|
|
| Menu location |
|---|
| Sketch → B-Spline Tools → Increase Knot Multiplicity |
| Workbenches |
| Sketcher |
| Default shortcut |
| None |
| Introduced in version |
| 0.17 |
| See also |
| Sketcher BSplineDecreaseKnotMultiplicity |
Description
The 
Sketcher BSplineIncreaseKnotMultiplicity tool increases the multiplicity of a B-spline knot.
Usage
- Select a B-spline knot.
- There are several ways to invoke the tool:
- Press the Increase Knot Multiplicity button.
- Select the Sketch → B-Spline Tools → Increase Knot Multiplicity option from the menu.
- Press the
Example
B-splines are basically a combination of Bézier curves (nicely explained in this and this video). The points where two Bézier pieces are connected are called knots. A knot with multiplicity m on a B-spline with degree d means the curve to the left and right of the knot has at least an equal n order derivative (called Cn continuity) where n = d - m.
In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots. The knots have multiplicity 1.
The multiplicity is indicated by the numbers in round brackets. See 
Toggle B-Spline Knot Multiplicity.
B-spline where both knots have multiplicity 1.
A multiplicity of 3 will change this B-spline so that even the first order derivatives are not equal (C0 continuity). Here is the same B-spline where the multiplicity of the knot on the left was increased to 3:
Same B-spline with knot multiplicity 3. A control point was moved to show that the knot has C0 continuity.
A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. Meaning changing one control point will only affect the B-spline locally.
This can be seen in this example, where the B-spline with knot multiplicity 1 from the first image above was taken, and the second control point from the right was moved up. As a result the complete shape of the B-spline has changed:
After increasing the multiplicity of the knots to 2, moving the second control point from the right results in significant changes on the right side of the shape only:
Notes
- Knot multiplicity can also be increased with Sketcher BSplineInsertKnot.
このページは以下から取得されています https://wiki.freecad.org/Sketcher_BSplineIncreaseKnotMultiplicity