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GuiCommand: Name: Sketcher BSplineDecreaseKnotMultiplicity MenuLocation: Sketch , Sketcher B-spline tools , Decrease knot multiplicity Workbenches: Sketcher_Workbench Version: 0.17 SeeAlso: Sketcher_BSplineIncreaseKnotMultiplicity

Sketcher BSplineDecreaseKnotMultiplicity

Description

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

Usage

Select a B-spline knot.
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 C^3^ 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.

⏵ documentation index > Sketcher > Sketcher BSplineDecreaseKnotMultiplicity

This page is retrieved from https://github.com/FreeCAD/FreeCAD-documentation/blob/main/wiki/Sketcher_BSplineDecreaseKnotMultiplicity.md