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 Show/hide B-spline knot multiplicity, Sketcher BSpline Increase knot multiplicity |
Description
The Sketcher BSplineDecreaseKnotMultiplicity tool decreases the multiplicity of a B-spline knot. See this page for more information about B-splines.
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
Note: If you decrease the multiplicity, the knot vanishes, because mathematically it appears then 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 when you look at the multiplicity: For example degree = 3 then multiplicity = 0 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 (that is a polynom with degree 3) , this means both sides must be part of the same curve. So there is then actually no longer a knot connecting 2 different Bézier curves, the former knot is then simply a point onto one Bézier curve.
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 "edge", you can create two splines and connect them.)
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