Diminui a multiplicidade do nó

From FreeCAD Documentation
This page is a translated version of the page Sketcher BSplineDecreaseKnotMultiplicity and the translation is 8% complete.
Other languages:

Sketcher BSplineDecreaseKnotMultiplicity

Menu location
Sketch → Sketcher B-spline tools → Decrease knot multiplicity
Default shortcut
Introduced in version
See also
Sketcher BSplineIncreaseKnotMultiplicity


The Sketcher BSplineDecreaseKnotMultiplicity tool decreases the multiplicity of a B-spline knot.


  1. Select a B-spline knot.
  2. There are several ways to invoke the tool:
    • Press the Decrease knot multiplicity button.
    • Select the Sketch → Sketcher B-spline tools → Decrease knot multiplicity option from the menu.


See Sketcher_BSplineIncreaseKnotMultiplicity


If you decrease the multiplicity of a knot to zero, the knot vanishes. Mathematically it then appears zero times in the knot vector, meaning there is no longer a basis function. Understanding this requires some math, but it will also be clear if you look at the multiplicity. For example a knot with multiplicity 0 on a B-spline with degree 3 means that at the position of the knot two Bézier pieces are connected with C3 continuity. So the third derivative should be equal on both sides of the knot. However for a cubic Bézier curve this means that both sides must be part of the same curve. There is then effectively no longer a knot connecting two Bézier curves.