Sketcher BSplineGradErhöhen

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Revision as of 19:39, 14 May 2024 by FBXL5 (talk | contribs) (Created page with "In diesem kubischen B-Spline (Grad 3) gibt es 3 Abschnitte, d.h. 3 Kurven, die an 2 Knoten verbunden sind.")

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:

Beispiel

B-Splines sind im Grunde eine Kombination aus Bézierkurven (sehr schön erklärt in diesem und diesem Video).

In diesem kubischen B-Spline (Grad 3) gibt es 3 Abschnitte, d.h. 3 Kurven, die an 2 Knoten verbunden sind.

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.