Sketcher BSplineIncreaseKnotMultiplicity/de

Beschreibung
Erhöht die Knotenvielfalt eines B-Spline Kurvenknotens (siehe B-Spline).

B-splines are basically a combination of Bézier curves (nicely explained in this and this video). The points where two Bézier curves are connected to form the spline are called knots. A knot on a degree d spline with the multiplicity m means that the curve left and right to the knot has at least an equal n order derivative (called Cn continuity) whereas $$n=d-m$$. Here is a cubic spline ($$d=3$$) whose knots have the multiplicity 1. The multiplicity is indicated by the number in parentheses. The indication can be changed using the toolbar button ):



A multiplicity of 3 will change this spline so that even the first order derivatives are not equal (C0 continuity). Here is the same spline where the left's knot multiplicity was increased to 3:



A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. This means the change of one control point only affects the spline locally to this changed point. This can be seen in this example, where the spline from the first image above was taken and its second control point from the right side was moved up:



One can see that the spline with knot multiplicity 1 is completely changed while the one with multiplicity 2 kept its form at its left side.

Anwendung

 * 1) Wähle einen B-Spline Knoten aus.
 * 2) Rufe das Werkzeug mit mehreren Methoden auf:
 * 3) * Drücke die  Schaltfläche in der Werkzeugleiste.
 * 4) * Verwende den Eintrag im oberen Menü.