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 BSplineIncreaseKnotMultiplicity |
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.
- Press the
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 C3 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 2 Bézier curves.
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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- Additional: Sketcher Dialog, Preferences, Sketcher scripting
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