# Difference between revisions of "Sketcher BSplineDecreaseKnotMultiplicity"

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Sketch → Sketcher B-spline tools → Decrease knot multiplicity
Workbenches
Sketcher
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Introduced in version
0.17
Show/hide B-spline knot multiplicity, Increase knot multiplicity

## Description

Decreases the knot multiplicity of a B-spline curve knot (see 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 is called the knot. A knot with the multiplicity 1 means that the curve left and right to the knot has at least the same first order derivative (called C1 continuity). Here is a spline whose knots have the multiplicity 1 (indicated by the number in parentheses,
indication can be changed using the toolbar button ):

B-spline where both knots have the multiplicity 1. You can see that the second order derivatives left and right to the knots are not equal.

A multiplicity of 2 will change the spline so that the second order derivatives becomes equal (C2 continuity). Here is the same spline where the multiplicity was increased to 2:

B-spline where both knots have now the multiplicity 2. Note that control points were added and changed to achieve this.

Another consequence of a multiplicity of 2 is that you gain local control. This means the change of one control point only affects the splice locally to this changed point. This can be seen in this example, where the splines from the images above were taken and their the second control point from the right side was moved up: Effect of locality due to different multiplicity.

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

## Usage

1. Select a B-spline knot
2. Either:

Note: Decreasing the multiplicity from 1 to 0 will remove the knot since the result would be a curve with an "edge" at the knot position (C0 continuity) and this is not supported. (To create curves with an "edges", you can create two splines and connect them.)