April 2024
Sketcher BSplineKnotenVielfachheitErhöhen |
Menüeintrag |
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Sketch → B-Spline-Werkzeuge → Vielfachheit eines Spline-Knotens erhöhen |
Arbeitsbereich |
Sketcher |
Standardtastenkürzel |
Keiner |
Eingeführt in Version |
0.17 |
Siehe auch |
BSplineKnotenVielfachheit, BSplineKnotenVielfachheitVerringern |
Beschreibung
Erhöht die Vielfachheit eines B-Spline-Knotens. (Siehe die Seite B-Splines für weitere Informationen über B-Splines).
Anwendung
- Einen B-Spline-Knoten auswählen.
- Es gibt mehrere Möglichkeiten den Befehl aufzurufen:
- Die Schaltfläche Vielfachheit eines B-Spline-Knotens erhöhen drücken.
- Den Menüeintrag Sketch → B-Spline-Werkzeuge → Vielfachheit eines B-Spline-Knotens erhöhen auswählen.
Example
B-splines are basically a combination of Bézier curves (nicely explained in this and this video). The points where two Bézier pieces are connected are called knots. A knot with multiplicity m on a B-spline with degree d means the curve to the left and right of the knot has at least an equal n order derivative (called Cn continuity) where n = d - m.
In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots. The knots have multiplicity 1.
The multiplicity is indicated by the numbers in round brackets. See Show/hide B-spline knot multiplicity.
B-spline where both knots have multiplicity 1.
A multiplicity of 3 will change this B-spline so that even the first order derivatives are not equal (C0 continuity). Here is the same B-spline where the multiplicity of the knot on the left was increased to 3:
Same B-spline 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. Meaning changing one control point will only affect the B-spline locally.
This can be seen in this example, where the B-spline with knot multiplicity 1 from the first image above was taken, and the second control point from the right was moved up. As a result the complete shape of the B-spline has changed:
After increasing the multiplicity of the knots to 2, moving the second control point from the right results in significant changes on the right side of the shape only:
Notes
- Knot multiplicity can also be increased with Sketcher BSplineInsertKnot.
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