Sketcher BSplineIncreaseKnotMultiplicity
|
|
| Menu location |
|---|
| Sketch → Sketcher B-spline tools → Increase knot multiplicity |
| Workbenches |
| Sketcher |
| Default shortcut |
| None |
| Introduced in version |
| 0.17 |
| See also |
| Show/hide B-spline knot multiplicity, Decrease knot multiplicity |
Description
Increases 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 
Show/hide B-spline knot multiplicity):
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:
File:Sketcher KnotMultiplicity multiplicity2.png
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 din this example:
Difference of locality due to different multiplicity.
The spline with knot multiplicity is completely changed while the one with multiplicity 2 is not due to the additions control points to keep the second order derivative equal.
B-spline curve showing increasing knot multiplicity.
Usage
- Select a B-spline knot.
- Either:
- Press the button
B-spline increase knot multiplicity. - Use the menu Sketch → Sketcher B-spline tools → Increase knot multiplicity.
- Press the button
Sketcher
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- Sketcher B-spline tools: Show/hide B-spline degree, Show/hide B-spline control polygon, Show/hide B-spline curvature comb, Show/hide B-spline knot multiplicity, Show/hide B-spline control point weight, Convert geometry to B-spline, Increase B-spline degree, Decrease B-spline degree, Increase knot multiplicity, Decrease knot multiplicity, Insert knot, Join curves
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