Sketcher: Aumentare la molteplicità dei nodi di una BSpline

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This page is a translated version of the page Sketcher BSplineIncreaseKnotMultiplicity and the translation is 20% complete.
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Arrow-left.svg Pagina precedente: Sketcher BSplineIncreaseDegree.svg Aumenta di grado
Pagina successiva: Diminuisci la molteplicità Sketcher BSplineDecreaseKnotMultiplicity.svg Arrow-right.svg

Sketcher BSplineIncreaseKnotMultiplicity.svg Aumenta la molteplicità di nodo

Posizione nel menu
Sketch → Strumeti B-spline → Aumenta la molteplicità di nodo
Ambiente
Sketcher
Avvio veloce
Nessuno
Introdotto nella versione
0.17
Vedere anche
Crea B-spline

Descrizione

Aumenta la molteplicità del nodo di curva B-spline (vedere: 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 .
Here is a cubic spline () whose knots have the multiplicity 1. The multiplicity is indicated by the number in parentheses. The indication can be changed using the toolbar button Sketcher BSplineKnotMultiplicity.svg Show/hide B-spline knot multiplicity):

Sketcher KnotMultiplicity multiplicity1.png

B-spline where both knots have the multiplicity 1.

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:

Sketcher KnotMultiplicity multiplicity3.png

B-spline from above 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. 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:

Sketcher KnotMultiplicity locality.png

Effect of locality due to different multiplicity.

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.

Utilizzo

  1. Selezionare un nodo di una B-spline
  2. Richiamare lo strumento usando uno di questi metodi:
    • Premere il pulsante Sketcher BSplineIncreaseKnotMultiplicity.svg Aumenta la molteplicità del nodo nella barra degli strumenti.
    • Usare la voce Sketch → Strumenti B-spline → Sketcher BSplineIncreaseKnotMultiplicity.svg Aumenta la molteplicità del nodo dal menu principale.
Arrow-left.svg Pagina precedente: Sketcher BSplineIncreaseDegree.svg Aumenta di grado
Pagina successiva: Diminuisci la molteplicità Sketcher BSplineDecreaseKnotMultiplicity.svg Arrow-right.svg