Sketcher BSplineIncreaseDegree: Difference between revisions
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|MenuLocation=Sketch → Sketcher B-spline tools → Increase Degree of B-spline |
|MenuLocation=Sketch → Sketcher B-spline tools → Increase Degree of B-spline |
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|Version=0.17 |
|Version=0.17 |
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|SeeAlso=[[ |
|SeeAlso=[[Sketcher_BSplineDegree|Show/hide B-spline degree]], [[Sketcher_BSplineDecreaseDegree|Decrease B-spline degree]] |
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Increases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]). |
Increases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]). |
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B-splines are basically a combination of [https://en.wikipedia.org/wiki/Bezier_curve#Constructing_B%C3%A9zier_curves Bézier curves] (nicely explained in [https://www.youtube.com/watch?v=bE1MrrqBAl8 this] and [https://www.youtube.com/watch?v=xXJylM2S72s this] video). These curves have degree - 1 control points.<br/>In this cubic spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots<br>(degree is indicated by the number, indication can be changed using the toolbar button {{Button|[[File:Sketcher_BSplineDegree.svg|24px]] [[Sketcher_BSplineDegree|Show/hide B-spline degree]]}}): |
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[[File: |
[[File:Sketcher_BSplineDegree3.png|400px]] |
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{{Caption|B-spline with degree 3 and 2 knots that each have the multiplicity 1.}} |
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The outer segments have each 2 control points, the inner one none to fulfill the constraint that the knots have multiplicity 1. (see [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation of the multiplicity) |
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{{Caption|Same B-spline with different Degrees.}} |
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Increasing the degree will add control points so that the shape of the spline is not changes. Therefore segments will be added. For our example you see a lot of new spline segments with each one control point and the shape of the spline has only slightly been changed: |
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[[File:Sketcher_BSplineDegree4.png|400px]] |
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{{Caption|Same B-spline where the degree was changed from 3 to 4. Note that also the knot multiplicity was increased.}} |
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If you take this result and decrease the degree, you cannot get the initial state of the spline because information was lost by the increase of the degree. For our example decreasing the degree again leads to this: |
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[[File:Sketcher_BSplineDegree3from4.png|400px]] |
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{{Caption|Same B-spline where the degree was again changed from 4 to 3. Note that the knot multiplicity was not also decreased but increased again.}} |
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==Usage== <!--T:5--> |
==Usage== <!--T:5--> |
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# Select an edge from an existing B-spline, and press {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|24px]] '''Increase B-spline degree'''}}. |
# Select an edge from an existing B-spline, and press {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|24px]] '''Increase B-spline degree'''}}. |
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Revision as of 03:03, 1 November 2020
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|
| Menu location |
|---|
| Sketch → Sketcher B-spline tools → Increase Degree of B-spline |
| Workbenches |
| Sketcher |
| Default shortcut |
| None |
| Introduced in version |
| 0.17 |
| See also |
| Show/hide B-spline degree, Decrease B-spline degree |
Description
Increases the degree of the B-spline(see B-spline).
B-splines are basically a combination of Bézier curves (nicely explained in this and this video). These curves have degree - 1 control points.
In this cubic spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots
(degree is indicated by the number, indication can be changed using the toolbar button 
Show/hide B-spline degree):
B-spline with degree 3 and 2 knots that each have the multiplicity 1.
The outer segments have each 2 control points, the inner one none to fulfill the constraint that the knots have multiplicity 1. (see this page for an explanation of the multiplicity)
Increasing the degree will add control points so that the shape of the spline is not changes. Therefore segments will be added. For our example you see a lot of new spline segments with each one control point and the shape of the spline has only slightly been changed:
Same B-spline where the degree was changed from 3 to 4. Note that also the knot multiplicity was increased.
If you take this result and decrease the degree, you cannot get the initial state of the spline because information was lost by the increase of the degree. For our example decreasing the degree again leads to this:
Same B-spline where the degree was again changed from 4 to 3. Note that the knot multiplicity was not also decreased but increased again.
Usage
- Select an edge from an existing B-spline, and press
Increase B-spline degree.
Sketcher
- General: Create sketch, Edit sketch, Map sketch to face, Reorient sketch, Validate sketch, Merge sketches, Mirror sketch, Leave sketch, View sketch, View section, Toggle grid, Toggle snap, Configure rendering order, Stop operation
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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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