Sketcher BSplineDecreaseKnotMultiplicity

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 ):



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:



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:

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:
 * 3) * Press the button.
 * 4) * Use the menu.

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.)