Sketcher BSplineIncreaseDegree/de: Difference between revisions

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==Anwendung==
==Anwendung==


# Eine oder mehrere B-Splines auswählen.
# Einen oder mehrere B-Splines auswählen.
# Es gibt mehrere Möglichkeiten, das Werkzeug aufzurufen:
# Es gibt mehrere Möglichkeiten, das Werkzeug aufzurufen:
#* Die Schaltfläche {{Button|[[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree/de|Grad des B-Splines erhöhen]]}} drücken.
#* Die Schaltfläche {{Button|[[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree/de|Grad des B-Splines erhöhen]]}} drücken.
#* Den Menüeintrag {{MenuCommand|Sketch Sketcher B-spline tools → [[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] Grad des B-Splines erhöhen}} auswählen.
#* 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.
#* {{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.



Revision as of 19:28, 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:

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.