Sketcher BSplineDecreaseKnotMultiplicity

Sketcher BSplineDecreaseKnotMultiplicity
Menu location
Sketch → Sketcher B-spline tools → Decrease knot multiplicity
Workbenches
Sketcher
Default shortcut
None
Introduced in version
0.17
See also
Sketcher BSplineIncreaseKnotMultiplicity

Description

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

Usage

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.

Example

See Sketcher_BSplineIncreaseKnotMultiplicity

Notes

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.