This page is a translated version of the page Sketcher BSplineDecreaseDegree and the translation is 56% complete.
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Menüeintrag
Skizze → Skizzierer B-spline Werkzeuge → B-Spline Grad verringern
Arbeitsbereich
Skizzierer
Standardtastenkürzel
Keiner
Eingeführt in Version
0.19
Siehe auch

## Beschreibung

Verringert den Grad (die Ordnung) eines B-Spline (siehe diese Seite für weitere Informationen über B-Splines).

B-Splines sind im Grunde eine Kombination aus Bézier-Kurven (sehr schön erklärt in dies und dieses Video).

In diesem kubischen Spline (Grad 3) gibt es 3 Segmente, d.h. 3 Kurven sind an 2 Knoten verbunden
(der Grad wird durch die Zahl angezeigt, die Anzeige kann über die Schaltfläche in der Werkzeugleiste geändert werden ):

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

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)

Decreasing the degree will not delete control points but try instead to conserve the shape of the spline. Therefore segments will be added. For our example you see a lot of new spline segments with each one control point and the shape of the spline has only slightly been changed:

Same B-spline where the degree was changed from 3 to 2. Note that also the knot multiplicity was increased to conserve the spline shape. In effect the knots have now C0 continuity so that the spline will get "edges" when you move a control point. (see this page to for an explanation of the continuity)

If you take this result and increase the degree, you cannot get the initial state of the spline because information was lost by the prior decrease of the degree. For our example increasing the degree again leads to this:

Same B-spline where the degree was changed back from 2 to 3. Note that the knot multiplicity increased too because the information for a possible higher continuity was lost.

## Anwendung

1. Select an edge from an existing B-spline, and press Decrease B-spline degree.